[2409.11847] An efficient wavelet-based physics-informed neural network for multiscale problems

Computer Science > Machine Learning arXiv:2409.11847 (cs) [Submitted on 18 Sep 2024 (v1), last revised 25 Mar 2026 (this version, v3)] Title:An efficient wavelet-based physics-informed neural network for multiscale problems Authors:Himanshu Pandey, Anshima Singh, Ratikanta Behera View a PDF of the paper titled An efficient wavelet-based physics-informed neural network for multiscale problems, by Himanshu Pandey and 1 other authors View PDF HTML (experimental) Abstract:Physics-informed neural networks (PINNs) are a class of deep learning models that utilize physics in the form of differential equations to address complex problems, including those with limited data availability. However, solving differential equations with rapid oscillations, steep gradients, or singular behavior remains challenging for PINNs. To address this, we propose an efficient wavelet-based physics-informed neural network (W-PINN) that learns solutions in wavelet space. Here, we represent the solution using localized wavelets. This framework represents the solution of a differential equation with significantly fewer degrees of freedom while retaining the dynamics of complex physical phenomena. The proposed architecture enables training to search for solutions within the wavelet domain, where multiscale characteristics are less pronounced compared to the physical domain. This facilitates more efficient training for such problems. Furthermore, the proposed model does not rely on automatic differentiatio...