Corpus ID: 199064581

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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References

SHOWING 1-10 OF 20 REFERENCES
Some machine learning schemes for high-dimensional nonlinear PDEs
  • 60
  • PDF
Deep splitting method for parabolic PDEs
  • 39
  • PDF
Solving high-dimensional partial differential equations using deep learning
  • 405
  • PDF
...
1
2
...