Physics-Informed Neural Networks for Real-Time Gas Crossover Prediction in PEM Electrolyzers: First Application with Multi-Membrane Validation

This study presents and validates the predictive capabilities of Physics-Informed Neural Networks (PINNs) for analyzing various engineering and biological dynamical systems governed by ordinary differential equations (ODEs). Traditional numerical methods often face challenges in achieving convergence for complex problems, whereas PINNs provide a robust alternative. The research systematically evaluates the accuracy and efficiency of the PINNs framework using classical ODE problems as test cases, demonstrating its potential to embed physical laws into the learning process.

A new framework for solving nonlinear partial differential equations (PDEs) has been proposed, integrating perturbation theory with one-shot transfer learning in Physics-Informed Neural Networks (PINNs). This method decomposes nonlinear PDEs into linear subproblems, which are solved using a Multi-Head PINN. The approach allows for quick adaptation to new PDE instances with varying conditions, achieving errors around 1e-3 and adaptation times under 0.2 seconds, demonstrating comparable accuracy to classical solvers.

Neuro-Spectral Architectures (NeuSA) have been introduced as a new class of Physics-Informed Neural Networks (PINNs) aimed at solving complex partial differential equations (PDEs). Traditional MLP-based PINNs often struggle with convergence in intricate initial value problems, leading to solutions that can violate causality. NeuSA addresses these challenges by learning a projection of the underlying PDE onto a spectral basis, thus improving convergence and enforcing causality through its integration with Neural ODEs.

This study introduces a data augmentation strategy designed to enhance the training of neural networks, thereby improving prediction accuracy. By generating synthetic data using a compartmental model and incorporating uncertainty, the model is calibrated with available data and integrated with deep learning techniques. The findings indicate that neural networks trained on these augmented datasets demonstrate significantly better predictive performance, particularly with Physics-Informed Neural Networks (PINNs) and Nonlinear Autoregressive (NAR) models.