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Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations
[article]
2018
arXiv
pre-print
Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal grids. Inspired by modern deep learning based techniques for solving forward and inverse problems associated with partial differential equations, we circumvent the tyranny of numerical discretization by devising an algorithm that is scalable to high-dimensions. In particular, we approximate the unknown solution by a
arXiv:1804.07010v1
fatcat:xwtsic2p7bd2neqt7czg3kjjcm