Tackling the Curse of Dimensionality with Physics-Informed Neural Networks. (arXiv:2307.12306v3 [cs.LG] UPDATED)

The curse-of-dimensionality (CoD) taxes computational resources heavily with
exponentially increasing computational cost as the dimension increases. This
poses great challenges in solving high-dimensional PDEs as Richard 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. In this
paper, we develop a new method of scaling …

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