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

ArXi:2409.11847v3 Announce Type: replace 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.