5 papers
Deep Adaptive Dimension Reduction for Bayesian Inference in Inverse Problems
Yueyang Wang, Xili Wang, Kejun Tang +3
Solving high-dimensional PDE-governed inverse problems is often challenging due to complex non-Gaussian posterior distributions, expensive forward model evaluations, and misspecifi…
Moving sample method for solving time-dependent partial differential equations
Beining Xu, Haijun Yu, Jiayu Zhai +2
Solving time-dependent partial differential equations (PDEs) that exhibit sharp gradients or local singularities is computationally demanding, as traditional physics-informed neura…
Functional tensor train neural network for solving high-dimensional PDEs
Yani Feng, Michael K. Ng, Kejun Tang +1
Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct app…
Estimating Committor Functions via Deep Adaptive Sampling on Rare Transition Paths
Yueyang Wang, Kejun Tang, Xili Wang +3
The committor functions are central to investigating rare but important events in molecular simulations. It is known that computing the committor function suffers from the curse of…
APTT: An accuracy-preserved tensor-train method for the Boltzmann-BGK equation
Zhitao Zhu, Chuanfu Xiao, Kejun Tang +2
Solving the Boltzmann-BGK equation with traditional numerical methods suffers from high computational and memory costs due to the curse of dimensionality. In this paper, we propose…