Evaporation is a very important process; it is one of the most critical factors in agricultural, hydrological, and meteorological studies. Due to the interactions of multiple climatic factors, evaporation is considered as a complex and nonlinear phenomenon to model. Thus, machine learning methods have gained popularity in this realm. In the present study, four machine learning methods of Gaussian Process Regression (GPR), K-Nearest Neighbors (KNN), Random Forest (RF) and Support Vector Regression (SVR) were used to predict the pan evaporation (PE). Meteorological data including PE, temperature (T), relative humidity (RH), wind speed (W), and sunny hours (S) collected from 2011 through 2017. The accuracy of the studied methods was determined using the statistical indices of Root Mean Squared Error (RMSE), correlation coefficient (R) and Mean Absolute Error (MAE). Furthermore, the Taylor charts utilized for evaluating the accuracy of the mentioned models. The results of this study showed that at Gonbad-e Kavus, Gorgan and Bandar Torkman stations, GPR with RMSE of 1.521 mm/day, 1.244 mm/day, and 1.254 mm/day, KNN with RMSE of 1.991 mm/day, 1.775 mm/day, and 1.577 mm/day, RF with RMSE of 1.614 mm/day, 1.337 mm/day, and 1.316 mm/day, and SVR with RMSE of 1.55 mm/day, 1.262 mm/day, and 1.275 mm/day had more appropriate performances in estimating PE values. It was found that GPR for Gonbad-e Kavus Station with input parameters of T, W and S and GPR for Gorgan and Bandar Torkmen stations with input parameters of T, RH, W and S had the most accurate predictions and were proposed for precise estimation of PE. The findings of the current study indicated that the PE values may be accurately estimated with few easily measured meteorological parameters.

The traditional educational system, in certain aspects, limits personalized learning. This is mainly evident in the fact that average students, who do not have any learning difficulties, are required to solve the same tasks from the same textbook in the same order. Artificial intelligence and other smart learning tools present great opportunities for implementing a personalized learning system. Our previous surveys and literature reviews also show that educators see the greatest potential in personalized education for the assimilation of artificial intelligence into education. In this context, we have developed educational software called “Learn with M.E. as Math Educator”, which facilitates more personalized teaching of basic mathematical operations. This study presents the structure and operation of this application. We tested the usability of the software in several institutions. Our research target group consists of elementary school students, specifically those aged 11–15. This article provides a detailed overview of the accuracy and educational outcomes of the completed application. We evaluated the application and its effectiveness using both qualitative and quantitative methods. Our research design combined elements of educational technology development and effectiveness assessment. To evaluate student performance, we employed a control group methodology. Data were analyzed by comparing test results between students using the software and those receiving traditional instruction. We examined user satisfaction through survey questionnaires. Teachers’ opinions were gathered through structured interviews, and their responses were categorized using a SWOT analysis. The findings indicated that the use of the software significantly improved students’ mathematics performance compared to the control group. Students provided positive feedback on the software’s user interface, describing it as user-friendly and motivating. Teachers regarded the software as an effective educational tool, facilitating differentiated instruction and enhancing student engagement. The results suggest that digital educational tools, such as the developed software, can provide substantial added value in education.

In this paper, a neural network-based optimal control synthesis is presented for distributed optimal control problems. We deal with solutions of systems controlled by parabolic differential equations with control and state constraints and discrete time delays. The given optimal control problem is transformed into a discrete nonlinear problem and then implemented into a feed-forward adaptive critic neural network. We propose a new algorithm to reach optimal control and an optimal trajectory using a feed-forward neural network. We present a concrete application of this simulation method on the SEIR (Susceptible—Exposed—Infectious—Recovered) optimal control problem of a distributed system for disease control. The results show that the adaptive-critic-based neural network approach is suitable for the solution of optimal distributed control problems with delay in state and control variables subject to control-state constraints and simulates the spread of disease in the SEIR system.

In recent years, hybrid systems combining data-driven and physics-based approaches have gained increasing attention for solving complex real-world problems where deterministic modeling alone is insufficient. Within this framework, Physics-Informed Neural Networks and related hybrid models have been successfully applied across physics, engineering, and biological systems to improve predictive accuracy under uncertainty. However, their stability and sensitivity to noise and model misspecification remain open questions. This study investigates a hybrid Lotka–Volterra population dynamics model augmented with a neural correction term, aiming to analyze how the strength of the neural contribution, controlled by the coupling parameter $\lambda$ ($0\le \lambda \le 1$), affects model performance under noisy and distorted conditions. Here, $\lambda =0$ corresponds to the purely physical Lotka–Volterra system, whereas $\lambda =1$ represents the fully neural-corrected model. Three experimental setups were implemented: (1) evaluation on noisy data, (2) analysis of the $\lambda$ sensitivity and its stabilizing effect, and (3) compensation of parameter distortion through neural adaptation. The results indicate that, in the absence of parameter-induced distortions, relying solely on noisy data, moderate neural correction provides the most accurate and stable model behavior, whereas excessive neural influence may distort the original system dynamics. Conversely, when the underlying Lotka–Volterra model incorporates biased parameters, neural correction with a higher $\lambda$ effectively compensates for structural inaccuracies, enhancing predictive robustness.