2023/08/17 by Taniya Kapoor, Kapoor, Taniya, Abhishek Chandra +9 · 4 citations
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #FOS: Computer and information sciences #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing #Neural and Evolutionary Computing (cs.NE)
paper · pdf · doi:10.48550/arxiv.2308.08989
openalex publication_date 2023/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A primary challenge of physics-informed machine learning (PIML) is its generalization beyond the training domain, especially when dealing with complex physical problems represented by partial differential equations (PDEs). This paper aims to enhance the generalization capabilities of PIML, facilitating practical, real-world applications where accurate predictions in unexplored regions are crucial. We leverage the inherent causality and temporal sequential characteristics of PDE solutions to fuse PIML models with recurrent neural architectures based on systems of ordinary differential equations, referred to as neural oscillators. Through effectively capturing long-time dependencies and mitigating the exploding and vanishing gradient problem, neural oscillators foster improved generalization in PIML tasks. Extensive experimentation involving time-dependent nonlinear PDEs and biharmonic beam equations demonstrates the efficacy of the proposed approach. Incorporating neural oscillators outperforms existing state-of-the-art methods on benchmark problems across various metrics. Consequently, the proposed method improves the generalization capabilities of PIML, providing accurate solutions for extrapolation and prediction beyond the training data.