Probabilistic Numerical Methods for Nonlinear PDEs
Dr. Jianfeng Zhang
University of Southern California
Abstract: In this talk, we consider numerical methods for multidimensional nonlinear parabolic PDEs. Due to the curse of dimensionality, the standard numerical methods in PDE literature, e.g. the finite difference method, typically works only for dimension $d$ less than or equal to $3$. We shall instead use probabilistic numerical methods, which is less sensitive to the dimension. In this talk, we will introduce two Monte Carlo methods, based on two different types of probabilistic representation for the solution to the PDE. These methods work for $10$ or even higher dimensional problems.
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