3 papers
math.NA2024
Generalization Error Analysis of Deep Backward Dynamic Programming for Solving Nonlinear PDEs
Du Ouyang, Jichang Xiao, Xiaoqun Wang
We explore the application of the quasi-Monte Carlo (QMC) method in deep backward dynamic programming (DBDP) (Hure et al. 2020) for numerically solving high-dimensional nonlinear p…
math.NA2024
Deep Learning Based on Randomized Quasi-Monte Carlo Method for Solving Linear Kolmogorov Partial Differential Equation
Jichang Xiao, Fengjiang Fu, Xiaoqun Wang
Deep learning algorithms have been widely used to solve linear Kolmogorov partial differential equations~(PDEs) in high dimensions, where the loss function is defined as a mathemat…
math.NA2024
Error analysis for empirical risk minimization over clipped ReLU networks in solving linear Kolmogorov partial differential equations
Jichang Xiao, Xiaoqun Wang
Deep learning algorithms have been successfully applied to numerically solve linear Kolmogorov partial differential equations~(PDEs). A recent research shows that if the initial fu…