A deep branching solver for fully nonlinear partial differential equations

• URL: http://arxiv.org/abs/2203.03234v2
• Date: Sat, 9 Sep 2023 02:12:19 GMT
• Title: A deep branching solver for fully nonlinear partial differential equations
• Authors: Jiang Yu Nguwi, Guillaume Penent, and Nicolas Privault
• Abstract summary: We present a multidimensional deep learning implementation of a branching algorithm for the numerical solution of fully nonlinear PDEs. This approach is designed to tackle functional nonlinearities involving gradient terms of any orders.
• Score: 0.1474723404975345
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a multidimensional deep learning implementation of a stochastic branching algorithm for the numerical solution of fully nonlinear PDEs. This approach is designed to tackle functional nonlinearities involving gradient terms of any orders, by combining the use of neural networks with a Monte Carlo branching algorithm. In comparison with other deep learning PDE solvers, it also allows us to check the consistency of the learned neural network function. Numerical experiments presented show that this algorithm can outperform deep learning approaches based on backward stochastic differential equations or the Galerkin method, and provide solution estimates that are not obtained by those methods in fully nonlinear examples.

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