Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks

arXiv:2312.14499v2 Announce Type: replace
Abstract: Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data and physics. However, extending PINNs to high-dimensional and even high-order PDEs encounters significant challenges due to the computational cost associated with automatic differentiation in the residual loss. Herein, we address the limitations of PINNs in handling high-dimensional and high-order PDEs by introducing Hutchinson Trace Estimation (HTE). Starting with the second-order high-dimensional PDEs …

abstract arxiv challenges computational cost cs.ai cs.lg cs.na data differential math.ds math.na networks neural networks physics physics-informed stat.ml type