Tackling the Curse of Dimensionality with Physics-Informed Neural Networks

arXiv:2307.12306v5 Announce Type: replace
Abstract: The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional PDEs, as Richard E. Bellman first pointed out over 60 years ago. While there has been some recent success in solving numerically partial differential equations (PDEs) in high dimensions, such computations are prohibitively expensive, and true scaling of general nonlinear PDEs to high dimensions has never been achieved. We develop a new method …

abstract arxiv challenges computational cost cs.ai cs.lg cs.na curse-of-dimensionality differential dimensionality math.ds math.na networks neural networks physics physics-informed resources richard stat.ml success taxes the curse of dimensionality type