Data exported by the i-ekbase web tool. Source: Adapted from the i-ekbase system.
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More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\\n\\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\\n\\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\\n\\nAdditionally, each book published by IntechOpen contains original content and research findings.
\\n\\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\nSimba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\nIntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\nSince the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\nMore than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\nAdditionally, each book published by IntechOpen contains original content and research findings.
\n\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n\n\n
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Availability of water is one of the basic conditions for life on planet Earth. However, it is a limited resource, currently at risk of extinction. Global population growth, climate change and demand from several economic sectors such as industry and agriculture put into question the availability of drinking water to all living beings on planet. In particular, irrigated farming is one of the sectors that consume more water per day, and can reach 90,000 liters/hectare, while the average consumption per capita in Brazil is 162 liters per day [1].
\nThe United Nations Food and Agriculture Organization (FAO) predicts that global demand for food by the year 2050 will increase by at least 60% above 2006 levels, and in order to meet this demand it would need to double or triple agricultural production. However, most of the food production increase must have come from yield increases [2]. According to [3], the adoption of irrigated agriculture makes it possible to increase productivity and diversify agricultural crops. However, there is a limitation in water resources and, therefore, the use of water in agriculture needs to be more efficient.
\nThe [4, 5, 6] present an overview of precision agriculture. The authors state that the term can be used in everything that refers to activities performed more accurately by means of electronic systems; however, they make a note regarding the applications of inputs uniformly, which would be only conventional systems and not deal with the spatial variability of crops. Automation and instrumentation solutions are required for better application of inputs, and in order to achieve a distinct water management in each sector of a planted area, irrigation systems must perform water application taking into account the spatial variability of the crop and the soil so that the maximum efficiency of the crop can be reached [7].
\nAuthors such as [8, 9, 10, 11, 12, 13] discuss some solutions for water application using spatial correction and conclude that the central or linear pivot or irrigator are particularly suited to the precision irrigation condition, especially because of their current levels of automation and large area reached by the pivot. However, the major limitation for the adoption of irrigation that complies with spatial and time variability, usually called variable rate irrigation, is associated with the development of great irrigation management.
\nThe availability of sensors is currently a constraint to the automation of irrigation control, and it is expected that the requirements of advanced process control for irrigation also fosters the development of new sensors. In [14] brings a review of the existing literature on advanced process control in irrigation and its requirements of sensors and adaptability to the field conditions, besides discussing the obstacles in area sensing.
\nIn order to deliver detailed spatial and temporal information regarding soil and crop response to varied management practices and dynamic environmental conditions, and to avoid the time-consuming process for installing and maintaining sensors over each field, the use of remote sensing techniques has been improving in precision agriculture [15, 16]. According to the authors, remote sensing images are already widely used and proved to do a good prediction on required irrigation amount for each type of crops. Remote sensing by satellite has been very promising in on-field monitoring, but still presents problems such as accuracy, cloud coverage, and the high cost to obtain good spatial resolution [17].
\nThe application of process control techniques for variable rate irrigation has recently been reviewed in [18, 19, 20, 21, 22, 23, 24]. Artificial intelligence (AI) can be applied in an interdisciplinary way, besides bringing about a paradigm shift of how we understand agriculture today. Solutions in AI technology not only enable farmers to do more with less, but also improve quality and ensure a faster introduction into the market.
\nAI technologies assist farmers in soil analysis and crop health, among others, besides saving time and allowing them to grow the right crop at each season, thereby maximizing the crop production. In this context, tools with knowledge representation and reasoning about imprecision present as a feasible alternative. In this way, fuzzy logic allows intelligent computational systems to “reason”, considering aspects inherent to uncertainty and realistic processes. Moreover, it is a very interesting methodology to be applied in decision making, because it is possible to model perceptions and preferences similar to the style of a human being.
\nDecision support systems are tools that can be used in fuzzy set theory [25] to provide a conceptual framework for representing knowledge and reasoning about imprecision and consequent uncertainty. The fuzzy set provides adequate tools for modeling and dealing with expert rules [26]. By modeling linguistic variables in the form of fuzzy sets, it was possible to transform expert rules into mathematical terms, and in addition, fuzzy set theory offers a wide variety of operators that can aggregate and combine these rules. The application of linguistic variables and fuzzy conjunction methods provide an adequate method to model the human reflection process and, in so doing, make the interface of these systems simpler and more natural as planning tool on the farm by the manager or farmer.
\nThe fuzzy decision support system is considered useful due to its interactive nature, flexibility in approach and evolution of the graphical characteristics, and can be adopted for any similar situation to classify the alternatives. More often, ambiguity in agricultural decision-making is aggravated by inaccuracy and intuition. The ability of fuzzy systems to deal with complex systems can help farmers to make better decisions in agricultural processes [27]. There is a very significant advantage in using fuzzy decision-making systems for the variable rate irrigation process: the advantage of not needing the full amount of relevant information by simply selecting the variables that play the role of the irrigation calculation according to [28].
\nThis chapter is organized as follows, the present section aims to contribute to a refinement of the studies on the application of fuzzy control systems for the exploration of precision irrigation modeling and management. In the next section, we provide a literature review of the latest related research, divided into three subsections, namely: (a) the most important concepts for understanding the main characteristics in a central pivot irrigation system; (b) concepts fundamental to the understanding of fuzzy logic, relevant to the structuring and development of the intelligent irrigation system and (c) remote sensing. In Section 3, we thoroughly describe the basic mathematical framework that involves the three techniques. Finally, a representative case study on the intelligent control of variable rate irrigation systems is presented.
\nAvailable bibliographies give different names to describe the concept of precision agriculture such as spatially prescriptive agriculture, computer farming, satellite farming, high technology for sustainable agriculture, soil specific crop management or site-specific crop management. It is considered a revolutionary approach to improving resource management and sustainable agricultural development and is a promising technology. [29, 30, 31, 32, 33].
\nPrecision agriculture studies were started in countries such as the USA, Canada, Australia, and Germany, besides the Western Europe, in the mid-1980s, and only began to receive great interest as a new experimental tool in the 1990s [29]. In [34] is define the specific management of a study zone as the electronic monitoring and control applied to data collection, information processing and decision support for the temporal and spatial allocation of inputs for agricultural production. The specific control zone, as shown in Figure 1, is spatially defined by soil elements, crop type, pests and other elements required for efficient management of inputs.
\nDifferent management zones within the same planting area. Source: Embrapa. (https://www.macroprograma1.cnptia.embrapa.br/redeap2).
Technologies on agricultural production are expected to impact in two areas: profitability for producers and ecological/environmental for the public. Increased costs with water, fertilizer and pesticides, coupled with environmental concerns, lead to a growing acceptance of the concept of specific management of an operating zone.
\nVariable rate irrigation (VRI) is a specific management tool used to apply the adequate amount of water in the sectors or zones of a planting area, for example Figure 2, presents control regions where the zones in reddish colors need more water, and those of bluish colors are with the humidity within the limits that the plant needs. The development of the prescription of variable rate irrigation is a field of active research, studied in [13, 14, 35].
\nSpatial variability of irrigation water needs. Source: VALLEY. (http://ww2.valleyirrigation.com/valley-irrigation/pt/tecnologia-de-comando/rega-de-taxa-vari%C3%A1vel/vri-controle-de-velocidade).
Once established, prescriptions can, within a management variability, remain fixed, or these zones can dynamically change a small number of times during a growing season. Characteristics of crops and soil type are the main factors that contribute to determine the space and time variability of a planted area. This information is incorporated into a geographic information systems (GIS) database and, therefore, used for interpretation and decision support [36].
\nIrrigation systems are a set of techniques aimed to distribute water to crops in adequate quantities in order to promote appropriate plant development with a minimum of water consumption [37]. Irrigation systems can be divided into two subsystems: catchment and application subsystem. The way the water is applied depends on different methods of application, and each has its specificities. They are divided into three groups: surface irrigation, localized irrigation, and sprinkler irrigation.
Surface irrigation: the water from the distribution system (channels and pipes) to any point of infiltration within the area to be irrigated is made directly on the surface of the soil. They are classified as infiltration furrows and flooding or submersion;
Localized irrigation: the water is applied directly on the root area, with small intensity and high frequency. Classified as: micro-sprinkler and drip;
Sprinkler irrigation is the method of irrigation in which water is sprayed on the surface of the land, like a rainfall, because the water jet is fractioned in drops. They are classified as: conventional spraying, central pivot, self-propelled, and linear system. Since this is the scope of this chapter, central pivot irrigation will be further detailed.
\nAmong the sprinkler systems, the central pivot has been used with relative success due to the lower labor demand [37, 38]. It was first built in 1948 by Frank L. Zybach, who sent the invention for analysis, finally patented in 1952 in Colorado, United States (see Figure 3). In 1954, Zybach sold the manufacturing rights to the American company Valley, located in the State of Nebraska. In 1968, the Lindsay Company also started to produce pivots, and currently both companies share the leadership of the world market of pivots.
\nStructure of a central pivot. (a) Basic components, and (b) irrigated land. Source: Adapted from [38].
The speed of the lateral displacement of a central pivot is controlled in the last tower, which is established by a timer, installed in the central control box of the pivot, which controls the time of activation and the stop of the motor of the last tower. For example, the condition in which the motor standstill time is equal to the movement time corresponds to the setting of 50% of the maximum speed set by the timer control percentage. At maximum speed of 100%, the motor of the last tower is continuously moving [37, 39].
\nIrrigated agriculture does not allow reductions in crop productivity due to lack or excess of applied water. The application of little water (deficit irrigation) can be an obvious waste, since production could not obtain the expected benefit. On the other hand, the excessive application is much more destructive, because soil saturation occurs, which prevents its aeration and leaches the nutrients, inducing a higher rate of evaporation and salinization [40]. So, it is important to develop an irrigation scheduling program for deciding when and how much to irrigate. For this purpose, we used the fuzzy logic system to simulate the amount and the frequency of irrigation needed.
\nFuzzy sets theory was introduced in 1965 by the Iranian mathematician Lotfi Asker Zadeh, a professor at the University of Berkley, USA [41], especially intended to offer a mathematical treatment to some subjective linguistic terms such as “approximately” and “around”, among others. This would be a first step in programming and storing vague concepts in computers, making it possible to produce calculations with inaccurate information, such as the human being [42]. In other words, while decision making in classical theory would be like Eq. (1), fuzzy logic would be like Eq. (2) [43].
\nThe most evident characteristic of fuzzy logic is to consider that between two values (zero and one) there may be intermediate values, and these values are analyzed according to a degree of pertinence, which indicates the level that the information belongs to a specific set in a universe of discourse, according to [44].
\nFuzzy set theory provides a method for manipulating sets whose boundaries are imprecise rather than restricted. The uncertainty of an element, that is, its fractional degree of pertinence, can be conceived as a measure of possibility, in other words, the possibility that an element is a member of the set [42].
\nIn many practical systems, relevant information comes from two sources: human experts, who describe their knowledge about the system in natural languages, and sensory measures and mathematical models proposed according to physical laws. An important task, therefore, is to combine these two types of information into systems designs [45].
\nThe fuzzy inference system consists of a fuzzification interface, a rule base, a database, a decision-making unit or inference unit, and finally a defuzzification interface. The functional blocks are shown in Figure 4.
\nFuzzy inference system. Source: Adapted from Ross [46].
The function of each block is:
A rule base containing a number of “if-then” fuzzy rules;
A database that defines the functions of association of fuzzy sets used in fuzzy rules;
A decision unit that performs rule inference operations;
A fuzzification interface that transforms crisp inputs into degrees of correspondence with linguistic values;
A defuzzification interface that transforms the fuzzy results of the inference into a crisp output.
Based on natural language, a fuzzy logic system is simple to understand and enables the representation and processing of human knowledge in a computer. The inputs, outputs, and fuzzy logic rules are easy to modify. These fuzzy logic features make it particularly well suited for use in a decision support system and is able to assist in the construction of vague rate-based irrigation control maps based on results of an imaging system in real time or by prescriptive maps based on the soil-plant-atmosphere transfer.
\nDeveloped by Mamdani [47], the inference method is the most common in practice and literature. To begin the general view of this idea, it is considered a simple system of two rules, where each rule comprises two antecedents and one consequent. The graphic procedures herein illustrated can be easily extended and maintained for fuzzy rule bases or fuzzy systems with any number of antecedents and consequents. Two different cases of two-input Mamdani systems are considered, where the inputs to the system are scalar values and a max-min inference method is used. Thus, the Mamdani inference method for a set of conjunctive rules for \n
This equation has a very simple graphical interpretation, exemplified in Figure 5, and illustrates graphical analysis of two rules, where symbols A11 and A12 refer to the first and second fuzzy antecedents of the first rule, respectively, and symbol B1 refers to the consequent fuzzy of the first rule. The symbols A21 and A22 refer to the first and second fuzzy antecedents, respectively, of the second rule, and the symbol B2 refers to the consequent fuzzy of the second rule.
\nInterpretation of the Mamdani method. Source: Adapted from Ross [46].
Although originally proposed by Takagi and Sugeno [48], this method is also known in the literature as Takagi-Sugeno-Kang (TSK) model. This is due to the subsequent works by Sugeno and Kang [49] related to methodologies developed to identify this type of model. The fuzzy TSK model consists of an inference system capable of describing, in an exact or approximate way, non-linear dynamic systems through a set of linear, locally valid dynamic systems, smoothly interpolated, non-linear and convex. A typical rule in a Sugeno model, which has two inputs, x and y, and one output z, is in the form of Eq. (4).
\nUsually, f (x, y) is a polynomial function at the x and y inputs, but it can be any general function as long as it describes the output of the system within the fuzzy region specified in the antecedent of the rule to which it is applied. When \n
Graphic interpretation of the Sugeno method. Source: Adapted from [50].
Remote sensing technologies are being used more and more often in the precision agricultural applications. This is because that the variables (crop stress, soil type, disease,) to be measured and controlled are very disperse in remote areas with limited wireless communications or no power supply. Also, the measurements of each variable at spatial and temporal scale are expensive and time-consuming for installing and maintaining sensors over each field. Sensors can be multispectral cameras on Satellites or mounted on Unmanned Aerial Vehicle (UAV, or “drones”). In this chapter, we focalized on the using of satellites images for agricultural applications.
\nRemote sensing imagery can be used for mapping soil properties, classification of crop species (land use), detection of crop water stress, monitoring of irrigation, and predicting of crop yield. The use of remote sensing in precision agriculture depends principally on the spatial, temporal, radiometric and spectral resolution. Satellite remote sensing has shown a very strong potential for irrigation management at large scale through using a different data (optical, thermal and radar) acquired from different satellites.
\nOptical reflectances in red and near infrared (0.4–12.5 μm) have the potential to access the vegetation indices (VI) that are directly related the different crop parameters like crop coefficient (Kc) used in estimating the crop water requirements. Several studies (e.g., [51, 52, 53, 54, 55, 56, 57, 58, 59]) have been specifically dedicated for estimating Kc from Normalized Difference Vegetation Index NDVI [60] and Soil Adjusted Vegetation Index SAVI [61].
\nFor thermal data, land surface temperature (LST) derived from thermal infrared remote sensing data have been used in a variety of applications such as, among others, climate studies [62, 63], the monitoring of crop water consumption and water stress detection [64, 65, 66, 67], vegetation monitoring [68, 69], soil moisture estimation [70, 71, 72]. Canopy temperature has long been recognized as a good indicator for crop water status and as a potential tool for irrigation scheduling. Stomatal closure is one of the first responses to plant water stress that causes a decrease in plant transpiration and thus an increase in plant temperature. An increase in plant temperature is a sign that the vegetation is undergoing water stress. The crop water stress index (CWSI) is the most frequently used index to quantify the crop water stress based on canopy surface temperature [73].
\nRegarding the radar images, a significant effort has been recently dedicated to exploit these images to estimate soil moisture (SM) due to (i) the high-spatial resolution achievable by synthetic aperture radars (SAR) and (ii) the advent of SAR data available at high-temporal resolution. Especially, the Sentinel-1 (S1) constellation (composed of two satellites S1-A and S1-B) potentially provides SAR data at 20 m resolution every 3 days [74]. Thus, numerous studies have investigated and exploited the sensitivity of the radar signal to SM [70, 75, 76, 77, 78, 79, 80].
\nThe present stage shed light on the form that the construction of the proposed system is given, presenting as each fundamental characteristic of an irrigation project is appropriate to be added to the basic elements of fuzzy system.
\nThe development of the intelligent irrigation system follows the structure shown in Figure 7. The structure of the proposed system enables the elaboration of a systematic, autonomous and automated management map to control an irrigation system. The output values of the intelligent system will be the inputs of the central pivot movement speed control and the sprinkle valve opening control. However, it is important to emphasize that the commercial systems most used by farmers are not yet capable of elaborating this type of control map in the same way proposed by this work.
\nStructure for intelligent irrigation system strategy.
Over the last decade, new information technologies, such as the geographic positioning system (GPS) and the geographic information system (GIS) have been introduced, which enabled to reduce the scale of management to the field level [81]. There are different software programs available in the market that can create maps from data point files, such as Surfer (GoldenSoftware, Inc.), ArcView (ESRI) and Global Mapper (Global Mapper).
\nThe free QGIS1 software will be used in this work for pre-processing and editing the file provided by the i-ekbase web-tool. QGIS is an open source geographic information system (GIS), licensed under GNU General Public License. It is an official open source geospatial foundation (OSGeo) project that runs on Linux, Unix, Mac OSX, Windows and Android, and supports several formats of vectors, rasters, databases and functionalities. QGIS has a plug-in infrastructure, and it is possible to add new features by writing plug-ins in C++ or Python.
\nAs mentioned above, vegetation indices generated from remote sensing data are an important tool for the monitoring of natural or anthropogenic changes in land use and land cover. These rates have been used to estimate several vegetation parameters such as leaf area index (LAI) and amount of green biomass, as well as in the evaluation of land use and management and the recovery of degraded areas [82].
\nIn this study, satellite image information was used, and in this case, the reading values of NDVI—Normalized Difference Vegetation Index—is defined as the difference between Near infra-red and red reflecatnces divided by its sum. It measures the vegetative cover and its color on the land surface over wide areas. Dense and green vegetation absorbs strongly the red wavelengths of sunlight and reflect in the near-infrared wavelengths resulting high values of NDVI, near to 1. For bare soil (no vegetation), NDVI values are between 0 and 0.14 depending on the moisture and roughness of soil. The practice of plant irrigation management has inherent complexity in visualizing the symptoms of water deficit, which are difficult to detect. On some occasions, they are discovered very late, that is, when observed, their effects have already compromised the production or quality of the product. Usually these symptoms are related to leaves coloring, leaf winding, leaf angle, etc.
\nHowever, it is possible to establish a correlation between the values of NDVI and the crop coefficient (Kc), [83, 84]. The estimated Kc values (Kc-NDVI) and the Kc values observed in Allen [85] for maize and soybean crops to guide the irrigation schedule during the season. Another way of relating the development of the plantation by means of remote sensing is the use of canopy temperature and infrared thermometry. A plant under water stress reduces transpiration and typically presents a higher temperature than the non-stressed crop [86], which can be a powerful tool for monitoring and quantifying water stress.
\nCanopy temperature increases when solar radiation is absorbed [87] but, is cooled when latent energy or sweating is used to evaporate water instead of heating plant surfaces. Algorithms based on canopy temperature are strongly correlated with quantifiable crop yields [88], such as productivity, water use efficiency, seasonal evapotranspiration, leaf water potential at noon time, irrigation rates and damage caused by herbicides.
\nIn order to study satellite images, data will be provided by a specialized company, by means of its intelligent environmental knowledgebase (i-ekbase), and made available via web tool, with limited and free use, for research related to the topic. The web tool will provide data from the area chosen initially for the study. The intelligent environmental knowledgebase (i-ekbase)2 is an autonomous Big Data Analytics engine with a CLOUD system, and a fully automated geographic information system (GIS) [89]. Figure 8 illustrates an example image provided by the i-ekbase tool, while Table 1 shows the data generated by the web tool in the CSV (Comma Separated Values) format.
\nLand surface temperature image by the i-ekbase web tool. Source: Adapted from the i-ekbase system.
Lat | \nLong | \nCanopy nitrogen (%) | \nLeaf area index (m2/m2 | \nNDVI (%) | \nBio-mass (tn/ha | \nSoil salinity (dS/m) | \nSoil moisture (%) | \nCanopy temp. (°C) | \n
---|---|---|---|---|---|---|---|---|
−15.2464 | \n−54.0157 | \n0.0 | \n0.0 | \n13.49 | \n0.0 | \n3.35 | \n13.52 | \n36.48 | \n
−15.2464 | \n−54.0156 | \n0.09 | \n0.0 | \n15.24 | \n0.14 | \n3.32 | \n13.19 | \n36.81 | \n
−15.2464 | \n−54.0155 | \n0.41 | \n0.0 | \n15.36 | \n0.15 | \n3.39 | \n13.93 | \n36.07 | \n
−15.2464 | \n−54.0159 | \n3.36 | \n0.0 | \n22.76 | \n0.76 | \n3.16 | \n11.61 | \n38.39 | \n
−15.2464 | \n−54.0158 | \n4.96 | \n0.0 | \n26.68 | \n1.09 | \n3.10 | \n11.00 | \n39.00 | \n
−15.2463 | \n−54.0162 | \n7.37 | \n0.0 | \n31.78 | \n1.52 | \n2.87 | \n8.65 | \n41.35 | \n
−15.2463 | \n−54.0162 | \n9.30 | \n1.0 | \n36.34 | \n1.89 | \n2.80 | \n8.03 | \n38.97 | \n
−15.2463 | \n−54.0161 | \n11.59 | \n1.0 | \n41.42 | \n2.32 | \n2.68 | \n6.84 | \n40.16 | \n
Data exported by the i-ekbase web tool. Source: Adapted from the i-ekbase system.
The i-ekbase system services provide larges area-wise resource management maps, with supporting remote digital scouting for decision support systems and rapid intervention of issues. For developing the experimental system were processed 12 months of Data, these remote sensing imageries were acquired by Landsat (with a spatial resolution of 30 m, but for this experiment the Data was upscale to 10 m) and Sentinel (with a spatial resolution of 10 m) satellites. Data that constitute this image have more than 14,000 georeferenced points, containing at each point or pixel the attributes of the agricultural analysis. Due to the extension of the data, only a few lines are shown in Table 1.
\nIn order to apply this approach to the commercial field scale, the remote sensing data required to describe the soil-plant-atmosphere relationship can be acquired from satellite [90] and aircraft images [91, 92]. However, high costs, spatial resolution, data frequency and data availability [93, 94], in addition to cloudless satellite imagery, are a challenge for the correct execution of models based on remote sensing [95]. These issues can limit the efficiency of real-time variable rate irrigation management.
\nFrom the remote sensing data, those that best describe the soil-plant-atmosphere relationship for the intelligent irrigation system of the plantation site will be selected. In this phase, the correct selection of these data is fundamental to correctly calculate the results. A simple but promising approach uses crop coefficients derived from the normalized difference vegetation index (NDVI) along with local climate data to infer quantities of evapotranspiration (ETc) from variable crops almost in real time [57, 83, 96].
\nBased on the choice of planting site and type of crop to be irrigated, in relation to plant type data, the crop coefficient will be used along with information from the satellite images. In this case, the reading values of NDVI, near soil moisture and vegetative canopy temperature will be used. The latter is an important parameter for irrigation management and should be adjusted according to local growing conditions.
\nThe study site is a farm located in the municipality of Primavera do Leste, MT, latitude 15° 14′24.73 “S and longitude 54 ° 0’53.29” W. This site has areas of cultivation irrigated by central pivot, and the crops planted are soybean, cotton and second-crop corn. The delimited area presents a total of 140 ha, in a radius of 667 m, see Figure 9. The area delimited by the red circle has central pivot irrigation, and the information used in the case study is from a 2015/2016 second-crop corn cycle. Irrigation in maize crop means to meet the minimum water requirements for the development of the crop.
\nRGB images of the location of study area in in the municipality of primavera do Leste, state of Mato Grosso, Brazil.
Maize expresses high sensitivity to droughts. Therefore, the incidence of periods with reduction of the water supply to the plants at critical moments of the development of the crop, from flowering to physiological ripeness, can cause a direct reduction in the final harvest. In order to obtain maximum output, maize planting requires approximately 650 mm of water during its cycle [97], which can vary from 110 to 140 days in medium-cycle hybrids. For this preliminary analysis, data on daily average precipitation were used, provided by INMET (National Institute of Meteorology), from April to September 2016, to the city of Primavera do Leste, in the State of Mato Grosso, Brazil. Figure 10 shows the data obtained.
\nDaily average precipitations obtained in the period of 2016. Fonte: INMET.
These readings recorded during the development of the plantation under study corroborate the supposition of water stress due to lack of rainfall (from June to September), which would indicate the possibility of complementing water demand by irrigation.
\nIn this step, a fuzzy system will be used, which in this case will be capable to infer the variations of linear speeds of the pivot according to the images provided by the satellite. For the creation of the control map, a system with artificial intelligence will be developed, capable of manipulating data and knowledge.
\nThree input variables (NDVI, near-soil moisture and canopy temperature) were used to infer the speed that the pivot should have to improve the level of irrigation within the management area, so that an adequate speed could be found for the movement of the pivot in relation to the amount of water sprayed by the sprinklers. The decision unit or inference machine to perform rule-based inference operations will be implemented using the Mamdani method, with crisp inputs and crisp output value3.
\nIn this first stage of development, the water depth that the irrigation system provides will be considered constant, and the database, which defines the functions of association of the sets used in the fuzzy rules, will be implemented as shown in Table 2 and Figure 11.
\nInput variables | \nLinguistic variables | \n||
---|---|---|---|
Low | \nAverage | \nHigh | \n|
Canopy temperature (°C) | \n<14 | \n14 < ϕ < 27 | \n>24 | \n
Upper layer soil moisture (%) | \n<14 | \n12 < ϕ < 24 | \n>21 | \n
NDVI (%) | \n<16 | \n12 < ϕ < 27 | \n>27 | \n
Fuzzy input set for the fuzzy inference system.
Corresponding membership functions for each system entry, (a) canopy temperature, (b) upper layer soil moisture, (c) NDVI.
With the remote sensing data, it is possible to construct the universes of discourse of each input variable and thus transform the database into linguistic variables, such as those presented in the table above. Each of these inputs was previously limited in the universe of discourse in question and associated with a degree of pertinence in each fuzzy set by means of specialist knowledge. In this manner, in order to obtain the degree of pertinence of a given crisp input, it is necessary to search for this value in the knowledge base of the fuzzy system. The fuzzification of the decision-making system is shown in Figure 11, and it is possible to visualize the corresponding membership functions, considering these intervals as the universe of discourse of these variables.
\nTriangular membership functions were chosen because they simplify the calculation of the fuzzy inference mechanism. Well distributed triangular membership functions transform the input values into fuzzy values (low, medium and high), as shown in Figure 5, as well as the values of soil moisture and NDVI (Figure 11b and c, respectively). The fuzzy output set, which represents the rotational speed of the central pivot, was built on five linguistic variables: very low (VL), low (L), normal (N), high (H) and very high (VH). These sets were interpreted by means of their degrees of pertinence, illustrated in Figure 12.
\nFunction of pertinence of the speed corresponding to the defuzzification of the system.
If the center of gravity method is used for defuzzification, the fuzzy set produced after aggregation will be a numerical output composed of the union of all rule contributions. This calculation is made according to Eq. (5):
\nThe values \n
Finally, the basis of fuzzy rules IF-THEN was elaborated and presented in Table 3, the fuzzy rule relating to rotation speed contains 27 rules, thus, the Mamdani inference method for a set of conjunctive rules is given by Eq. (3), for example: IF NDVI is Low AND Canopy temperature is Low AND Near-soil moisture is Low THEN Rotation Speed is Low.
\nInputs | \nOutput | \n||
---|---|---|---|
NDVI | \nTemperature | \nNear-soil moisture | \nRotation speed | \n
Low | \nLow | \nLow | \nLow | \n
Medium | \nLow | \n||
High | \nVery low | \n||
Medium | \nLow | \nLow | \n|
Medium | \nLow | \n||
High | \nVery low | \n||
High | \nLow | \nLow | \n|
Medium | \nLow | \n||
High | \nVery low | \n||
Medium | \nLow | \nLow | \nNormal | \n
Medium | \nNormal | \n||
High | \nHigh | \n||
Medium | \nLow | \nNormal | \n|
Medium | \nNormal | \n||
High | \nHigh | \n||
High | \nLow | \nLow | \n|
Medium | \nNormal | \n||
High | \nNormal | \n||
High | \nLow | \nLow | \nHigh | \n
Medium | \nVery high | \n||
High | \nVery high | \n||
Medium | \nLow | \nVery high | \n|
Medium | \nVery high | \n||
High | \nVery high | \n||
High | \nLow | \nVery high | \n|
Medium | \nVery high | \n||
High | \nVery high | \n
Fuzzy rules for central pivot speed control.
This set of rules is based on the basic knowledge about irrigation, according to a methodology adopted by [37, 39].
\nThe rules were constructed with the connective “AND”, and are based on the supposition that where there is little leaf growth, there is soil water deficit. Together with the characteristic of the high canopy temperature, indicating a lower evapotranspiration, that is, water stress of the plants, the values of near-soil moisture provided by the web tool are readings of the locations where there are few leaves, and it is possible to estimate their value.
\nThe development of the crop is evidenced captured by the images throughout the crop, and the information contained in this sensing is the NDVI values. By analyzing the information contained in Figure 13, it is possible to verify the similarity between the values attributed to Kc. It is noticed that as the crop evolves, the greater the exposure of the leaf area, and thus it is possible to establish a relation of NDVI. This process is described in [56], with ratios to calculate the base crop coefficient (Kcb) for cotton as a function of NDVI. When we look closely at each stage of the development of the plantation, two distinct areas are noticed: one with little growth and the other with normal growth. From this type of differentiation, it is possible to construct water demand maps, as well as speed control maps.
\nVariation of NDVI in one crop cycle.
Data contained in this remote sensing are described in Table 4. In this configuration, the table presents the preprocessed data, near-soil temperature, soil moisture, and NDVI, besides latitude and longitude.
\nLat | \nLong | \nNDVI (%) | \nNear-soil moisture (%) | \nCanopy temperature (°C) | \n
---|---|---|---|---|
−15.2463 | \n−54.0157 | \n5.96 | \n25.75 | \n30.75 | \n
−15.2463 | \n−54.0156 | \n6.49 | \n25.68 | \n30.24 | \n
−15.2463 | \n−54.0154 | \n6.67 | \n25.68 | \n30.03 | \n
−15.2463 | \n−54.0153 | \n6.85 | \n25.68 | \n30.19 | \n
−15.2463 | \n−54.0152 | \n6.66 | \n25.8 | \n30.63 | \n
−15.2463 | \n−54.015 | \n6.47 | \n25.92 | \n30.67 | \n
−15.2463 | \n−54.0149 | \n6.82 | \n25.84 | \n30.44 | \n
−15.2463 | \n−54.0142 | \n7.01 | \n25.77 | \n29.33 | \n
−15.2463 | \n−54.0141 | \n6.37 | \n25.88 | \n29.58 | \n
Pre-processed data.
Canopy temperature, near-soil moisture and NDVI data, analyzed and processed, will be the set of inputs for the intelligent fuzzy system. The following are illustrated in Figure 14: (a) NDVI images, (b) temperature images, and (c) soil moisture images.
\nInput data from the fuzzy inference system, (a) NDVI data, (b) canopy temperature data, (c) near-soil moisture data.
The inputs, as shown in Figure 14, are arranged according to the linguistic variables of the fuzzy system and separated by tonalities for better visualization. The intelligent system gave the result shown in Figure 15, where it is possible to verify different regions within the area, with different values for the pivot rotation speed. The indirect relationship between the pivot rotation speed and the level of the applied water depth implies a smaller applied water depth in a higher speed, and a higher water application in the soil in a lower rotation speed [98]. When analyzing the input data, it is possible to identify two large areas with a lower leaf development, which may indicate a lack of water for development. After processing this input data, the intelligent irrigation system indicates that these areas with lower leaf development, in a redder color, indicate that the pivot should reduce its speed and thus increase the water depth in that area.
\nControl map of pivot rotating speed, (a) speed control map, (b) pivot turning speed setpoints.
The expected result is the creation of control maps, and in this case, it was possible to determine the speed reference values for the eight zones initially programmed. The areas that presented different coloration in Figure 14 are in the control map result. It is possible to verify well divided zones, and in each one there is a determined value for the speed that the pivot must develop to decrease or increase the water depth in the cropped area. The result shown in Figure 15b corresponds to the reference values that should be sent to the pivot controller, since the control systems of these devices work with percentage of rotation speed.
\nThe data analyzed and processed by the GIS were used as inputs to the intelligent fuzzy system. They are illustrated in Figure 16: (a) NDVI images, (b) temperature images and (c) soil moisture images.
\nInput data from the fuzzy inference system, (a) NDVI data, (b) canopy temperature data, c) near-soil moisture.
Similar to the previous case study, the study of June 28 presents the values of the input variables of the fuzzy system with the linguistic definitions necessary for interpretation. The results of the intelligent irrigation system are shown in Figure 17, where is also possible to observe different regions within the crop area, with different values for the pivot rotation speed. A higher speed of rotation implies a smaller applied water depth, and with a lower speed of rotation, there is a greater application of water to the soil, if the application flow is kept constant by the sprinklers.
\nPivot rotating speed control map, (a) speed control map, (b) pivot rotation speed setpoints.
When comparing satellite images once again, it is seen that NDVI and canopy temperature are essential for the decision-making of the intelligent irrigation system. It is possible to see that there are large areas with a lower leaf development, which may indicate a lack of water for development. In the case of intelligent irrigation system output, areas in a redder color indicate that the pivot should slow down.
\nThe expected result is the creation of the control maps, and for this study it was possible to find the reference values of the central pivot rotation speed for the eight irrigation zones initially programmed, shown in Figure 17. In this result, it is also possible to identify the areas that presented different colors in Figure 16. The irrigation management zones are fairly divided, and in each one a value is determined for the pivot rotation speed, decreasing or increasing the water depth applied to the crop area. The result in Figure 17b corresponds to the reference values to be sent to the pivot controller.
\nThe fuzzy control system for irrigation developed is original and ground breaking, and there is no literature about a rotation speed control map for center pivot in the same approach presented in this work. In addition, there is no available information that commercial systems can build this type of map autonomously.
\nThe experiments point to the efficiency result for pivot operation, since it is possible to note differences between the speeds per management zone that could be employed in the pivot. The system follows the definition of variable rate irrigation, since when changing the speed, the amount of water applied also changes.
\nIn this context, it was observed that the fuzzy logic can be widely used in farming, and it is feasible to aggregate precision irrigation knowledge with the formulation of a decision support system. The implementation was successful for the application of variable rate water to central pivots. However, a broader commercial application depends on the integration of data collection systems, management strategies, and hardware control.
\nThese studies were motivated by a broader research effort on the applications of fuzzy systems in agriculture. In addition, fuzzy control applied in variable rate irrigation (VRI) was explored in this domain in order to provide a better understanding of the relation between agricultural factors involving complexity and uncertainty and solutions with A.I. technologies. Future development and application of these methodologies in agricultural engineering are required especially in the context of decision support in precision irrigation. The results are favorable to the continuity of the studies on precision irrigation and application of the fuzzy logic for the development of control maps for central pivots irrigation systems.
\nThe authors thank the Federal Institute of Education, Science and Technology of Mato Grosso—IFMT—for the financial support, and to the Post-Graduation Program in Electrical and Computer Engineering of the Federal University of Rio Grande do Norte—PPGEEC/UFRN—for the technical and administrative support. Finally, we thank the Coordination of Improvement of Higher Education Personnel—Ministry of Education (Capes—MEC) for granting the PRODOUTORAL scholarship to the corresponding author.
\nThe authors declare no conflict of interest.
In the past several decades, nanophotonics has been demonstrated as an ideal platform to manipulate the light-matter interaction and engineer the wavefront of the electromagnetic wave at will. The rapid development on nanophotonics has led to tremendous applications ranged from lasing, Lidar, biosensor, LED, photodetector, integrated photonic circuit, invisibility cloak, etc. Nanophotonics covers many exciting topics: photonic crystal, plasmonics, metamaterials, and nanophotonics based on some novel materials (e.g., two-dimensional materials, perovskite). Currently, the building blocks for nanophotonics are made from either metallic or dielectric elements with regular shapes, such as rectangular wire, cylinder, cuboids, and sphere for plasmonic and dielectric metasurfaces. Usually, limited parameters are provided for such a regular structure, and, thus, the optimisation process can be done in a reasonable short time. For example, a single dielectric cylinder with only two parameters, including diameter and height, are involved. Due to the limited freedom, the performance of photonic devices based on the regular pattern is far away from the optimal one. Inverse design method has been widely used to tackle this problem because the full parameter space can be explored [1]. Conventional inverse design methods that include topology optimisation, genetic algorithm, steep descent, and particle swarming optimisation shown in Figure 1a, however, require the vast computational source and take a long time to find the optimal local structure. As a branch of machine learning, deep learning has received much attention worldwide because it can efficiently process and analyse a vast number of datasets. It has already found great success in computer vision and speech recognition. Recently, researchers and scientists have applied it to quantum optics, material design and optimisation of nanophotonic devices due to its outstanding capability of finding optimal solution from enormous data. At the same time, the computational cost is much lower compared to other inverse design methods [2, 3]. Several neural networks including deep neural network, generative neural network and convolutional neural network are frequently used to retrieve the optimal structure parameters for irregular structure with limited sets of data and shorter time when many structure parameters are involved for opmisation. This book chapter is organised as follows: In Section 2, we will discuss the inverse design enabled by deep learning on four different topics: multilayer structure, plasmonic metasurface, dielectric metasurface, chiral metamaterials (See Figure 1b). In Section 3, we review the recent progress on all-optical neural networks. Then, concluding remarks and outlook are presented in Section 4.
(a) Inverse design methods in nanophotonics. (b) Application of deep learning in nanophotonics.
Recently, deep learning using an artificial neural network has emerged as a revolutionary and powerful methodology in nanophotonics field. Applying the deep learning algorithms to the nanophotonic inverse design can introduce remarkable design flexibility which is very challenging and even impossible to achieve based on conventional optimisation approaches [1]. In this section, we will provide a brief review of the implementation of deep learning to solve nanophotonic inverse design problems.
Multilayer nanostructures can exhibit unique optical properties including field enhancements and distributions, special transmission/reflection spectra, based on the interference of different modes supported by different layers in the nanostructures. Machine learning has emerged as a more and more promising tool to solve the inverse design of photonic nanostructures. It will enable effective inverse design by simultaneously considering various inter-linked parameters such as geometric parameters, material types, etc., simultaneously (unlike the current regular approaches, which optimise one or two parameters only, at a time).
A recent work done by Peurifoy et al. has demonstrated using deep neural network (DNN) to relate the geometry of SiO2/TiO2 multilayer spherical core-shell nanoparticles with their light-scattering properties (Figure 2a) [4]. The transfer matrix method has been used to analytically solve the scatterings to generate 50,000 different combinations of the shell thickness as the total examples for training, validation, and testing. The forward learning model was a fully-connected dense feed-forward network with four hidden layers. The inputs were set to be the thickness of each shell of the nanoparticles, and the outputs were the corresponding scattering cross section spectra. During the learning process, the output of the network was compared with the target response to provide a loss function against which the weights can be trained and updated. After the forward-feeding training process, by fixing the weights, and setting the inputs as a trainable variable and fix the output to the desired output, they run the neural network backwardly, let the neural networks to iterate the inputs and provide the desired geometry to give the target spectrum. After training, as can be seen from Figure 2a, for an arbitrarily given spectrum (blue curve), the DNN can successfully predict the thickness of each shell of the nanoparticles that can generate a similar scattering spectrum as wanted, with some minor deviations.
Application of DL for multilayer nanostructure design: (a) using DNN to retrieve the layer thicknesses of a multilayer particle based on its scattering spectrum. Inset: Network architecture. (b) Left: Geometry of three-layered core-shell nanoparticles with changeable materials and thicknesses. Right: Network architecture. (c) Left: Multilayer thin films of SiO2 and Si3N4. Right: The architecture of the tandem network composed of an inverse design network and a forward modelling network. (d) Left: Evolution of the training cost of the network. Right: Performance of the network using a Gaussian-shaped spectrum.
A further improvement of this approach is to take into account the different material combinations for the core-shell nanoparticles. In another work done by So et al., they have considered a simultaneous inverse design of materials and structural parameters using the deep learning network (Figure 2b) [5]. Here, they use the network to map the extinction spectra of the electric dipole (ED) and magnetic dipole (MD) to the core-shell nanoparticles, including the material information and shell thicknesses. The DL model consists of two networks: a designed network to learn a mapping from optical properties to design parameters, and a spectrum network to learn from design parameters to optical properties. Here, in order to adapt the network to the different types of input data (materials and thicknesses), the loss function has been devised accordingly by the weighted average of material and structural losses:
A similar network has also been used to explore the optical transmission spectra from multilayer thin films (Figure 2c,d) [8]. Here, Liu et al. combined the forward network modelling and inverse design in tandem architecture to overcome the data inconsistency which originates from the non-uniqueness in inverse scattering problems, i.e., the same optical responses can correspond to different designs. This non-uniqueness of the response-to-design mapping will cause conflicting examples within the training set and might lead to non-convergence of the neural network. The TN architecture consists of an inverse-design network connected to a forward model network. The forward network learns the mapping from the structural parameters to the optical responses and is trained separately first. After the forward network is trained, it is placed after the inverse-design model network, and its network weights remain fixed during the training of the inverse-design model network. The inverse-design network learns a mapping from the optical responses to the structural parameters. After the training process, such a DNN can efficiently predict the geometry of a device which is both promising and much faster as compared with the conventional electromagnetic solvers. As shown in the right diagram of Figure 2d, the learning curve of this tandem neural network has demonstrated a fast convergence during the training process. The structures designed by the network matches the desired transmission spectra with high fidelity.
Plasmonic metasurfaces have become the building blocks for the meta-optics field. It allows for manipulating the wavefront of the electromagnetic wave at will. In this section, we are going to give a summary of the current status applying deep learning approach for inversely designing plasmonic metasurfaces.
In recent years, with the burgeoning field of metasurfaces, deep learning has emerged as a powerful tool for realising efficient inverse design of different types of plasmonic metasurfaces for different applications including spectral control, near-field design [9, 10, 11]. In 2018, Malkiel et al. introduced a novel bidirectional DNN model which can realise both the design and characterisation of plasmonic metasurfaces [12]. The network consists of two standard DNNs: a geometry-predicting network (GPN) to solve the inverse design and a spectrum-predicting network (SPN) to solve the spectra prediction tasks for plasmonic metasurfaces of “H”-shaped gold nanostructures. They have shown that by combing these two networks and optimise them together, they can co-adapt to each other, which is more effective than training them separately, as shown in Figure 3a. The training data for the GPN consists of three groups of data: desired spectra for x-polarised pump and y-polarised pump, and the materials’ properties. Each group of data is fed into a different layer and three DNNs in parallel before they join the fully connected joint layers. This architecture has considered the differences of properties in the inputs’ data, thus allows a better performance of the networks suitable for the nanophotonic design. After that, they were using the predicted geometry from the GPN to feed the SPN and returns the predicted transmission spectra as the outputs. Then the backpropagation is used to optimise both networks. The networks show excellent agreement between the measurements, predictions and simulations, as demonstrated by two examples shown in Figure 3b using the network to realise the inverse design of “H”-shaped gold metasurfaces for target spectra.
Application of DL for plasmonic metasurfaces inverse design: (a) architecture of the DNN composed of xxx. (b) Demonstration of the inverse design of “H”-shaped gold metasurfaces. (c) The architecture of a proposed GAN model composed of a generator, a simulator, and a critic. (d) Transmission spectra of the original (left) and generated (right) patterns from the proposed GAN approach.
As the structural complexity grows, the generation of the training data sets takes enormous time. Furthermore, the requirement for more degrees of freedom in metasurface patterns makes the problems more and more challenging for conventional neural networks. To solve this issue, generative adversarial network (GAN) has been employed for metasurface designs recently [13]. A GAN involves placing two neural networks (a generator and a critic) in competition with each other and trying to reach an optimum, as shown in Figure 3c. Here, the simulator was first pretrained using 6500 full-wave finite element method (FEM) simulations for metasurfaces with different shapes. After the training, the simulator was used to approximate the transmission spectra of any input patterns rather than using the full-wave FEM simulations to do it. This has significantly reduced the number of datasets for the network. The generator is used to produce the metasurface patterns in response to a given input spectra T, and then fed into the simulator to get the approximated spectra T′. The critic will compare the original input geometric data corresponding to T and the generated patterns from the generator and guide the generator to produce patterns that share common features with the geometric input data. Figure 3d gives one example demonstrating the excellent performance of this network on predicting and identifying the structure to produce the target spectra with only minor deviations.
Recently, dielectric metasurface has triggered extensive interests in the past decades. Analogous to metallic nanostructures supporting plasmonic resonance, high index dielectric nanostructures provide multipole electric and magnetic resonance (also called as Mie resonance), which enable 2π phase coverage without ease. Besides, the intrinsic material loss is much lower for high index semiconductor than the counterpart of noble metals. These two unique properties make it possible to develop high-performance photonic devices based on dielectric metasurface. Although dielectric metasurfaces with such regular elements have much better performance compared to the plasmonic metasurfaces, they still do not reach the optimal one with the best efficiency. In order to further improve the performance of dielectric metasurface, inverse design approaches, including adjoint-based topology optimisation and genetic algorithms, have been widely used. The iterative optimisation methods lead to the findings of devices with high efficiency with irregular patterns which are usually beyond human intuition. However, these methods rely on extremely heavy computation, making them hard to apply to sophisticated devices featured by a very high dimensional design space. The recently developed deep learning approach, which is based on artificial neural networks, is viewed as the perfect solution of dealing massive data while reducing the computation cost. It has already found great success in computer vision and natural language processing. Recently, researchers have transferred deep learning to the inverse design of nanophotonic devices. Up to date, most frequently used neural networks in the design of dielectric metasurfaces are DNN, GAN, and convolution neural networks (CNN) In the following, we will illustrate them one by one and also discuss their unique strengths and drawbacks.
DNN with fully connected layers has been demonstrated as a versatile and efficient way of engineering a high-Q resonance with desired characteristics, including linewidth, amplitude, and spectral location [14]. The structure considered here is double identical silicon nanobars sitting on the substrate, as shown in Figure 4b. The width and length of nanobars are,, respectively, denoted as W and L while the centre to centre distance between nanobars is denoted as 2x0. To reduce the structure complexity, the period of the unit cell and the thickness of silicon bars are fixed as p = 900 nm and t = 150 nm, respectively. Previous studies have demonstrated that such an array structure support a Fano resonance induced by the quasi bound state in the continuum. Since there are three parameters to be tuned, it is very challenging to find the desired structure parameters by one by one brute-force searching when the spectrum response is predefined. DNN can correctly address this issue in an reduced time period. 25,000 sets of the training data are randomly generated with rigorous coupled-wave analysis (RCWA). It is worth noting that it is straightforward and easy to train the network mapping from structure parameters to reflection/transmission spectrum because one set of structure parameters can only produce a given spectrum. The objective is to search the structure parameter for the desired spectra response. It might be challenging to use an only forward neural network to find out the required parameters because the non-uniqueness issue arises. In other words, different designs may produce the same far-field electromagnetic response because the optical resonance is mainly governed by the volume of structure but shows weak dependence on the structure shape. To solve this one-to-many issue, as shown in Figure 4a, a Tandem neural network consisting of inverse design model network and the forward model network is proposed. More specifically, the forward network is trained first to learn the mapping from structure parameters to the optical response. After the training of the forward network is done, inverse design model network is trained while the weight and bias for the forward network are fixed. Once the full training process is completed, one can retrieve the structure parameters in several milliseconds while the optical spectrum is predefined. In order to test the validity of Tandem network, Figure 4c–e compares the predefined spectrum and predicted spectrum of Fano resonance with different wavelength, linewidth and amplitude. The excellent agreement can be found between two, indicating the effectiveness of the deep learning approach in the inverse design of nanophotonics. Note that only amplitude of transmission spectrum is considered here. In many applications of dielectric metasurface (e.g., metalens), both amplitude and phase should be considered to shape the wavefront of electromagnetic wave. Since optical resonance is always accompanied by π phase-shift, which may make training difficult for phase spectra because it is better to be differentiated for output parameters (i.e., phase or amplitude). Instead of using phase and amplitude, researchers adopt both real and imaginary parts of the reflection/transmission spectrum as the output of training data.
(a) The architecture of the tandem network, which consists of inverse-design model network followed by the pretrained forward mode network. (b) Schematic drawing of the unit cell made of two identical silicon nanobar. Inverse design of metasurface supporting Fano profile spectra (c) λ0 = 1450 nm and 1500 nm, Δλ = 15 nm, q = 0.8. (d) λ0 = 1500 nm, Δλ = 10 nm, q = 0.3 and q = 0.5. (e) λ0 = 1500 nm, Δλ = 5 nm and Δλ = 15 nm, q = 0.7. (f) Schematic of the conditional GLOnet for metagrating design. (g) Optimised efficiency of metagrating from the conditional GLOnet.
Moreover, because of the huge mismatch between the dimensions of input and output, a revised neural network was applied. The first standard linear neural network was replaced with the bilinear tensor layer that can correlate two entity vectors in multiple dimensions. Training results indicated that modified neural network converges faster than the standard linear neural network. This is because input parameters are interdependent on each other. Taking an array of dielectric nanodisk as an example, the structure is fully described by four parameters: refractive index of materials, radius and height of disk, the gap between disks. As we mentioned previously, the optical resonance is mainly determined by the refractive index and volume of structures. In other words, the spectrum response is governed by permittivity (ε = n2) and volume (V = πr2h). Therefore, multiplication of two entities by bilinear tensor can better describe the nonlinearity, and thus facilitate the training process. However, it is worth pointing out that there are some limitations on deep neural network. First, the design solution retrieved from deep learning must fall into the boundary of the training data set. Second, it only works for structure defined by several simple parameters. When more parameters are involved, tens, hundreds of thousands of training data are required to guarantee the prediction accuracy. As a consequence, generating such a large amount of data may consume a long time and cause a high computational cost. Moreover, it will be challenging to train the data for dielectric metasurface with free form geometry via DNN.
GAN has been found to overcome the above limitations effectively. GAN is originally proposed in the computer vision. It is capable of creating artificial images that even cannot be distinguished from true images by the computers [15]. GAN has been successfully applied to the design of subwavelength scale metallic nanostructures and multifunctional dielectric metasurface [13, 16]. The operation principles of GAN in the design of metasurface are described as follows. The unit cell of the metasurface is divided into N*N (i.e., N = 32, 64) pixel images while the thickness of structure and period of the unit cell is fixed. There are two neural networks in GAN: generator and discriminator. The generator networks try to create the image so that it cannot be differentiated to the real image. In contrast, the discriminator networks are trained to distinguish the image produced by the generator from the real image sets. The competing process between these two networks leads to the creation of artificial images that cannot be distinguished from the real one. In fact, the topology optimisation method or deep learning approach does not always work alone. They can be combined together to build up a new generative network. Such a generative network has been proposed to optimise the efficiency of metagrating at large angle across a broadband wavelength range because it took both the advantages of GAN and adjoint-based topology optimisation [17]. Although GAN requires less training sets, the training data may be optimised first and thus demand more computation source. More recently, global topology optimisation networks (GLOnets) was proposed by Jiang et al. from Stanford [18, 19]. It incorporates the adjoint-based optimisation into the generative neural networks. Unlike DNN and GAN methods, it does not require pre-calculation of training data based on the electromagnetic solver. Instead, it adopts the generator networks followed by the adjoint-based topology optimiser, allowing for direct learning the physical relationship between geometry parameters of the device and electromagnetic response, as shown in Figure 4f. Such a global optimiser does not only reduce the computation time but also further improve the efficiency of metagrating at large angles compared to the topology optimisation method (See Figure 4g).
Another example of deep learning’s application in nanophotonics is to design plasmonic chiral metamaterials [20, 21]. Chirality corresponds to the structure–property of an object which cannot superpose to its mirror image by any combination of rotation and translation. It shows different response under the illumination of left circular polarisation (LCP) and right circular polarisation (RCP) incidence. This concept is originated from molecules or ions in chemistry. However, the optical chirality in nature is extremely weak due to the small interaction volume in the visible wavelength. The emergence of metamaterials makes it possible to realise a strong optical chiral response. It is well established that a pair of rotating gold split-ring resonators (SRRs) separated by a dielectric spacer can induce strong chirality. The question of how to optimise the chirality at the given frequency still remain unanswered because so many parameters involved make it difficult to find out the optimal design [20]. The advent of machine learning approach provided the possibility of processing many parameters at once in a reasonable short time. Ma et al. developed a deep learning-based model to design and optimise three-dimensional plasmonic chiral metamaterials at the desired wavelength. The structure they considered is shown in Figure 5a. The period of the unit cell is fixed as 2.5 μm while the thickness and width of gold SRR are set as 200 nm and 50 nm, respectively. Other parameters, such as length of top and bottom SRR (l1 and l2), top and bottom dielectric space layer (t1 and t2), and the twisted angle α between two SRRs, are set as input parameters. For output parameters, 201 points are sampled in the reflection spectrum from 30 to 80 THz. Here, four characteristic reflection spectra that include RLL (LCP-input: LCP-output), RLR (LCP-input: LCP-output), RRR (RCP-input: RCP-output) and chirality spectrum are investigated as output parameters. Figure 5b shows the structure of DNN that consists of primary networks (PN) and auxiliary network (AN). Both networks have a forward path and an inverse path. For the forward path of PN, the huge mismatch of dimension between input parameters (1 × 5) and output parameters (3 × 201) makes it hard to converge. This is especially obvious around the resonant frequency. To avoid this issue, a neural tensor network followed by the unsampled module is used. Instead of using DNN with fully connected layers that are formed by simply linear recombination from previous neurons, the first hidden layer is replaced as the neural tensor network to model second-order relationships because the input parameters are not independent with each other. Figure 5c compares the reflection spectra obtained from electromagnetic simulation and prediction of PN. The excellent agreement can be found for most wavelengths except around resonant wavelengths. This issue is well addressed by introducing another AN which learns the relationship between structural parameters and chirality spectrum. The results are shown in Figure 5d. After finishing the training both PN and AN, one can construct any chirality spectrum feature by single or double resonances as well as optimise the chirality at predefined spectrum. Note that such networks are not the only one which can design and optimise the chiral metamaterials. Li et al. developed a self-consistent framework termed BoNet (Bayesian optimisation (BO) and CNN) [21], which can conduct self-learning on the optical properties of nanostructure (i.e., near field and far-field). The unit cell of structure, as shown in Figure 5e, is divided into 40 × 40 pixels, where the empty area is denoted as 0, and the gold brick area is denoted as 1. Other parameters, such as period and thickness, are fixed. DNN used here is composed of convolution layers followed by several fully connected layers (see Figure 5f). Successful training on the BoNet can help to optimise the chirality at an arbitrary wavelength in the visible wavelength range. Figure 5g shows the chirality spectra of measurement and prediction from BoNet. The discrepancy can be attributed to the tolerance of fabrication and measurements.
(a) Schematic drawing of unit cell for chiral metamaterials. (b) Architecture of neural network used for the inverse design of chiral metamaterials. (c) Reflection spectra calculated from numerical simulation and predicted from DNN. (d) Chirality spectra for both numerical simulation and DNN prediction. (e) Schematic drawing of unit cells of structure used for inverse design. (f) Schematic of BoNet for optimisation of the far-field spectrum. (g) BoNet predicted and experimental verification of far-field circular dichroism spectra at the desired wavelength of 650, 700, 750 and 800 nm.
(a) Schematic of a generic two-layer artificial optical neural network with linear operation realised via programmable SLM and nonlinear activation by employing nonlinear media. (b) Optical micrograph and highlighted region of the implemented optical neural network of 22-mode on-chip interference unit. The system acts as an optical FPGA. Matrix multiplication and amplification are realised fully optically via Mach-Zehnder interferometer (MZI) phase-shifters.
As was discussed above, neural networks have been successfully used to solve rather complex problems in nanophotonics in particular. There are two fundamentally different alternatives for the implementation of neural networks: a software simulation in conventional computers or a particular hardware solution capable of dramatically decreasing execution time. Software simulation can be useful to develop and debug new algorithms, as well as to benchmark them using small networks. However, if large networks are to be used, software simulation is not enough. The problem is the time required for the learning process, which can increase exponentially with the size of the network.
At the same time, there are ongoing attempts to implement this architecture in a hardware form, which should allow for substantial gains for scaling and distributed approaches. Digital circuits are usually implemented by using robust CMOS technology, where the neuron state summation is realised via common multipliers and adders. The activation function is more complicated to implement, which require a highly nonlinear response. One of the technical difficulties is related to the implementation of communication channels. In general, the connection scales as a square of the number of inputs. One of the solutions to this problem can be provided by optical networks, where the communication channels do not need to be hard-wired [22, 23]. Also, in free space, light waves can cross each other without affecting the carrying information. Other benefits include low energy to transmit the signal and high switching time up to 40 GHz. Thus, analogue optical technology allows to implement artificial neural networks directly in hardware, with data encoded in pulses of light and neurons made from optical elements, such as lenses, prisms, beam splitters, waveguides and spatial light modulators (SLMs), see Figure 6a. In particular, SLMs are used for algebraic operations, including matrix multiplication with a specific phase mask design [24].
Recently, another approach to realise optical neural networks was based on Mach-Zehnder interferometers (MZIs) to calculate matrix products [25, 26], see Figure 6b. By carefully manipulating a specific phase shift between a coherent pair of incoming light pulses allow to multiply a two-element vector, encoded in the amplitude of the pulses, by a two-by-two matrix [27, 28]. An array of the interferometers can then perform arbitrary matrix operations, which is widely used, for example, in the boson sampling approach.
One of the main challenges for the successful realisation of the optical neural networks is to find a suitable implementation of the activation function. Due to its inherent nonlinear response, light pulses are required to interact with a nonlinear media. Various nonlinear effects have been proposed for such functionality. To avoid optical signal loss, mostly dielectric materials have been considered. It includes photorefractive crystals, liquid crystals, and various semiconductors [29]. Most promising nonlinear effects are based on harmonics generation, phase conjugation, optical limiter, and bistable response. Recently, researchers from The Hong Kong University of Science and Technology proposed a new approach based on cold atoms exhibiting electromagnetic induced transparency effect to implement the nonlinear activation function [24]. Importantly, it requires very weak laser power and is based on nonlinear quantum interference. It is also possible to produce different activation functions by varying the positions of counterpropagating beams.
The group from the University of Münster has suggested an alternative approach by exploiting the wavelength-division multiplexing (WDM) to transport and sum multiple pulses at different wavelengths using single waveguides [30]. Importantly, they suggest a phase-change material (PCM) for both linear summing and nonlinear firing. In this approach, each neuron is implemented as a ring-shaped resonator of varying diameters to tap light signals with corresponding resonant wavelengths from a common waveguide. When the total power of all those signals exceeds a certain threshold, they then switch another piece of PCM, this time embedded in a resonator at the neuron’s output.
Despite recent progress in all-optical implementation of neural networks, various groups investigated hybrid optoelectronic systems in which neurons convert signals from light into electricity and then back to light. The group from Princeton suggested using electro-absorption modulation for the optimal integrated photonics implementation of the neural networks [31]. One of the essential aspects is the integration density. The electro-optical induced nonlinearity is realised by using photodiode couplers. Moreover, it also allows for spiking signal processing, which enables the direct implementation of neuromorphic computing. It led to the development of a new and quite promising platform of neuromorphic photonics combining the advantages of optics and electronics to build systems with high efficiency, high interconnectivity and high information density.
Although deep learning was proposed and found great success in the context of computer vision and speech/image recognition, it has become a powerful approach to solve complex problems in biology, physics and chemistry. As a branch of physics, nanophotonics has witnessed huge progress based on deep learning. Deep learning allows us to inversely design nanophotonic devices with even less computation source and time compared to conventional computational approaches, such as topology optimisation and genetic algorithm. Currently, the research interests and efforts are still fast-growing and expanding in deep learning-enabled nanophotonics. More research opportunities may be brought in this area.
On the one hand, although deep learning has been successfully applied to retrieve the structure parameters for any given spectrum, it remains an opening question that whether it is possible to realise narrowband or broadband absorbers at the specified wavelength or wavelength range. On the other hand, by combining deep learning and topology optimisation, beam steering at relatively large deflection angle with high efficiency has been demonstrated for single- or bi-operation wavelengths. Next step is to utilise deep learning to optimise the metasurface design with multi-functionalities further. For example, current broadband achromatic metalens has limited focusing efficiency. We believe the deep learning can entirely overcome this limitation by providing more irregular combinations of metaatoms that cannot be found by regular cylinder metaatoms. Finally, since nanophotonics offers a powerful and versatile platform to realise optical neural networks, more advanced and fast photonic chips that can bypass the computational capability based on traditional electric chips will be developed and paved the way toward the photonic computer.
The authors acknowledge the funding support provided by UNSW Scientia Fellowship and ARC Discovery Project (DP170103778).
The authors declare no conflict of interest.
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