The need for accurate solar energy forecasting is paramount as the global push towards renewable energy intensifies. We aimed to provide a comprehensive analysis of the latest advancements in solar energy forecasting, focusing on Machine Learning (ML) and Deep Learning (DL) techniques. The novelty of this review lies in its detailed examination of ML and DL models, highlighting their ability to handle complex and nonlinear patterns in Solar Irradiance (SI) data. We systematically explored the evolution from traditional empirical, including machine learning (ML), and physical approaches to these advanced models, and delved into their real-world applications, discussing economic and policy implications. Additionally, we covered a variety of forecasting models, including empirical, image-based, statistical, ML, DL, foundation, and hybrid models. Our analysis revealed that ML and DL models significantly enhance forecasting accuracy, operational efficiency, and grid reliability, contributing to economic benefits and supporting sustainable energy policies. By addressing challenges related to data quality and model interpretability, this review underscores the importance of continuous innovation in solar forecasting techniques to fully realize their potential. The findings suggest that integrating these advanced models with traditional approaches offers the most promising path forward for improving solar energy forecasting.

In 2009, T. Mansour, M. Schork, introduce the concept of bridge graphs. A bridge graph B(G₁, G₂, … , G_m ) = B(G₁, G₂, … , G_m; v₁, v₂, … , v_m) of with respect to the vertices is the graph obtained from the graphs G₁; G₂; … ; G_m by connecting the vertices v_i and v_i+1 by an edge for all I = 1; 2; … ; m-1. In this paper, we determine hyper-Zagreb index, first multiple Zagreb index, second multiple Zagreb index, Zagreb polynomials and M-polynomial for nano structures of bridge graphs.

Solar energy (SE) is vital for renewable energy generation, but its natural fluctuations present difficulties in maintaining grid stability and planning. Accurate forecasting of solar irradiance (SI) is essential to address these challenges. The current research presents an innovative forecasting approach named as Transformer-Infused Recurrent Neural Network (TIR) model. This model integrates a Bi-Directional Long Short-Term Memory (BiLSTM) network for encoding and a Gated Recurrent Unit (GRU) network for decoding, incorporating attention mechanisms and positional encoding. This model is proposed to enhance SI forecasting accuracy by effectively utilizing meteorological weather data, handling overfitting, and managing data outliers and data complexity. To evaluate the model’s performance, a comprehensive comparative analysis is conducted, involving five algorithms: Artificial Neural Network (ANN), BiLSTM, GRU, hybrid BiLSTM-GRU, and Transformer models. The findings indicate that employing the TIR model leads to superior accuracy in the analyzed area, achieving R² value of 0.9983, RMSE of 0.0140, and MAE of 0.0092. This performance surpasses those of the alternative models studied. The integration of BiLSTM and GRU algorithms with the attention mechanism and positional encoding has been optimized to enhance the forecasting of SI. This approach mitigates computational dependencies and minimizes the error terms within the model.

In the evolving field of solar energy, precise forecasting of Solar Irradiance (SI) stands as a pivotal challenge for the optimization of photovoltaic (PV) systems. Addressing the inadequacies in current forecasting techniques, we introduced advanced machine learning models, namely the Rectified Linear Unit Activation with Adaptive Moment Estimation Neural Network (RELAD-ANN) and the Linear Support Vector Machine with Individual Parameter Features (LSIPF). These models broke new ground by striking an unprecedented balance between computational efficiency and predictive accuracy, specifically engineered to overcome common pitfalls such as overfitting and data inconsistency. The RELAD-ANN model, with its multi-layer architecture, sets a new standard in detecting the nuanced dynamics between SI and meteorological variables. By integrating sophisticated regression methods like Support Vector Regression (SVR) and Lightweight Gradient Boosting Machines (Light GBM), our results illuminated the intricate relationship between SI and its influencing factors, marking a novel contribution to the domain of solar energy forecasting. With an R² of 0.935, MAE of 8.20, and MAPE of 3.48%, the model outshone other models, signifying its potential for accurate and reliable SI forecasting, when compared with existing models like Multi-Layer Perceptron, Long Short-Term Memory (LSTM), Multilayer-LSTM, Gated Recurrent Unit, and 1-dimensional Convolutional Neural Network, while the LSIPF model showed limitations in its predictive ability. Light GBM emerged as a robust approach in evaluating environmental influences on SI, outperforming the SVR model. Our findings contributed significantly to the optimization of solar energy systems and could be applied globally, offering a promising direction for renewable energy management and real-time forecasting.

A variety of dendrimers exist, and each has biological properties such as polyvalency, selfassembling, electrostatic interactions, chemical stability, low cytotoxicity, and solubility. These varied characteristics make dendrimers a good choice in the medical field and pharmaceuticals. A topological index is actually designed by transforming a molecular structure into a numeric number. These topological indices correlate certain physicochemical properties like boiling point, stability, strain energy etc of chemical compounds. It is reported that these indices are useful in the study of anti-in ammatory activities, anticancer therapies and diagnostic imaging of certain chemical networks. In this paper, we determine hyper Zagreb index, first multiple Zagreb index, Second multiple Zagreb index, Zagreb polynomials for nanostar dendrimers, Benzenoid and phenylenes.