Deep backward schemes for high-dimensional nonlinear PDEs

Understand

We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs).

• Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, our algorithms estimate simultaneously the solution and its gradient by deep neural networks.
• These approximations are performed at each time step from the minimization of loss functions defined recursively by backward induction.
• The methodology is extended to variational inequalities arising in optimal stopping problems.