Fresh water is absolutely essential for human societies since they rely on it for development and survival (Zheng, 2017). Around 71% of the earth is covered with water; however, about 96.5% of this water is in the brackish form or saline, which means that it cannot be directly used for irrigation and drinking, and just less than 1% of fresh water resources are within human reach (Tiwari et al., 2003; Chauhan et al., 2021). Regarding the uneven distribution of fresh water in different regions of the world, the increase in demand due to population growth, and the essence of water for human survival and activities, desalination has gained more importance in recent years. Desalination is known as a treatment process of water that includes salt removal from saline water to make it appropriate for drinking (Mito et al., 2019). Desalination of water with the salinity more than normal levels is one of the ways (Tzen and Morris, 2003), and probably the most applicable one, to overcome the mentioned problems related to the unavailability of fresh water. The nature of the desalination process is energy-consuming, and it is crucial to properly supply the required energy. Improving the efficiency of the systems and utilizing the renewable energy sources are recommended to solve the problems related to the energy demand of desalination systems. Renewable energy sources can be used for desalination in direct and indirect ways. In direct approaches, thermal energy is mainly used for water evaporation and reducing the salinity of water, while renewable energies can be used for indirect desalination by producing electricity and applying the power in reverse osmosis (RO) technologies (Caldera et al., 2016). Among the renewable energy sources, solar energy is attractive for the desalination purpose since it can be used in different ways such as thermal technologies or photovoltaic/RO systems.

Numerous studies have been performed on the various kinds of solar-based desalination systems to find the influential factors and improve their performance (Mostafa et al., 2020). Depending on the type of solar desalination, the factors affecting the performance can be differed. Solar radiation is one of the most important factors on the output of the systems. For instance, Joseph et al. (2005) found that by increasing the solar radiation from 400 W/m² to 900 W/m², the efficiency of a single-stage solar desalination system increased from 15 to 26%. In addition to solar radiation, the components of the system and their configuration affect the performance of these systems. As an example, Altarawneh et al. (2020) investigated the performance of a solar still composed of two parabolic troughs and two rectangular absorbers under different working conditions. They found that the rim angle of the troughs can influence the productivity of the desalination. Moreover, it was observed that reducing the pressure could remarkably improve the productivity of the desalination system. In another work, Geng et al. (2021) investigated the performance of an RO system powered by a solar dish Stirling engine. They found that by an increment in the temperature of the absorber, productivity of water increased, while there was an optimum temperature at which the exergy efficiency of the system reached its maximum value. In addition to the technical aspects, solar desalinations have been investigated from the economic point of view. For instance, Kettani and Bandelier (2020) carried out techno-economic assessment on large-scale solar powered desalination systems in Morocco by considering photovoltaics (PVs) and concentrated solar power (CSP) for supplying energy. They found that using the PV/RO system without a storage unit is the cheapest configuration today and by 2030. In another work (Zheng and Hatzell, 2020), solar thermal desalination was thermo-economically analyzed, and it was found that construction costs of solar collectors were the largest total investments of the system. Other types of desalination systems have been modeled by using data-driven methods. For instance, Faegh et al. (Faegh et al., 2021) applied different artificial neural network (ANN)-based methods to model the gain output ratio and heat transfer rate of the evaporator and evaporative condenser of a heat pump-assisted desalination system and found that the R-squared of the models were more than 0.91 for all the outputs.

As mentioned in the previous paragraph, the performance of desalination units is affected by several elements such as the applied technology, operating conditions, and the properties of the saline or brackish water. Since the experimental works are costly and time-consuming, it would be useful to propose models for performance prediction and assessment of the desalination systems. Data-driven methods, with outstanding ability in modeling of complex systems, would be attractive options for performance forecasting of desalination systems (Gao et al., 2007; Chauhan et al., 2020; Adda et al., 2021). These methods have shown their outstanding performance in a wide variety of applications such as predicting the properties of materials (Ramezanizadeh et al., 2019a; Ramezanizadeh et al., 2019b), fault diagnosis (Venkatasubramanian and Chan, 1989), etc. (Rezaei et al., 2018). Current works focus on providing a comprehensive review on the applications of data-driven methods in modeling the performance of various solar desalination systems, which is performed for the first time. In addition, a table is prepared that summarizes the main findings of the reviewed works, inputs of the proposed models, applied approaches, and algorithms, which will be useful for the scholars working on the similar fields of study. Finally, according to the knowledge of the authors and the investigation of the previous studies, some suggestions are recommended for future works in the relevant subjects. The findings and information represented in this study will facilitate upcoming works to concentrate on the modeling of desalinations systems, especially the ones using solar energy.

There are different data-driven methods used in modeling of energy systems. The mostly used approaches in energy system modeling are multilayer perceptron (MLP) ANN, adaptive neuro-fuzzy inference system (ANFIS), radial basis function (RBF), and support vector machines (SVMs). In this regard, these approaches are briefly described in the following subsections.

There are three main principle approaches used for desalination, which are thermal, pressure, and electrical. Thermal distillation can be considered as the oldest approach in which water with high salinity is boiled and the generated steam is collected. The condensed form of the collected steam can now be used as fresh water. In the electrical approach, electrical current is applied to separate the salt and water. In these types of desalination units, a permeable membrane is used, in which ions move across it by use of electric current as a driving force. In the RO type of desalination, pressure acts as a driver for moving water through a selectively permeable membrane, leaving the salt behind (Parise, 2011). The majority of the desalination market belongs to thermal and RO types. Although the majority of the installed capacity of desalination systems is of the RO type, there are some benefits in thermal desalinations. For instance, the waste heat of plants can be used for the thermal desalination units, which leads to a high overall efficiency of the system. The majority of the studies performed on the applications of data-driven methods in solar desalination systems have focused on thermal types (Elsheikh et al., 2021). For instance, Zarei and Behyad. (2019) employed ANN to model the output of a humidification–dehumidification-type solar desalination used for humidifying the interior space of the greenhouse and supplying fresh water. The inputs of the model were width and length of the seawater greenhouse, front evaporator height, and the roof transparency, and the output was water yield of the system. Their different structures with one and two hidden layers were examined. They observed that applying one hidden layer with nine neurons led to the highest exactness with R² of 0.997. In addition to the architecture of the model, the applied functions and optimization methods could affect the outputs of the models proposed for solar desalinations. For instance, Nazari et al. (2020) compared the performance of ANN with and without the imperialist competition algorithm (ICA) optimization method in forecasting energy and exergy efficiencies and productivity of single-slope solar stills. They noticed that using the optimization method led to significant reduction in mean absolute errors of the model in predicting the mentioned outputs by up to 54.3% for water productivity. In another work (Mashaly and Alazba, 2017a), the output of an inclined passive solar still fed by agricultural drainage water was modeled by applying ANN with different architectures and multiple linear regression (MLR). The inputs for the modeling of the instantaneous thermal efficiency were relative humidity, ambient temperature, solar radiation, wind speed, feed temperature and its total dissolved solids, and feed mass flow rate. They found that ANN outperforms MLR and the best structure was in the case of using six neurons in the hidden layer. In addition to differing numbers of neurons in the hidden layer, it would be useful in terms of exactness enhancement by changing the number of hidden layers (Ramezanizadeh et al., 2019b); however, it must be considered that an increase in the number of hidden layers may lead to overfitting.

The applied method and algorithm are among the most important factors that influence the exactness of the data-driven methods in forecasting the outputs of solar stills (Mashaly and Alazba, 2015; Mashaly and Alazba, 2017b; Mashaly and Alazba, 2018a; Mashaly and Alazba, 2018b; Mashaly and Alazba, 2019a). For instance, Wang et al. (2021) used random forest (RF), ANN, and multilinear regression to forecast the productivity of the system based on time, solar radiation intensity, wind speed, temperatures of feed water, basin plates, salt water, cover, and ambient temperature. They found that using RF led to the prediction with the least error compared with others. In order to reach further exactness, the Bayesian optimization algorithm was applied to search the most appropriate hyperparameters which led to significant enhancement in the accuracy of the ANN-based model by increasing the determination coefficient from 0.7098 to 0.9614. In another study (Essa et al., 2020), the performance of ANN with the Harris Hawk optimizer was compared with the traditional ANN and SVM in predicting the productivity of an active solar still. In their models, ambient temperature, time, speed of wind, solar irradiance, and velocity of vapor were considered as inputs. They found that ANN outperformed SVM and could be further enhanced by using the optimizer. In their work, the R-squared values of the model for ANN and SVM were 0.9703 and 0.9701, respectively, while this value for the ANN-based model coupled with the optimizer reached 0.9834. Improved accuracy of the models through the coupling optimizer can be attributed to better adjustment of the parameters affecting the performance of the modeling approach. In another work, performance of ANFIS, ANN, and Multiple Regression (MR) in forecasting the performance of an inclined passive solar still was compared. In all the proposed models, solar radiation, relative humidity, feed flow rate, and total dissolved solids of brine and feed were used as inputs. The utilized function in the structure of data-driven methods is another influential factor. As an example, Mashaly and Alazba (2017c) tested different membership functions including triangle, trapezoid, Pi curve, and difference between two sigmoidal functions in ANFIS-based models to propose a model with the highest exactness. In their models, inputs were dissolved solids of the feed and brine, feed flow rate, relative humidity, and solar radiation. They found that the Pi curve and triangle membership functions can provide outputs with higher accuracy compared with the others. In cases of using these methods, the correlation coefficient of the regression for training data sets was around 0.999. The most proper function in the structure of networks for modeling can be dependent on the physics of the problem which can be obtained by testing different types of functions.

In modeling the system with data-driven methods, it is essential to consider all the effective elements as inputs. In this regard, some models have included more inputs to reach better accuracy or improved the comprehensiveness. As an example, Abujazar et al. (2018) used wider variables such as cloud cover, day and month numbers, number of hours per day, difference between the temperatures of inner and outer surfaces of glass in addition to the factors used in the majority of the studies such as ambient temperature, solar radiation, humidity, wind speed, and temperatures of water, basins, and vapor to forecast productivity of an inclined stepper solar still. In their work, cascaded forward ANN with different numbers of neurons and a linear model and regression were used. They found that the ANN model was more reliable in predicting the productivity of the system. The values of root-mean-squared error (RMSE) for regression, the linear model, and the ANN-based model were 50.21, 80.36, and 41.01, respectively. Despite more comprehensiveness of this model compared with previously mentioned ones, it can be further improved by considering other factors such as the specifications of the system such as the dimensions of different parts and properties of the materials affecting the performance of the systems.

Solar desalination can be integrated with other components to reach higher productivity. Data-driven methods are applicable for performance forecasting of these systems (Bagheri et al., 2020). As an example, Bagheri et al. (2021) used ANN to model a solar desalination system composed of PVs, a heater, a battery, a cylindrical parabolic collector, etc. The panel was applied to supply the power of the heater used in the tank that was employed for preheating the saline water prior to its entrance to the collector. In the collector, saline water was further heated before entering the still. The schematic of the system is shown in Figure 4. By testing different architectures of the network and by varying the number of neurons in the hidden layer, they found that the highest accuracy of the model was obtained in the case of using 24 neurons with an R² of 0.993. These methods can be developed for other hybrid systems such as solar/wind RO desalination technologies in the near future; however, more inputs such as wind speed and other factors affecting the systems must be considered. Since the inputs of the systems are increased for hybrid technologies, the modeling process would be more complicated.

Data-driven methods are employable for modeling the dynamic performance of solar desalination systems. In a study carried out by Sohani et al. (2021), different ANNs including backpropagation (BP), feedforward (FF), and RBF were used to estimate water temperature and hourly water production of a solar still with enhanced design. The inputs of their models were wind speed, ambient temperature, received radiation from the Sun, and water depth in the basin. Comparison of the estimated data and the corresponding actual vales revealed that RBF and FF were the most powerful approaches in predicting water temperature and hourly water production, respectively. Despite its novel idea in dynamic modeling of a solar desalination, the comprehensiveness of their model was limited and could be further enhanced by considering other inputs such as wind speed and feed temperature.

Utilizing nanofluids in solar stills can improve their performance. Intelligent methods can be applied for accurate evaluation of these solar stills. Kandeal et al. (2021) tested various data-driven methods including ANN, Support Vector Regression (SVR), linear SVR, and RF to model the performance of a double-slope solar still utilizing the carbon black nanofluid in 1.5% wt concentration. The inputs of the proposed model were air ambient temperature, solar radiation, wind speed, vapor temperature, basin temperature, and temperatures at the glass inlet and outlet. The models were coupled with the Bayesian optimization algorithm to tune the approaches and obtain the outputs with the highest accuracy. They found that all the proposed models were able to predict the performance of the system with relatively high exactness; however, utilizing RF led to the highest accuracy. The performance of the nanofluidic solar desalination system integrated with other modules can be modeled by data-driven methods. For instance, Bahiraei et al. (2020) used ANN coupled with the genetic algorithm (GA) and Imperialist Competition Method (ICM) to model the performance of a nanofluidic solar still integrated with a thermoelectric module. The inputs of their model were time, solar radiation, ambient temperature, power of the applied fan, concentration of the nanofluid, and temperatures of water, glass, and basins, while the output of the proposed models was water productivity. They observed that the exactness of the model through coupling the mentioned optimization approaches significantly improved, while using ICM was more influential in terms of accuracy enhancement. In addition to the optimization method, the algorithm used for modeling affects the exactness of the predicted values of nanofluidic solar desalinations. For instance, Bahiraei et al. (2021) used Particle Swarm Optimization (PSO)-ANFIS and PSO-ANN for modeling the performance of a solar still with Cu₂O nanoparticles. The inputs of the models were similar to those of the previous work, while the output of the designed model was efficiency of the system. They found that in both types of models, coupling the optimization methods led to exactness enhancement; however, the maximum accuracy in modeling was observed in the case of using PSO-ANFIS with an R² of 0.9884. In another work (Mashaly and Alazba, 2016), the performance of MLR and MLP ANN was compared in predicting the instantaneous thermal efficiency of a solar still. They found that using MLP ANN provided a model with higher exactness compared with MLR. Higher exactness of MLP ANN can be attributed to its more complex structure, which enables it to model the complicated systems with better performance.

The outputs of the ANN-based model can be used for designing an optimal condition for the performance of the desalination systems (Azad et al., 2021). As an example, in a study carried out by Porrazzo et al. (2013), an ANN-based optimizing control system was utilized for a solar-powered membrane desalination module. ANN was used for performance prediction of the system under different operating conditions by considering radiation and the rate of feed flow inlet temperature of cold channel as the inputs. Afterward, a control system was implemented to optimize the distillate production of the system. The proposed system allowed to set the feed flow rate at the optimal values in order to reach continuous maximum production of the distillate. As another example, Maleki et al. (2016) applied ANN to forecast the weather condition and optimize a hybrid system, solar-wind-powered RO desalination. By using the outputs of the network and performing optimization, the optimum design of the system was obtained.

To sum up the findings of the study, it can be declared that the accuracy of the models is under the influence of the applied method, optimization algorithm, etc. Generally, intelligent methods such as ANNs are preferred in terms of accuracy due to their more complex structures which enable them to model complicated systems with higher accuracy. In addition, it is found that applying optimization algorithms and coupling them with the intelligent methods improve the accuracy since the parameters affecting the exactness are used in their optimum values. In addition to the abovementioned factors, the considered inputs influence the exactness. Considering more influential factors as the inputs will provide more accurate models (Ahmadi et al., 2018). The other factors that may cause the differences in the model can be attributed to the noise of data, which is inevitable in experimental data used for modeling. In Table 1, the important outcomes of the studies in the topic of this article are provided.

Despite the fact that there are several works on utilization of data-driven methods in performance prediction of solar desalination systems, there are some limitations in modeling the outputs of solar desalination systems. For instance, it is difficult to propose comprehensive models with applicability for different types of solar-assisted desalination systems. For this purpose, the type of desalination must be defined as a meaningful variable. In addition, different working conditions may affect the performance of the systems, which must be distinguished and considered in inputs of the models. Furthermore, since the experimental data are used for modeling, it may cause some problems due to different accuracies of measuring systems. Despite the mentioned problems and limitations, there are some recommendations that can improve the upcoming studies. First of all, the majority of the works are on thermal desalination modules, while these methods can be developed for the solar-powered RO systems and other desalination systems powered by solar-based hybrid systems such as solar/geothermal or solar/wind. In addition, most of the proposed models are applicable for just one type of solar desalination, while their comprehensiveness can be improved by considering more inputs. For instance, using the dimensions of desalination systems is one of the ways that can be used to extend the application of the models. Furthermore, in the case of nanofluidic solar desalination, using the properties of nanofluids such as their concentration and properties of particles can lead to proposing a model with a higher level of applicability. Another point that must be considered in the future works is utilizing more recent optimization approaches to reach higher exactness. In this regard, hybrid optimization algorithms would be attractive options. Furthermore, it would be useful to use data-driven methods for other purposes such as modeling systems from economic and environmental points of view. In addition, the majority of the studies have focused on water productivity as the output of the model, while it would be useful and beneficial to model other technical criteria such as energy and exergy efficiency of the systems. Finally, it is suggested to compare different approaches in terms of the required time for the training process.

In the provided article, applications of data-driven methods in solar desalination system modeling are provided. Different variables have been used as the inputs in the models proposed for solar desalination systems including solar radiation, ambient conditions, etc. The main findings of this review article are as follows:

• Compared with the correlation, intelligent methods can model the solar desalination systems more accurately.