Enhancing Photovoltaic Energy Output Predictions Using ANN and DNN: A Hyperparameter Optimization Approach

Abstract

This study investigates the use of artificial neural networks (ANNs) and deep neural networks (DNNs) for estimating photovoltaic (PV) energy output, with a particular focus on hyperparameter tuning. Supervised regression for photovoltaic (PV) direct current power prediction was conducted using only sensor-based inputs (PanelTemp, Irradiance, AmbientTemp, Humidity), together with physically motivated-derived features (ΔT, IrradianceEff, IrradianceSq, Irradiance × ΔT). Samples acquired under very low irradiance (<50 W m⁻²) were excluded. Predictors were standardized with training-set statistics (z-score), and the target variable was modeled in log space to stabilize variance. A shallow artificial neural network (ANN; single hidden layer, widths {4–32}) was compared with deeper multilayer perceptrons (DNN; stacks {16 8}, {32 16}, {64 32}, {128 64}, {128 64 32}). Hyperparameters were selected with a grid search using validation mean squared error in log space with early stopping; Bayesian optimization was additionally applied to the ANN. Final models were retrained and evaluated on a held-out test set after inverse transformation to watts. Test performance was obtained as MSE, RMSE, MAE, R², and MAPE for the ANN and DNN. Hence, superiority in absolute/squared error and explained variance was exhibited by the ANN, whereas lower relative error was achieved by the DNN with a marginal MAE advantage. Ablation studies showed that moderate depth can be beneficial (e.g., two-layer variants), and a simple bootstrap ensemble improved robustness. In summary, the ANN demonstrated superior performance in terms of absolute-error accuracy, whereas the DNN exhibited better consistency with relative-error accuracy.

1. Introduction

The growing global interest in renewable energy sources driven by the urgent need to combat climate change, reduce greenhouse gas emissions, and address increasing energy demands has become more evident in recent years. Among various renewable options, solar power stands out as one of the most promising alternatives. Photovoltaic (PV) systems, which directly convert sunlight into electricity, play a critical role in harnessing solar energy. However, an accurate prediction of PV energy output is essential for effective integration into power grids, ensuring system stability, reliability, and optimal energy resource management. Such predictions are challenging due to the stochastic nature of solar irradiance and the influence of environmental factors such as temperature, humidity, and cloud cover [1]. Traditional statistical methods often fail to capture these complex nonlinear relationships, prompting increased interest in advanced machine learning techniques, particularly artificial neural networks (ANNs) and deep neural networks (DNNs), which are capable of learning from large datasets and modeling intricate dependencies. Therefore, there has been rising interest in applying advanced machine learning techniques for making more accurate PV output predictions. This concept has earned much attention in this field, which can be attributed to its capability to simulate complex nonlinear relationships and learn from huge amounts of data, with artificial neural networks (ANNs) and deep neural networks (DNNs) as the basis. Artificial intelligence is the basic area of computer science used for machine learning and development of computers that can perform tasks that require human intelligence. As a result, various deep learning techniques advanced from artificial neural networks (ANNs) to more sophisticated ones such as recurrent neural networks (RNN), long short term memory (LSTM), and deep neural networks (DNN), among others, with reinforcement learning [2].

Accurate PV solar forecasts are needed in order to efficiently manage electrical grids, integrate solar energy more effectively into electricity systems, and reduce dependence on fossil fuels. This leads the users, therefore, to improve forecasting models that help balance supply and demand, reduce power outage risks, and increase the overall reliability of an energy system. Such systems can optimize energy distribution, lower operating expenses, and facilitate wider use of renewable energy sources by means of the incorporation of accurate PV energy forecasts. When looking at the literature, the architectural configuration of ANNs, that consists of several layers, has been observed to be useful in numerous predictive tasks, such as PV power forecasting. Some of the notable studies in the literature are as follows. Bellagarda et al. presented a novel approach for utilizing Artificial Neural Networkartificial neural networks (ANNs) to anticipate solar power output in situations where there is a scarcity of actual data. A simulator has been employed to generate a precise dataset. The simulator has generated a large dataset of PV power generation that is both artificial and realistic. This dataset has effectively been used to train and test various ANN models. The developed models have predicted the PV power generation of the installation with acceptable accuracy [1]. ANN and Analog Ensemble (AnEn) are utilized both in conjunction and separately for power prediction in three distinct power plants located in Italy. The findings have indicated that a combined AnEn + ANN solution produces the most favorable outcomes and that the suggested approach is highly suitable for large-scale computing [3]. Another ANN study used historical photovoltaic (PV) output data of central and southern Jordan. A stacked long short-term memory network (LSTM) was used in order to estimate electricity production. While the dynamic NARX ANN and LSTM models performed similarly, the NARX model surpassed the LSTM model in replicating the time dependent behavior of PV systems with variable data [4]. In another study, ANN and DNN were compared on panel output. This study has presented two methods for forecasting PV generation, using a multilayer feedforward artificial neural network (ANN) and a deep neural network (DNN) with a convolution neural network (CNN) and recurrent neural network (RNN) layer. On a residential building, a PV production dataset was tested using both approaches. In all computed measures, the ANN has performed better than DNN, with the least errors and the most acceptable forecast errors [5]. Another study in Korea developed a model that predicted photovoltaic power generation by obtaining a three day weather forecast from meteorology. For the algorithm of prediction, adaptive neurofuzzy inference system and artificial neural network (ANN) techniques such as DNN (dynamic neural network), RNN (recurrent neural network), and LSTM (long short term memory) were chosen. This revealed that ANN worked better than the neurofuzzy method, and compared to DNN, RNN, and LSTM, it was suitable for time series data structures [2]. A further investigation has used machine learning techniques to precisely forecast the electricity generation of a solar system. An artificial neural network (ANN) model has been created to forecast power outputs from a real power plant in Puglia, southern Italy, using temperature and solar radiation data obtained from the Global Data Assimilation System (GDAS) sflux model outputs. The findings demonstrated that the examined numerical weather model can be integrated with machine learning techniques to accurately simulate the performance of photovoltaic (PV) systems, with an error rate of less than 10%, even in the absence of onsite weather data [6]. On the other hand, deep neural networks (DNN) are a machine learning method (they commonly employ algorithms such as Random Forest, Support Vector Machine, and K-Nearest Neighbors) that are widely utilized in several domains, drawing inspiration from the architecture of mammalian visual systems and extracting hierarchical features from datasets. This allows for the creation of more efficient representations [7,8,9,10]. DNNs are much deeper versions of ANNs, which enhance their ability to capture complex patterns hidden in data. deep neural networks (DNN) utilize deep architectures in neural networks (NN) and have the ability to express functions with more complexity [11]. Numerous studies have employed DNNs for solar photovoltaic energy estimation, including Rai et al.’s, where a novel multi-directed differential attention-based differential attention net model was used for accurate solar power prediction. The suggested net was compared to various hybrid deep learning models, such as those that include the recurrent neural network, gated recurrent unit, and LSTM. The results of the study have validated the efficacy of the suggested model [12]. Also, support vector machines (SVM) with improved ant colony optimization were used to optimize PV power generation with remarkable improvements observed in prediction accuracy. The findings suggested that the regression coefficient (R²) of the model may be enhanced by 6.8% with appropriate data preparation [13]. Moreover, a wavelet transform-based CNN-BiLSTM model has been proposed by Gu et al., that outperforms previous models for day-ahead forecasting of PV power [14].

Forecasts for PV electricity can range from seconds to years, depending on the forecast horizon. Generally, the forecast horizon is divided into three time periods: short term, medium term, and long term [15,16,17]. There is also a category in the literature called “very short-term forecasting” that can be used to improve real time optimizations [18]. The figure shows the three forecast horizons described in the literature and how they are used to forecast PV power production [19]. The accuracy of the PV power forecast is affected by the forecast horizon [20]. The PV power output forecasting horizon and term category is given in Figure 1.

Based on previous research, which is given in Table 1, it has been found that environmental factors significantly affect the fluctuations of photovoltaic power data, while their impact on trend components is relatively minor. Therefore, most of the studies in the literature take part in the short-term forecasting category. In addition, with the strong correlation between environmental factors and PV power outputs, it is possible to effectively reduce fluctuations in medium- and long-term forecasts caused by seasonal meteorological changes.

Despite significant advancements in the prediction of PV output performance, there is still a significant research gap in the optimization of hyperparameters. Different AI models may require different weights, constraints, or learning rates to generalize various data patterns. These parameters are hyperparameters and they should be set properly for the model to perform well in solving the problem. In terms of this, the progression made in utilizing ANN and DNN models for PV energy prediction, one of the essential factors that greatly affects these algorithms is the selection and optimization of hyperparameters. Hyperparameters such as learning rate, number of hidden layers, and number of neurons per layer are significant in determining a model’s learning capacity and generalization ability. The process of selecting the right set of hyperparameters is often referred to as tuning. Poorly chosen hyperparameters can result in suboptimal performance, overfitting, or underfitting [15]. A hyperparameter defines a parameter whose value determines the way learning takes place. Some of the hyperparameter optimization methods are decision theoretic, Bayesian optimization (BO), multi-fidelity optimization techniques, and metaheuristic algorithms [21]. The decision theoretic optimization method’s initial step is to construct the search space of hyperparameters, then identify different permutations of the hyperparameters within the boundaries, and finally obtain optimal combinations. Two methods are used for this. One of them is a grid search (GS), and the other is a random search (RS). As the name suggests, a random search does random research and does not consider all possibilities. On the contrary, a grid search trains the network with all the specified criteria and reveals the parameters that give the best results. It was recognized as one of the most commonly employed methods for investigating the hyperparameter configuration space [22,23].

Table 1. Summary of literature review on direct PV power forecasting.

Reference	Method	Category	Forecasting Horizon	Time Span	Highlights/Notes
[24]	Statistical and sky cam-based model	Real time/ Short term	1 year	10 s–10 min	The integration of statistical and sky cam-based methodologies enhances the precision of forecasting in comparison to using each method individually.
[25]	Feedforward neural network (FNN), convolutional neural network (CNN), and long short-term memory (LSTM)	Short term	A day ahead	1 h	Among the nine models examined in this study, the retrained transferred LSTM model exhibited the highest level of accuracy, as indicated by its low mean absolute error (MAE) of 0.211, mean squared error (MSE) of 0.168, mean absolute percentage error (MAPE) of 74%, root mean squared error (RMSE) of 0.403, and weighted mean absolute percentage error (wMAPE) of 32.04.
[26]	Deep convolutional neural network (CNN) structure; AlexNet, BT, DTR, LR, and SVR	Short term	For 1 h to 5 h ahead	1 h	Among the CNN architectures considered in the study, AlexNet demonstrated the best correlation coefficient (R) and the lowest root mean square error (RMSE), mean absolute error (MAE), and SMAPE values across all time horizons and meteorological conditions, specifically for forecasts ranging from 1 h to 5 h ahead. The suggested technique yields average R values of 97.28%, 95.77%, 94.49%, 93.61%, and 92.62%, respectively.
[16]	LSTM and GRU	Short term	from 10 a.m. to 3 p.m.	from 6 a.m. to 9 a.m.	The GRU model had superior accuracy in all test instances, and it was noted that its performance improved as the generated photovoltaic (PV) output rose.
[27]	ML techniques			covers 269 days for the year 2017
[28]	Support vector machine (SVM), gate recurrent unit (GRU), feed forward neural network (FFNN), and long short term memory (LSTM)	Short term	5 min, 15 min, 30 min, 1 h, 3 h, 6 h, 12 h,24 h	dataset 1; 8:00 a.m. to 3:55 p.m., dataset 2; 8:00 a.m. to 5:30 p.m.	The study, which combined SVM and GRU models, demonstrated the best correlation coefficient (R) of 0.9986.
[29]	Johansen vector error correction model (VECM)	Short term	-	over a one year period from July 2019 to June 2020, between 4:30 p.m. and 7:30 a.m.	Subsequently, the efficacy of the Johansen model is evaluated in comparison to a traditional artificial neural network (ANN) forecasting model. The findings indicated that the Johansen VECM cointegration strategy exhibited superior performance compared to the artificial neural network (ANN) model. The Johansen model achieved the greatest R2 score of 0.9859 in January.
[30]	Feedforward artificial neural network (ANN) and long short term memory (LSTM)	Medium term	five day ahead	1 h	In the study, findings clearly demonstrate that taking into account various orientations of the solar panels enhances the predictability of the rooftop solar power facility.
[31]	Machine learning (ML), artificial neural network (ANN), decision tree (DT), extreme gradient boosting (XGB), and long short-term memory (LSTM)			from 21 January 2011 to 3 March 2012, which accounts for 407 days, 5 min	Comparisons of predicting scores indicate that the ANN algorithm outperforms other models, namely the ANN16 model, which achieves the lowest mean absolute error (MAE) of 0.4693, the lowest root mean squared error (RMSE) of 0.8816 W, and the highest coefficient of determination (R2) of 0.9988.
[32]	ARIMA (Autoregressive Integrated Moving Average) statistical approach, and ANN (Artificial neural network)	Short term	One day	15 min, 10 days	The study results confirmed that the ARIMA model is more efficient than the ANN model and closely approximates the experimental scenario.
[33]	Artificial neural network (ANN) and multiple linear regression (MLR)	Short term		randomly during the year	The study results indicate that the R2 value of the artificial neural network (ANN) trained with the Levenberg–Marquardt method was shown to be 98.9%. The MLR study showed an R2 value of 94.8%.
[34]	Artificial neural network (ANN) model, long short-term memory (LSTM), and the gated recurrent unit (GRU)	Short Term	One day	1 h, from 21 February 2021 to 13 June 2021.	The LSTM and GRU models exhibited superior predicted outcomes.
[25]	Feedforward neural network (FNN), convolutional neural network (CNN), and LSTM model	Short Term	A day ahead	1 h	The LSTM model has the highest level of accuracy. RMSE: 0.403.
[35]	An artificial neural network	Short Term	One day	5 s and average of them every 5 min	For sunny days ANN, average correlation coefficient of 99.988%, for cloudy days 99.845%
[36]	Long short term memory (LSTM), adaptive neurofuzzy inference system (ANFIS), fuzzy c means (FCM), and ANFIS with grid partition (GP)	Short Term	One hour ahead	1 h	The LSTM model yields optimal outcomes. The root mean square error (RMSE), mean absolute error (MAE), and correlation coefficient (R) were 60.66 kWh, 30.47 kWh, and 0.9777, respectively.
[37]	Hourly time series classification method, a new cluster selection algorithm, and a multilayer perceptron neural network (MLPNN)	Medium term	1–48 h	1 h	Combination of a novel clustering technique, a new hourly time-series classification, a new cluster selection algorithm, and MLPNN model has the higher accuracy performance.
[38]	Elman neural network (ENN)	Medium term	3 days ahead	15 min	In the study, researchers used the method ENN, showing that it has a significant effect on random PV power time series data.

Table 1. Summary of literature review on direct PV power forecasting.

Reference	Method	Category	Forecasting Horizon	Time Span	Highlights/Notes
[24]	Statistical and sky cam-based model	Real time/ Short term	1 year	10 s–10 min	The integration of statistical and sky cam-based methodologies enhances the precision of forecasting in comparison to using each method individually.
[25]	Feedforward neural network (FNN), convolutional neural network (CNN), and long short-term memory (LSTM)	Short term	A day ahead	1 h	Among the nine models examined in this study, the retrained transferred LSTM model exhibited the highest level of accuracy, as indicated by its low mean absolute error (MAE) of 0.211, mean squared error (MSE) of 0.168, mean absolute percentage error (MAPE) of 74%, root mean squared error (RMSE) of 0.403, and weighted mean absolute percentage error (wMAPE) of 32.04.
[26]	Deep convolutional neural network (CNN) structure; AlexNet, BT, DTR, LR, and SVR	Short term	For 1 h to 5 h ahead	1 h	Among the CNN architectures considered in the study, AlexNet demonstrated the best correlation coefficient (R) and the lowest root mean square error (RMSE), mean absolute error (MAE), and SMAPE values across all time horizons and meteorological conditions, specifically for forecasts ranging from 1 h to 5 h ahead. The suggested technique yields average R values of 97.28%, 95.77%, 94.49%, 93.61%, and 92.62%, respectively.
[16]	LSTM and GRU	Short term	from 10 a.m. to 3 p.m.	from 6 a.m. to 9 a.m.	The GRU model had superior accuracy in all test instances, and it was noted that its performance improved as the generated photovoltaic (PV) output rose.
[27]	ML techniques			covers 269 days for the year 2017
[28]	Support vector machine (SVM), gate recurrent unit (GRU), feed forward neural network (FFNN), and long short term memory (LSTM)	Short term	5 min, 15 min, 30 min, 1 h, 3 h, 6 h, 12 h,24 h	dataset 1; 8:00 a.m. to 3:55 p.m., dataset 2; 8:00 a.m. to 5:30 p.m.	The study, which combined SVM and GRU models, demonstrated the best correlation coefficient (R) of 0.9986.
[29]	Johansen vector error correction model (VECM)	Short term	-	over a one year period from July 2019 to June 2020, between 4:30 p.m. and 7:30 a.m.	Subsequently, the efficacy of the Johansen model is evaluated in comparison to a traditional artificial neural network (ANN) forecasting model. The findings indicated that the Johansen VECM cointegration strategy exhibited superior performance compared to the artificial neural network (ANN) model. The Johansen model achieved the greatest R2 score of 0.9859 in January.
[30]	Feedforward artificial neural network (ANN) and long short term memory (LSTM)	Medium term	five day ahead	1 h	In the study, findings clearly demonstrate that taking into account various orientations of the solar panels enhances the predictability of the rooftop solar power facility.
[31]	Machine learning (ML), artificial neural network (ANN), decision tree (DT), extreme gradient boosting (XGB), and long short-term memory (LSTM)			from 21 January 2011 to 3 March 2012, which accounts for 407 days, 5 min	Comparisons of predicting scores indicate that the ANN algorithm outperforms other models, namely the ANN16 model, which achieves the lowest mean absolute error (MAE) of 0.4693, the lowest root mean squared error (RMSE) of 0.8816 W, and the highest coefficient of determination (R2) of 0.9988.
[32]	ARIMA (Autoregressive Integrated Moving Average) statistical approach, and ANN (Artificial neural network)	Short term	One day	15 min, 10 days	The study results confirmed that the ARIMA model is more efficient than the ANN model and closely approximates the experimental scenario.
[33]	Artificial neural network (ANN) and multiple linear regression (MLR)	Short term		randomly during the year	The study results indicate that the R2 value of the artificial neural network (ANN) trained with the Levenberg–Marquardt method was shown to be 98.9%. The MLR study showed an R2 value of 94.8%.
[34]	Artificial neural network (ANN) model, long short-term memory (LSTM), and the gated recurrent unit (GRU)	Short Term	One day	1 h, from 21 February 2021 to 13 June 2021.	The LSTM and GRU models exhibited superior predicted outcomes.
[25]	Feedforward neural network (FNN), convolutional neural network (CNN), and LSTM model	Short Term	A day ahead	1 h	The LSTM model has the highest level of accuracy. RMSE: 0.403.
[35]	An artificial neural network	Short Term	One day	5 s and average of them every 5 min	For sunny days ANN, average correlation coefficient of 99.988%, for cloudy days 99.845%
[36]	Long short term memory (LSTM), adaptive neurofuzzy inference system (ANFIS), fuzzy c means (FCM), and ANFIS with grid partition (GP)	Short Term	One hour ahead	1 h	The LSTM model yields optimal outcomes. The root mean square error (RMSE), mean absolute error (MAE), and correlation coefficient (R) were 60.66 kWh, 30.47 kWh, and 0.9777, respectively.
[37]	Hourly time series classification method, a new cluster selection algorithm, and a multilayer perceptron neural network (MLPNN)	Medium term	1–48 h	1 h	Combination of a novel clustering technique, a new hourly time-series classification, a new cluster selection algorithm, and MLPNN model has the higher accuracy performance.
[38]	Elman neural network (ENN)	Medium term	3 days ahead	15 min	In the study, researchers used the method ENN, showing that it has a significant effect on random PV power time series data.

In this study, we preferred the grid search because it implements a brute force method and exhaustive search that evaluates all possible combinations of hyperparameters given as a set. Also, existing research generally focuses on the functionality of developed models but rarely has tried combinations for hyperparameters in the power forecasting area. While hyperparameter optimization via grid search is established, our work introduces three context-driven innovations. First, empirically validated hyperparameter constraints reduced search space combination about by 90%. A grid search explored learning rates η ∈ {0.1, 0.05, 0.01, 0.005, 0.001} η ∈ {0.1, 0.05, 0.01, 0.005, 0.001} (where applicable), training epochs {100, 200, 300, 500} {100, 200, 300, 500}, ANN widths {4, 8, 16, 32} {4, 8, 16, 32}, and DNN hidden-layer configurations listed following part. The selection criterion was the validation mean squared error in log space (Val MSE(Log)).

These studies bridge a critical gap between theoretical optimization and operational deploy ability in resource-constrained PV systems. Consequently, a structured approach to hyperparameter optimization is crucial in order to maximize the accuracy of ANN and DNN models. This research seeks to enhance the predictions of PV energy output by employing ANN and DNN models that focus on hyperparameter optimization. It therefore seeks to determine the optimal settings using all possible combinations of hyperparameters, so as to find out which ones produce the highest degree of precision when making any forecasts. For each model, various hyperparameter combinations have been tested and the results were compared. Furthermore, our study was conducted using four predictors (solar radiation, panel temperature, ambient temperature, and humidity). The results will act as an input towards a more robust and efficient forecasting model that can be used for solar power integration into grid systems while facilitating the transition to sustainable energy systems at large. The following sections will outline all aspects of the methodology, including the data preparation process, model architecture, hyperparameter optimization methods, and performance evaluation metrics used. After the introduction, the Section 2 includes normalization and denormalization of data and briefly explains the ANN and DNN structure of the proposed system. The best performing hyperparameters are explained in this part. Also, details of the study are given in the flow chart. Lastly, in Section 3 the results of the proposed system are given, a comparison is made, and general recommendations are presented. Furthermore, we discuss the experimental outcome indicating improvements due to optimized settings for hyperparameters in Section 4. Finally in Section 5, the study concludes with some insights into this area.

2. Proposed Methodology

In this study, artificial neural network (ANN) and deep neural network (DNN) models have been developed and comparatively analyzed to predict the power output of a photovoltaic panel. Initially, in the data preparation process, features such as panel temperature, voltage, current, irradiance, ambient temperature, and humidity were utilized, and the power variable was calculated. The dataset was split into features (independent variables) and the target variable (dependent variable). In the preprocessing part, after taking input data for the models, normalization was applied. This process, required for the original data, is necessary to mitigate the dimensional impacts caused by varying data. Normalization is defined as the $X_{norm}$. Equation (1) represents the relationship between $x_{max}$ and $x_{min}$, where $X_{norm}$ and $x$ denote the normalized data and the original data, respectively. $x_{max}$ and $x_{min}$ correspond to the highest and lowest values of the input characteristics, respectively.

$$X_{norm}={\displaystyle \frac{x-x_{min}}{x_{max}-x_{min}}}$$

(1)

Subsequently, post processing has been performed before evaluating the forecast of any model. It is known that to obtain the actual predicted PV power and evaluate the performance of the model, if normalized data is used in the prediction model, it is necessary to de-normalize it first [17]. Thus, the most common method often used in the post processing part is anti-normalization [39].

The analysis and models are developed in MATLAB R2021a. Windows 10 Professional with an i7-10750H central processing unit (CPU) and a GTX 2060 graphics processing unit (GPU) were used for the analysis. The flow chart of the study is given in Figure 2. The data was randomly divided into 80% training and 20% testing sets. Data model training has involved testing various combinations of hyperparameters. The hyperparameters have included learning rates, epoch numbers, and the number of neurons in the hidden layers of both ANN and DNN models. The ANN model had a single hidden layer, while the DNN model was designed with a deeper structure consisting of two layers.

A supervised regression problem is considered to predict photovoltaic (PV) DC power output (W) from environmental and panel surface measurements. The available predictors per timestamp are as follows: Panel Temperature (°C), Irradiance (W/m²), Ambient Temperature (°C), and Humidity (%RH). To reduce false learning in very low illumination conditions, samples with Irradiance < 50 W/m² are excluded. All remaining predictors were standardized using training-set statistics only (z-score) (given in Equation (2)):

$$z={\displaystyle \frac{x-{\mu }_x}{{\sigma }_x+\epsilon }}$$

(2)

with $\epsilon$ = ${10}^{-8}$ to avoid division by zero. The target variable y (power, W) was modeled in log space to stabilize variance and emphasize relative errors (given in Equation (3)):

$$\tilde{y}=\mathrm{l}\mathrm{o}\mathrm{g} (y+\epsilon )$$

(3)

For ANN, we used gradient descent with adaptive learning and momentum (traingdx) or Bayesian regularization (trainbr) where stated; for DNN we employed the scalable conjugate-gradient solver trainscg, which was empirically more stable for deeper stacks. During hyperparameter selection, models were trained on an internal training subset and validated on a held-out validation subset (80/20 split of the training data). Early stopping was applied with a patience of 6 validation checks (max_fail = 6). After selecting the best configuration, final models were retrained on the full training set; for the deep networks we retained a randomized validation split to preserve early stopping. To assess the performance of the models, the performance evaluation indices used included mean square error (MSE), root mean square deviation; RMSE, mean absolute error (MAE), R-square or R squared, and mean absolute percentage error (MAPE). These metrics show how much the estimated power values differ from actual power values. The optimal hyperparameter combinations for both models were found. According to the findings, it is argued that, considering the deeper architecture of the DNN model, more reliable and accurate predictions can be made compared to the ANN model. In addition, by better learning the complexity of photovoltaic panel data, the DNN can be considered a valuable tool for forecasting in renewable energy sources.

The power output of photovoltaic (PV) systems is influenced by environmental parameters such as irradiance, temperature, humidity, and others. Therefore, PV power output forecasting technology has to be capable of understanding the correlation between these environmental elements and PV power output. Nevertheless, the precise influence of each environmental component remains ambiguous in the context of PV power forecasting, making it difficult to construct a highly accurate PV power forecasting model.

The objective of this research is to assess and contrast the efficacy of two prediction algorithms, namely artificial neural networks (ANN) and deep neural networks (DNN) on forecasting PV power outputs. The PV Power output forecasting scheme is given in Figure 3. This section gives an overview of the techniques employed in implementing these two algorithms.

The PV system was placed outdoors at the Aksaray University Engineering Faculty building in Figure 4. In

Table 2. Hyperparameters for tuning ANN and DNN models.

Hyperparameter	Values	Explanation
Learning Rate	0.1, 0.05, 0.01, 0.005, 0.001	Choice of how much to adjust the model’s weight with each update.
Number of Epochs	100, 200, 300, 500	It was tried by selecting more # of epochs. However, although the result led to better learning, it caused overfitting.
Hidden Layer Sizes	{{16 8}, {32 16}, {64 32}, {128 64}, {128 64 32}} {4, 8, 16, 32, 64}	For DNN, different neurons were used in 5 hidden layers, and different neural networks were tried using a single layer in ANN.

, the hyperparameters utilized for optimizing ANN and DNN models are given. Furthermore, the specifications of the 140 watt solar panel used are given in

Table 3. Solar PV panel properties.

Parameters	Values
Maximum Power (Pmax)	140 Wp
Open Circuit Voltage (Voc)	22 V
Short Circuit Current (Isc)	7.08 A
Maximum Power Voltage (Vmp)	17.6 V
Maximum Power Current (Imp)	6.81 A

. The brightness of the sun and temperature of the ambience were taken from 7:00 a.m. to 6:30 p.m. approximately every 5, 10 and 15 min on 21 August 2024. The datasets are given in Figure 5. In the study, a high-performance Optris PI 160 thermal camera was used to obtain the surface temperatures of the panel. The Optris PI thermal cameras are manufactured by Optris GmbH, which is based in Berlin, Germany. It uses an infrared detector with a resolution of 160 × 120 pixels and a refresh rate of 120 Hz. In total, 100 data points were taken from irradiances, ambient temperature, panel surface temperature, humidity, PV voltage, and the current outputs dataset for model input values. In addition to the four primary inputs, physically motivated derived features were constructed and concatenated to the design matrix:

$$\Delta T=PanelTemp-AmbientTemp$$

$$\mathrm{I}\mathrm{r}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{E}\mathrm{f}\mathrm{f}=\mathrm{I}\mathrm{r}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\ast [1-0.004(PanelTemp-25)]$$

$$\mathrm{I}\mathrm{r}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{S}\mathrm{q}={\mathrm{I}\mathrm{r}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}^2$$

$$\text{Irradiance\_x\_DeltaT}=\mathrm{I}\mathrm{r}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\ast \Delta T$$

Accordingly, the energy output data points (100 units) of the PV panels produced have been obtained from the measured voltage and current values.

2.1. Deep Neural Network Architecture

A typical deep neural network (DNN) consists of a series of layers, where each layer performs a nonlinear transformation from the input to the output. These layers improve the consistency and specificity of the representations [40]. Some examples of deep neural network designs are stacked autoencoders (SAE), restricted Boltzmann machines (RBMs), convolutional neural networks (CNN), recurrent neural networks (RNN), long short term memory (LSTM), max pooling CNN (MPCNN), and deep belief networks (DBN) [41]. A common depiction of deep neural networks (DNNs) is given in Figure 6.

2.2. Artificial Neural Network Architecture

The fundamental architecture of an artificial neural network (ANN) consists of three layers: the input layer, the output layer, and the hidden layer. Each layer is composed of a certain number of neurons, as seen in Figure 7. The layers are interconnected with weights that link the inputs to the intended output, as described by Equation (4).

$$y=\phi \left(\sum _{i=1}^n{w}^i{x}^i+b\right)$$

(4)

• n: # of input
• $w^i$: weight matrix
• $x^i$: Input from the previous layer
• b: bias
• $\phi$: activation function.

Figure 7. Artificial neural network architecture.

Figure 7. Artificial neural network architecture.

Thus, artificial neural networks (ANN) replicate the cognitive functions of the human brain. During the training phase, the artificial neural network (ANN) receives data samples as input features. At the start, weights are initialized randomly in order to provide a random output. The output value is evaluated against the actual output using cost functions such as RMSE, MSE, MAE, and others. Subsequently, this error is propagated backwards to modify the weights in a manner that aligns the output with the actual value. A predetermined learning rate is employed to determine the pace of learning and the magnitude of adjustment, as described in Equation (5).

$$W^t=W^{t-1}-a\ast E$$

(5)

• $a$: learning rate
• $W^t$: updated weights
• $W^{t-1}$: previous weights
• $E$: propagated error

3. Performance Metrics for ANN and DNN

In this study, various combinations of hyperparameters were tested for both models, and the results were compared. In particular, two feedforward neural families were investigated:

ANN (shallow)—single hidden layer with $h\in \{4, 8, 16, 32\}$, hidden activation poslin (ReLU-like) or tansig depending on the training algorithm; linear output (purelin).

DNN (deep)—multilayer perceptrons with hidden stacks {16, 8}, {32, 16}, {64, 32}, {128, 64}, {128, 64, 32}, hidden activation tansig for all hidden layers; linear output.

The output layer is linear to directly model $\tilde{y} (\mathrm{l}\mathrm{o}\mathrm{g} power)$. For completeness, a sequence baseline with a single-layer LSTM (32 units, “last” output mode) was also evaluated on fixed-length windows; this is reported as a reference and not as the primary approach. For the ANN model, the optimal hyperparameters were determined as a learning rate of 0.01, 500 epochs, and a single hidden layer with 8 neurons. In contrast, the best results for the DNN model were achieved with a learning rate that showed trainscg function, 300 epochs, and three hidden layers, including 128 64 32 neurons. Val MSE(Log) stands for the validation mean squared error computed in log space. It is a selection metric used to choose architectures/epochs (lower is better) and to trigger early stopping. According to this, DNN shows a better result (0.000710) (see

Table 4. The optimal hyperparameters values for proposed models.

Model	Learning Rate	Epochs	Hidden Layer Size	Val MSE(Log)
ANN	0.01	500	8	0.003054
DNN	n/a (trainscg)	300	128 64 32	0.000710

).

Figure 8 illustrates the variation of the Mean Squared Error (MSE) on a logarithmic scale across training epochs for two different optimization algorithms, trainlm (blue) and trainscg (red). At the initial epochs, both algorithms exhibit relatively high MSE values; however, the trainlm algorithm demonstrates a faster convergence rate, achieving a significant reduction in error within the first few iterations. In contrast, trainscg shows a slightly slower decrease in MSE but eventually follows a similar trend. After approximately the fifth epoch, the performance of both algorithms stabilizes, and the error values remain close to zero for the remainder of the training process. Overall, the results indicate that trainlm provides superior convergence speed and slightly better accuracy compared to trainscg in minimizing prediction errors.

To assess the performance of artificial neural networks (ANNs) and deep neural networks (DNNs) in predicting PV energy output, a number of statistical metrics are employed. These are mean squared error (MSE), root mean squared error (RMSE), mean absolute error (MAE), R squared, and mean absolute percentage error (MAPE): metrics which are given in

Table 5. Performance comparison of ANN and DNN models.

Model	MSE	RMSE	MAE	R2	MAPE
ANN	14.920	3.863	3.192	0.992	12.13%
DNN	32.621	5.712	3.118	0.982	6.92%

. These indicators give insights into how accurate, precise and generally efficient these models are. Also, performance metrics comparison between ANN and DNN are given in Figure 9.

On the test set, both models achieve high accuracy: for the ANN, MSE = 14.92 (RMSE = 3.86 W), MAE = 3.19 W, ${\mathrm{R}}^2$ = 0.992, and MAPE = 12.13%; for the DNN, MSE = 32.62 (RMSE = 5.71 W), MAE = 3.12 W, R² = 0.982, and MAPE = 6.92%. Thus, the ANN is superior on absolute and squared error metrics and explains more variance (higher ${\mathrm{R}}^2$), whereas the DNN yields notably lower relative error (MAPE) and a marginally lower MAE. Pearson correlations corroborate this pattern (ANN r = 0.9964; DNN r = 0.9914), indicating near-linear alignment with measurements, with the ANN being slightly stronger. In 5-fold cross-validation, averages are close (ANN: ${\mathrm{R}}^2$ = 0.941 ± 0.060; DNN: ${\mathrm{R}}^2$ = 0.936 ± 0.029; MAPE 6.52% ± 3.45 vs. 6.35% ± 2.49), suggesting slightly better mean performance for the ANN but lower dispersion (greater fold-to-fold consistency) for the DNN. The 95% bootstrap CIs for MAE largely overlap (ANN: [2.189, 4.264] W; DNN: [1.515, 5.283] W), and a paired t-test on absolute errors finds no significant difference (p = 0.9486). Finally, the DNN’s advantage in the validation criterion (log-space MSE: 0.000710 vs. 0.003054 for the ANN) indicates a better control of proportional errors in low-to-moderate power regions, while the ANN’s lower RMSE/MSE on the test set reflects fewer large squared deviations. Overall, the metrics show a clear trade-off: the ANN favors absolute-error accuracy, while the DNN favors relative-error accuracy.

4. Results and Discussions

Figure 10 presents a comparative analysis of the performance of artificial neural networks (ANN) and deep neural networks (DNN) in predicting power consumption. The blue line represents the actual recorded power values, serving as a benchmark for the predictive models. The dashed red lines illustrate the predictions made by the ANN and DNN models, while the green line depicts actual power output. The results show that both models generally follow the trend of the actual power consumption, with the ANN exhibiting instances of both closer approximations compared to the DNN.

A trade-off between absolute and relative accuracy was observed across architectures. Lower MSE/RMSE and higher R² (0.992) were obtained with the ANN, indicating fewer large deviations and superior variance capture on the test set. In contrast, a markedly lower MAPE (6.92%) and a slightly lower MAE were produced by the DNN, suggesting improved control of proportional errors across operating regimes. This pattern was consistent with the validation criterion in log space, for which the DNN achieved the lowest value (Val MSE(Log) = 0.000710 vs. 0.003054 for the ANN).

Upon analyzing the test set, Figure 11 displays a Pearson correlation heatmap with the axes labeled by the complete set of features: PanelTemp, Irradiance, AmbientTemp, Humidity, DeltaT, IrradianceEff, IrradianceSq, Irradiance_x_DeltaT, and the target variable Y (power) (as Figure 10). This matrix is symmetric, with a diagonal self-correlation unit; the color intensities range between –0.74 and 1.00 (the limits of the heatmap), clearly showing both negative and positive linear relationships. As is common with PV generation, the best positive associations are between Y and the derived irradiance variables (Irradiance, IrradianceEff, IrradianceSq, Irradiance_x_DeltaT). Thermal variables, PanelTemp and its difference, DeltaT, often Y’s weakest disciples, confirm the temperature-based efficiency losses. The block structure among irradiance features also indicates potential redundancy/multicollinearity with regard to features resulting from the engineering terms. This observation is useful concerning regularization decisions and follows permutation-importance analyses. The heatmap complements the known physics of PV systems by suggesting that irradiance-driven predictors are primary features for power estimation, while cautioning that closely related features may be tuned with measures like early stopping or L2 weight penalties to prevent overemphasizing the correlated features.

Also, Figure 12 presents permutation-based feature importance scores for the artificial neural network, measured as the reduction in the coefficient of determination (ΔR²) on the test set that follows the random shuffling of each predictor while leaving the others unchanged. A clear rank order becomes evident: the interaction of irradiance and temperature difference (Irradiance × ΔT) produces the steepest decline in performance, surpassing the subsequent block of predictors by more than tenfold. This is succeeded in importance by ΔT and PanelTemp, while the irradiance-related predictors (IrradianceSq, Irradiance, and IrradianceEff) occupy the next tier, and Humidity and AmbientTemp yield the smallest contributions. The predominance of the irradiance–thermal interaction is consistent with the underlying physics of photovoltaic systems, in which output power correlates with incident irradiance but is fundamentally constrained by cell temperature; the relatively weak additional gain provided by modified irradiance terms implies some degree of redundancy among these features. Collectively, the results indicate that the model’s explanatory strength is mainly rooted in combined irradiance and temperature responses, with minor further adjustments from isolated thermal and irradiance terms. Such redundancy underscores the continued utility of regularization and early stopping strategies to mitigate the risks of inflating the influence of collinear predictors.

In addition, cross-validation results indicated a similar mean performance and, in some metrics, reduced dispersion for the DNN, which may be attributed to training with trainscg and early stopping in deeper stacks. Uncertainty analyses supported these conclusions: MAE confidence intervals substantially overlapped, and the paired t-test did not reveal a significant difference in absolute errors, implying that the models could not be distinguished at conventional significance levels in terms of MAE.

Ablation experiments indicated that moderate depth and activation choice can be advantageous on this dataset, and that bootstrap-based ensembling reduces variance and outlier sensitivity, yielding incremental gains without added architectural complexity. The LSTM baseline underperformed; this was a result consistent with the predominantly pointwise predictors and the absence of explicit temporal covariates or strong long-range dependencies in the present setup. From an application perspective, selection can be guided by operational priorities: when tight absolute accuracy at higher loads is required, the ANN may be preferred; when relative performance tracking across varying regimes is critical, the DNN’s lower MAPE is advantageous. Future work is encouraged to investigate heteroscedastic or cost-sensitive objectives that jointly balance absolute and relative errors, uncertainty quantification for risk-aware operation, domain adaptation across seasons and sites, and lightweight physics-guided constraints to further stabilize extrapolation while retaining the observed data-driven gains. Furthermore, the use of advanced optimization techniques such as the Adam optimizer shows that these models can be used even more efficiently. Furthermore, according to the results of this research, hyperparameter tuning has been identified as a highly influential factor in the performance of NN models regarding photovoltaic energy (PVE) prediction. This is consistent with other studies in the broader literature, where hyperparameter optimization is considered an important element in improving machine learning performance. Thus, our work and others demonstrate how neural network models can be combined with advanced optimization methods and preprocessing techniques to improve the predictions they make.

5. Conclusions

This study emphasizes the importance of hyperparameter optimization using grid search methods in improving the accuracy of photovoltaic (PV) energy output predictions using artificial neural networks (ANN) and deep neural networks (DNN). Nonetheless, hyperparameter adjustment emerged as the principal determinant of performance and robustness. Decisions around model complexity (depth/width), activation function selection (tansig vs. poslin), optimizers (trainscg vs.), regularization, and early stopping based on validation split and max_fail, the training horizon defined by epochs, and the validation objective based on log-space MSE aligned to proportional error, led to material changes, and at times, a preference between shallow ANN and deeper DNN. In our case, the tuned DNNs exhibited the strongest validation loss, which was interpreted as improved control of relative errors, and a well-configured ANN was better on absolute and squared error for the held-out test set. Both findings were aligned with the metric used for the selection. These findings highlight the notion that performance is less predetermined by an architecture and more a result of tuning; in this case, suboptimal parameters led to unstable DNN behavior, but tuning the activation and optimizer pairing with early stopping, metric-consistent selection improved the performance and stability of generalization.