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An Uncertainty-aware, Mesh-free Numerical Method for Kolmogorov PDEs

An Uncertainty-aware, Mesh-free Numerical Method for Kolmogorov PDEs

This study introduces an uncertainty-aware, mesh-free numerical method for solving Kolmogorov PDEs. In the proposed method, we use Gaussian process regression (GPR) to smoothly interpolate pointwise solutions that are obtained by Monte Carlo methods based on the Feynman-Kac formula. The proposed method has two main advantages: 1. uncertainty assessment, which …