The intrinsic structural stability of ABO₃ perovskite materials is a pivotal factor determining their efficiency and durability in photovoltaic applications. However, accurately predicting stability, commonly measured by the energy above hull metric, remains challenging due to the complex interplay of compositional, crystallographic, and electronic features. To address this challenge, we propose a streamlined hybrid machine learning framework that combines the sequence modeling capability of Long Short-Term Memory (LSTM) networks with the robustness of Random Forest regressors. A genetic algorithm-based feature selection strategy is incorporated to identify the most relevant descriptors and reduce noise, thereby enhancing both predictive accuracy and interpretability. Comprehensive evaluations on a curated ABO₃ dataset demonstrate strong performance, achieving an $R^2$ of 0.98 on training data and 0.83 on independent test data, with a Mean Absolute Error (MAE) of 8.78 for training and 21.23 for testing, and Root Mean Squared Error (RMSE) values that further confirm predictive reliability. These results validate the effectiveness of the proposed approach in capturing the multifactorial nature of perovskite stability while ensuring robust generalization. This study highlights a practical and reliable pathway for accelerating the discovery and optimization of stable perovskite materials, contributing to the development of more durable next-generation solar technologies.

The nonhomogeneous Monge–Ampère equation, read as $w_{xx}{w}_{yy}-w_{xy}^2+h\left(w\right)=0$, is a nonlinear equation involving mixed second derivatives with respect to the spatial variables x and y, along with an additional source function $h\left(w\right)$. This equation is observed in several fields, including differential geometry, fluid dynamics, and magnetohydrodynamics. In this study, the Lie symmetry method is used to obtain a detailed classification of this equation. Symmetry analysis leads to a comprehensive classification of the equation, resulting in specific forms of the smooth source function $h\left(w\right)$. Furthermore, the one-dimensional optimal system of the associated Lie algebras is derived, allowing for symmetry reductions that yield several exact invariant solutions of the Monge–Ampère equation. In addition, conservation laws are constructed using the Noether approach, a highly effective and widely used method for deriving conserved quantities. These conservation laws can help evaluate the accuracy and reliability of numerical methods.

This paper examines the nonlinear behavior of the generalized stochastic intermediate dispersive velocity (SIdV) equation, which has been widely analyzed in a non-noise deterministic framework but has yet to be studied in any depth in the presence of varying forcing strength and noise types, in particular how it switches between periodic, quasi-periodic, and chaotic regimes. A stochastic wave transformation reduces the equation to simpler ordinary differential equations to make soliton overlap analysis feasible to analyze soliton robustness under deterministic and stochastic conditions. Lyapunov exponents, power spectra, recurrence quantification, correlation dimension, entropy measures, return maps, and basin stability are then used to measure the effect of white, Brownian, and colored noise on attractor formation, system stability, and spectral correlations. Order–chaos transitions as well as noise-induced complexity are more effectively described by bifurcation diagrams and by Lyapunov spectra. The results of this experiment improve the theoretical knowledge of stochastic nonlinear waves and offer information that will be useful in the fields of control engineering, energy harvesting, optical communications, and signal processing applications.