Research on UQ Problem Based on Feynman–Kac Formula and Neural Network

A high-dimensional adaptation method of neural network regression to obtain the expected mean solution of the uncertainty quantification problem based on Monte Carlo simulation and the Feynman-Kac formula is presented. In the numerical tests, by the Feynman-Kac formula, the numerical solution on each given point is obtained by rectangle method. Polynomial and neural network regression of different dimensions lead to obtain the expected mean solution of the UQ problem. This thesis illustrates that neural network are more conducive to high-dimensional problems. This thesis analyzes the effects of time step, simulation frequency, generations, hidden layers, and learning rate on the convergence by drawing convergence graphs.