ABSTRACT This study introduces a hybrid analytical–machine learning framework for solving the Schrödinger equation with complex potentials. The semi‐inverse variational method is first used to generate highly accurate eigenfunctions and eigenenergies for both 1D radial potentials (Yukawa and Cornell) and a 2D coupled anharmonic oscillator. Based on these rigorous, physics‐consistent results, we train supervised machine learning models; including Random Forest and Neural Network regressors; to predict energy eigenvalues across wide parameter ranges. Both models achieve near‐perfect predictive accuracy (R2 > 0.999) with errors of only a few millielectronvolts, while preserving fundamental quantum‐mechanical trends. Feature importance analysis confirms that the quantum number n and potential strength parameters dominate the energy scaling, in agreement with theoretical expectations. By integrating variational physics with data‐driven emulation, this hybrid framework reduces computational cost by orders of magnitude; enabling rapid, high‐throughput exploration of quantum systems across dimensions. The approach not only accelerates parameter screening but also serves as a discovery tool, uncovering emergent scaling laws and critical confinement behavior in mixed potentials. This synergy between analytical rigor and machine learning efficiency opens new pathways for quantum simulation, materials design, and the discovery of novel quantum phenomena.
Accurate fault diagnosis in photovoltaic (PV) systems is essential for ensuring reliable energy generation and system stability. This study presents a novel, lightweight fault diagnosis framework optimized for edge device deployment. The core innovation lies in a newly developed Adaptive Channel-wise (ACW) representation technique that automatically selects the most discriminative 2D transformation for each individual signal channel, addressing the limitations of fixed transformation methods such as Continuous Wavelet Transform (CWT), Gramian Angular Field (GAF), Markov Transition Field (MTF), and Hilbert-Huang Transform (HHT). Feature extraction is performed using pretrained backbones originally trained on large-scale image datasets. The ACW method is comprehensively benchmarked across multiple deep learning backbones including VGG16, InceptionV3, ResNet50, DenseNet121, NASNetMobile, and MobileNetV1. To the best of our knowledge, this is the first PV fault diagnosis framework to use automatic channel-wise selection of 2D transformations, bench-marked extensively on multiple deep learning backbones and validated for robust practical edge deployment. Experimental results on multi-class PV fault scenarios demonstrate high classification accuracy of 99.40% with extremely fast inference time (133 mu s). The proposed framework exhibits robustness under challenging real-world conditions such as noisy signals, sensor drop scenarios, and unbalanced fault distributions. These enhancements make the method particularly suitable for resource-constrained edge devices. While promising, some limitations remain, revealing directions for future research and practical adoption.
Accurate detection of cardiac arrhythmias from electrocardiograms remains challenging for rare rhythm classes due to class imbalance and morphological variability. We present a hybrid deep learning framework combining per-lead convolutional encoders with a cross-lead transformer that models relationships across different lead signals through self-attention, accepting variable lead configurations. To address minority-class scarcity, a generative adversarial network synthesizes physiologically plausible beat segments for underrepresented arrhythmias. Attention-based visualizations localize influential waveform regions aligned with clinically meaningful structures. Post-training pruning and INT8 quantization enable efficient deployment with minimal performance loss. Extensive experiments on the MIT-BIH Arrhythmia Database across sixteen heartbeat classes from two-lead recordings yield exceptional results over ten independent runs: accuracy of 99.67%, F1-score of 99.66%, and AUC of 99.8%. External validation on the ECG5000 single-lead dataset and the St Petersburg INCART twelve-lead dataset confirms robust generalizability with F1-scores of 97.6% and 98% respectively. Our framework delivers accurate, interpretable, stable, and deployable arrhythmia detection across diverse clinical settings.
An initial value problem involving mixed (ordinary and fractional) derivatives for non-autonomous variable-order differential equations is presented. We investigate the existence and uniqueness of solutions, as well as their Ulam-Hyers stability. Finally, we illustrate our results through numerical examples.
Accurate short-term forecasting of solar photovoltaic (PV) power is essential for grid stability and renewable energy integration, but remains challenging due to the inherent variability and intermittency of solar generation. This paper introduces a hybrid model that combines a Convolutional Neural Network (CNN) with a Bidirectional Long Short-Term Memory (biLSTM) network to address this challenge. The proposed CNN-biLSTM model is evaluated against four benchmark models, including Multilayer Perceptron (MLP), Support Vector Regression (SVR), Random Forest (RF), and a unidirectional CNN-LSTM, using historical meteorological and PV power data. Performance is assessed through a comprehensive suite of statistical metrics (R2, RMSE, MAE, MAPE, sMAPE, and normalised RMSE). The results demonstrate that the CNN-biLSTM achieves superior accuracy, with the highest coefficient of determination (R2=0.99848) and the lowest error metrics (RMSE=0.5939 W, MAE=0.398 W, and nRMSErange=1.18 %), significantly outperforming all benchmarks. The bidirectional architecture uniquely captures temporal dependencies in both forward and backward directions, enabling more effective modeling of nonlinear solar fluctuations. This work establishes the CNN-biLSTM as a robust and reliable solution for realworld solar energy management systems, enhancing forecasting precision and supporting the stable integration of renewable energy into smart grids.
