# Neural networks-based backward scheme for fully nonlinear PDEs

@article{Pham2019NeuralNB, title={Neural networks-based backward scheme for fully nonlinear PDEs}, author={H. Pham and X. Warin}, journal={ArXiv}, year={2019}, volume={abs/1908.00412} }

We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural networks, through a sequence of learning problems obtained from the minimization of suitable quadratic loss functions and training simulations. This methodology extends to the fully non-linear case the approach recently proposed in [HPW19] for semi-linear PDEs… Expand

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