Artificial Intelligence by Artificial Neural Networks to Simulate Oat (Avena sativa L.) Grain Yield Through the Growing Cycle

Artificial neural networks simulating oat grain yield throughout the crop cycle, can represent an innovative proposal regarding management and decision making, reducing costs and maximizing profits. The objective of the study is to develop biomathematical models via artificial neural networks, capable of predicting the productivity of oat grains by meteorological variables, nitrogen management and biomass obtained throughout the development cycle, making it possible to plan more efficient and sustainable managements. In each cultivation system (soybeans/oats; maize/oats), two experiments were carried out in 2017 and 2018, one for analyzing grain yield and the other for cutting every 30 days to obtain biomass. The experiments were conducted in a randomized block design with four replications for four levels of N-fertilizer (0, 30, 60 and 120 kg ha), applied in the stage of the 4th expanded leaf. The use of the artificial neural network makes it possible to predict grain yield by harvesting the biomass obtained at any stage of oat development, together with the handling of the nitrogen dose and meteorological information during cultivation. Therefore, a new tool Journal of Agricultural Studies ISSN 2166-0379 2020, Vol. 8, No. 4 http://jas.macrothink.org 613 to aid the simulation of oat productivity throughout the cycle, facilitating faster decision making for more efficient and sustainable management with the crop.


Introduction
The use of artificial neural networks (ANN) has been growing gradually in the representation of the complex system, mainly in a non-linear variable (Leal et al., 2015;Fleck et al., 2016). The ANN are mathematical models based on the biological nervous system, formed by neurons that can be distributed in several interconnected layers, which, through training, store knowledge and generalize the information learned, being able to solve complex problems and model the behavior of the variables involved (Saraceno et al., 2010;Azarpour et al., 2015). In agriculture, neural networks can be used to develop prediction models in complex systems and estimate desired parameters, enhancing process optimization and decision making (Huang, et al., 2010;Silva et al., 2014).
The implementation of new technologies for the management of agricultural crops has received attention from researchers in the search for a healthy diet. Due to the necessity to optimize food production with cost reduction and sustainability to ecosystems (Nikolla et al., 2014;Arenhardt et al. 2017). Furthermore, white oats are being used more in the food industry, as flakes, as it is an extremely nutritious and healthy cereal (Gutkoski et al., 2009;Silva et al., 2015).
Nitrogen as fertilizer is the essential element to assure proper oat grain yield requests from the industry (Marolli et al., 2017a;Scremin et al., 2017), but their management is one of the most complex because there are high losses by lixiviation, volatilization, which increase production costs and environmental damage (Brezolin et al., 2017;Marolli, et al., 2018). Is highlighted weather elements, the rainfall and air temperature, are strictly linked to the nitrogen gain and losses by the plant, also are the most related to oat grain (Simili et al., 2008;Marolli et al., 2017b). These elements are non-linear variables, which difficulties the modeling use to predict yield. However, the study of biological processes, the climate and the management all over the growth cycle by ANN, can represent a new technology to make decisions, adding important information to the biological variables and environment, of linear and non linear behavior. It allows the patterns recognition in the generation of prognosis with reduction in production costs and maximizing profits.
The study aimed to develop biomathematics models by ANN, capable of predicting oat grain yield per weather variable, nitrogen management and biomass, obtained all over the development cycle.
The seeds were sown with a seeder-fertilizer in five 5-m-length lines spaced by 0.20 m, with an experimental area of 5 m 2 . The population density was 400 seeds m -2 viable seeds, and the cultivar URS-Corona. During the work, applications were made tebuconazole fungicide of the commercial name FOLICUR® CE was applied in the dosage of 0.75 L ha -1 , and of the metsulfuron-methyl herbicide of the commercial name ALY® in the dose of 4 g ha -1 . In the sowing, 45 and 30 kg ha -1 of P2O5 and K2O were applied based on the contents of P and K in the soil in the expectation of grain yield of 3 t ha -1 respectively and 10 kg ha -1 of nitrogen (except in the unit standard experiment), with the residual to complete the proposal top-dressing dose in the phenological stage of fourth fully expanded leaves.
Two experimental studies was performed in each crop condition (soybean/ oat, maize/ oat systems). One to quantify biomass yield (BY, kg ha -1 ) through the cutting performed every 30 days until physiological maturity and the other to the grain yield estimative (GY, kg ha -1 ). Therefore, at the four experiments the trial design was in randomized blocks with four replicates for four N-fertilizer doses (urea) in the level (0, 30, 60, and 120 kg ha -1 ). The grain yield was obtained by cutting the three central lines of each plot at the harvest maturity, then was threshed and the grain moisture corrected to 13% at the laboratory to the grain yield estimative. To quantify biomass productivity (BY, kg ha -1 ) the material plant was harvested close to the soil by collecting a linear meter in the three central lines of each plot in 30, 60, 90, and 120 days after emergence, a total of four cuttings.
To estimate biomass productivity the plant material was dried in a forced-air oven at 65 º C until stabilized weight. The values of maximum air temperature and rainfall, obtained through the Total Automatic Station installed 500 meters from the experimental area.

ANN Simulation Model
The simulation of the oat grain yield for a development stage was mathematics modeling by ANN, using Neural Network Toolbox of Matlab software. These networks are trained using a backpropagation algorithm as activated function of the hidden layer hyperbolic sigmoid tangent, and the training rule Levemberg-Merquadt (LM). The backpropagation is a generalization of the learning algorithm Widrow and Hoff -Least Mean Square (LMS), known as delta rule (Faraco et al., 1998), falls under the category of supervised learning. Network performance is measured by an error function that considers, for each of the different standards p on input, the square of the difference between the expected value and the respective calculated output. In other words, the error is the sum of the quadratic errors, defined by the following expression: (1) represents the error of the i-th neural element, for the p-th input, is the output expected on the i-th neural element, for the p-th input and is the output produced, is the output produced, defined as: is the j-th input component .
The backpropagation algorithm acts on synaptic weights, minimizing the error function, using the descending gradient technique. In this method, the weight values are modified proportionally to the opposite of the error derivative, according to the following expression: , called the learning rate, it controls how big the "step" must be taken.
Defining k p i d , , as output expected in the i-th unit of the k-th layer, when the p-th pattern is presented to the network and, as the real output is, e , the error function, in the k layer, can be describe: The weights correction in the output layer K is given by applying the chain rule Similarly, it can be shown that in the hidden layers the correction is given by: The sigmoidal function is the most widely used, as it is a monotonic and easily derived function, with its basic model as: Levenberg-Marquardt training is a function that updates the bias weights and values according to Levenberg-Marquardt optimization. It is often considered to be the fastest of the error propagation training algorithms, but it requires more computational memory than the other algorithms. In the Levenberg-Marquardt algorithm, the changes in the weights are are obtained (Lera & Pinzolas, 2002), E is the mean square error of the network, ISSN 2166-0379 2020 N is the number of examples, is the network output corresponding to the example and is the desired output for that example.

Journal of Agricultural Studies
The matrix elements are given by: In each ANN architecture, the data was divided randomly at 70% for training (database with 128 samples), 15% for tests and 15% for validation. The input variables used in the artificial neural network were: N-fertilizer dose (0, 30, 60 e 120 kg ha -1 ), the oat development stage after emergence (30, 60, 90 e 120 days), the biomass yield, rainfall load and the medium temperature load in each development stage, the output variable of the neural network was oat grain yield.
To ensure that the data received equal attention during the training process, thus increasing its efficiency, both the input and output data of the neural network are standardized for the range of -1 to 1, by the data normalization process, expressed by the following equation: , is the normalized, dimensionless value; is the observed value; , is the minimum sample value; and , the maximum sample value. At the beginning of the training, the free parameters are generated randomly and that these initial values can influence the final result of the training, 10 networks of each architecture were trained. Before the ANN architecture training, were chosen the lowest mean relative error (MRE) regard the validation data, and the lowest mean squared error (MSE) related to the training data. Each network was composed of 3 layers (input, hidden and output), in input layer with 5 neurons, the hidden layer varied between 5 to 25 (adding every 5 neurons) and a output layer with 1 neuron. To represent the ANN architecture were used the signal "NI-NHL-NNO" NI = input variable numbers, NHL = hidden layer ISSN 2166-0379 2020 neuron numbers and NNO = output layer neuron numbers. For the training and validation of ANNs, were used the experimental data obtained in 2017 and 2018 in the field experiment.

Results and Discussion
In Figure 1 of the oat cultivation period, it was noticed that the air temperatures were higher in 2017 than in 2018. In addition, in 2017, the rainfall was 813 mm ( Figure 1A) and in 2018 it was 785 mm (Figure 1B), they were close to the average of the last 20 years (900 mm), however, with a different distribution between the years. In 2017, the volume of rainfall was low in the vegetative phase, accompanied by a high maximum air temperature. Circumstance that benefits nitrogen losses through volatilization and reduces the stimulus of new tillers, a component directly linked to grain productivity. The most intense rains occurred in the second half of the oat cultivation cycle and extended until close to the harvest in 2017, a condition that indicates less sunstroke and, consequently, reduction in the performance and efficiency of photosynthesis.
In 2018, the largest amount of rainfall was from sowing at 35 days of oat development and with milder maximum air temperature compared to 2017. These conditions favor the maintenance of soil moisture and increase the nitrogen efficiency used by the plant. In addition, from half the cycle to maturation, rainfall volumes were distributed with lesser intensity, improving the oats development conditions, justifying the higher grain productivity obtained in 2018.

Journal of Agricultural Studies
ISSN 2166-0379 2020, Vol. 8,No. 4 The location and environment are decisive factors for grain yield, with climatic variations throughout the development cycle is the factor that most contributes to the yield changes (Ferrari Neto et al., 2012;Costa et al., 2016). In wheat and oat the crop year condition is defined by the rainfall amount and air temperature Marolli et al., 2017a). These affect the rate of organic matter decomposition in contact with the soil and affect the efficiency of nitrogen use by the plant (Acosta et al., 2014). Air temperature is also a determining factor in the yield development, since it acts as a catalyst for biological processes, which is why plants require a minimum and maximum temperature for normal physiological activities (Guarienti et al., 2004;Tonin et al., 2014a;Tonim et al., 2014b). Arenhardt et al. (2015), highlight that longs rainfall season reduce the efficiency of harnessing sunlight and nutrients to photosynthesis, interfering in the development, productivity and quality of grains during harvest (Castro, 2012;Mamann et al., 2017). For oats, the favorable climate is described as milder temperatures with radiation quality, it favors tillering and grain filling, without the occurrence of rainfall in large quantities and intensity. However, it favors an adequate supply of moisture stored in the soil (Castro et al., 2012;Marolli et al., 2017b). Table 1 shows the mean square error in the training process and the mean relative error and variance, verified in the development of the artificial neural network. In the soybean/oat system the network architecture of 5-5-1 to 5-20-1 showed closest value of mean relative error next, but when variance is observed in the validation process, the architecture 5-5-1 showed minor value from the other. It represents that the error for all the data training decreased, but there will not necessarily be a reduction on the validation values. However, since it exhibits low value of variance, it does not express low mean relative error for the validation data (Table 1), in addition to presenting the relationship between the number of training samples and the number of hidden connections greater than 2, as indicated by Masters (1993). Besides, must be careful that networks with many neurons on the hidden layer can memorize training padrons instead of extracting generalizing characteristics (produce suitable outputs to inputs that were not present in the training (Braga et al., 2000;Teodoro et al., 2015). Thus, following the interpretation proposed by Masters (1993) and Braga et al., (2000), for this crop system the network architecture of 5-10-1, because it showed better capacity to predict oat grain yield. soybean/oat system 5-5-1 5.54E-3 1.01E-2 7.82E-3 5-10-1 5.51E-3 7.76E-3 1.42E-2 5-15-1 5.83E-3 6.29E-3 2.32E-2 5-20-1 5.64E-3 7.85E-3 2.32E-2 5-25-1 6.81E-3 1.44E-2 1.96E-2 maize/oat system 5-5-1 6.31E-3 4.77E-3 7.77E-3 5-10-1 6.75E-3 8.44E-3 6.37E-3 5-15-1 5.89E-3 5.69E-3 7.78E-3 5-20-1 6.39E-3 1.78E-2 8.32E-3 5-25-1 3.42E-3 9.62E-3 1.68E-2 ISSN 2166-0379 2020

NI= Number of input layer neurons; NH= Number of hidden layer neurons; NO= number of output layer neurons
In the maize/oat system (Table 1), the minor mean quadratic error was observed in the 5-25-1 architecture, but, with more validation variation. Then, following the precept on choosing the soybean/oat system, was selected to maize/oat system the 5-15-1 structure, to represent lower mean quadratic error than the other structure and to have lower mean relative error.
The results found in the 10 and 15 neurons configuration in the hidden layer showed there is not the need for complex structures, because the hidden layer does not represent linearity between the data (Soares et al., 2015;Dornelles et al., 2018) and, in this case, there is not more complexity on the structure to understand yield tendency by climate condition, and the biomass manager in oat. Braga et al. (2007) and Bullinaria, (2016) indicated simpler configuration to apply ANN, avoiding overfitting occurrence and making the research process and configuration optimization easier to a certain task.
In Figure 2, the determination coefficients of training (70% data), validation (15% data), test (15% data) and total network (100% data) of the soybean/oat and maize/oat system. The determination coefficients of the chosen networks demonstrate the reliability and confirm that the generated algorithm scales the behavior of the actual data obtained, effectively, presenting values close to 1, that is, 100%.  Table, the architecture 5-10-1 and 5-15-1 of the soybean/oat and maize/oat system, were compared the grain yield value obtain by the cumulative effect of the years 2017+2018 with the estimated value of ANN. To the input values of the artificial neural network were used the doses of N-fertilizer, the oat development stages, the biological yield, the accumulated rainfall mean and the maximum temperature mean accumulated in each stage of oat development ( Figure 2). ISSN 2166-0379 2020  BY= biological yield; GY= grain yield; ANN= Artificial neural network; Li= inferior limit; = X mean; Ls= superior limit In Table 2, soybean/oat system, the simulation showed high capacity to predict for oat grain yield, the values simulated by the ANN were between the truste interval of cumulative effects in the year 2017 and 2018. In the maize oat system (Table 3), the simulation also stayed between the truste interval. The ability to understand exemples and generalize information is the main problem solution by ANN, (Wasserman, 1989;Martins et al., 2016). The generalization that is associated with the network's ability to learn from a small set of examples and subsequently provide coherent responses to unknown data is a demonstration that a ANN go beyond simply mapping input and output relationships (Soares et al., 2014). These results show that the use of the network enables the predictability of grain yield at any OAT Journal of Agricultural Studies ISSN 2166-0379 2020 development stage, in any condition of use of the N-fertilizer and in different succession systems, becoming a tool to aid decision making regarding the management of culture.

Journal of Agricultural Studies
One thing to regard is that the Neural Network can accept different input data. Thus, data collected in the field, such as topographic conditions and measures, edaphic parameters, phytomass values, stage of development of agricultural crops, etc., can also be used as a source of definition and context for a specific target, important in the task of memorization thematic feature (Bucene & Rodrigues, 2004;Depiné et al., 2014;Dornelles et al., 2018). BY= biological yield; GY= grain yield; ANN= Artificial neural network; Li= inferior limit; = X mean; Ls= superior limit Despite the promising results of using a neural network system to predict oat yield throughout the development stages, there is a need to qualify this technique for future data analysis, with a Journal of Agricultural Studies ISSN 2166-0379 2020 greater number of predictor variables, both for the plant and the ground. Therefore, it is suggested to test different configurations of neural networks, in order to obtain a greater relationship between productivity data, soil attributes, plant attributes, management and climate, thus obtaining greater accuracy in the estimates of variables of interest in crops.

Conclusion
The use of the artificial neural network makes it possible to predict grain yield by harvesting the biomass obtained at any stage of oat development, together with the handling of the nitrogen dose and meteorological information during cultivation. Therefore, a new tool to aid the simulation of oat productivity throughout the cycle, facilitating faster decision making for more efficient and sustainable management with the crop.