Solving High Frequency and Multi-Scale PDEs with Gaussian Processes

arXiv:2311.04465v2 Announce Type: replace
Abstract: Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and multi-scale PDEs, which can be due to spectral bias during neural network training. To address this problem, we resort to the Gaussian process (GP) framework. To flexibly capture the dominant frequencies, we model the power spectrum of the PDE solution with a student $t$ mixture …

arxiv cs.ce cs.lg gaussian processes processes scale type