51 citations · 98 across the 14 of their papers we have counts for
14 papers
A transition-density-based operator learning method for Fokker-Planck equations with various initial conditions
Li Zeng, Xiaoliang Wan, Yaobin Wang +2
Solving Fokker-Planck equations (FPEs) for multiple initial conditions typically requires repeated computations, leading to substantial computational costs. In this work, we propos…
Adaptive deep density approximation for stochastic dynamical systems
Junjie He, Qifeng Liao, Xiaoliang Wan
In this paper we consider adaptive deep neural network approximation for stochastic dynamical systems. Based on the Liouville equation associated with the stochastic dynamical syst…
Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs
Kejun Tang, Jiayu Zhai, Xiaoliang Wan +1
Solving partial differential equations (PDEs) is a central task in scientific computing. Recently, neural network approximation of PDEs has received increasing attention due to its…
Bounded KRnet and its applications to density estimation and approximation
Li Zeng, Xiaoliang Wan, Tao Zhou
In this paper, we develop an invertible mapping, called B-KRnet, on a bounded domain and apply it to density estimation/approximation for data or the solutions of PDEs such as the…
Dimension-reduced KRnet maps for high-dimensional Bayesian inverse problems
Yani Feng, Kejun Tang, Xiaoliang Wan +1
We present a dimension-reduced KRnet map approach (DR-KRnet) for high-dimensional Bayesian inverse problems, which is based on an explicit construction of a map that pushes forward…
Adaptive deep density approximation for fractional Fokker-Planck equations
Li Zeng, Xiaoliang Wan, Tao Zhou
In this work, we propose adaptive deep learning approaches based on normalizing flows for solving fractional Fokker-Planck equations (FPEs). The solution of a FPE is a probability…
DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations
Kejun Tang, Xiaoliang Wan, Chao Yang
In this work we propose a deep adaptive sampling (DAS) method for solving partial differential equations (PDEs), where deep neural networks are utilized to approximate the solution…
Augmented KRnet for density estimation and approximation
Xiaoliang Wan, Kejun Tang
In this work, we have proposed augmented KRnets including both discrete and continuous models. One difficulty in flow-based generative modeling is to maintain the invertibility of…
Adaptive deep density approximation for Fokker-Planck equations
Kejun Tang, Xiaoliang Wan, Qifeng Liao
In this paper we present an adaptive deep density approximation strategy based on KRnet (ADDA-KR) for solving the steady-state Fokker-Planck (F-P) equations. F-P equations are usua…
VAE-KRnet and its applications to variational Bayes
Xiaoliang Wan, Shuangqing Wei
In this work, we have proposed a generative model, called VAE-KRnet, for density estimation or approximation, which combines the canonical variational autoencoder (VAE) with our re…
Coupling the reduced-order model and the generative model for an importance sampling estimator
Xiaoliang Wan, Shuangqing Wei
In this work, we develop an importance sampling estimator by coupling the reduced-order model and the generative model in a problem setting of uncertainty quantification. The targe…
Numerical approximation of elliptic problems with log-normal random coefficients
Xiaoliang Wan, Haijun Yu
In this work, we consider a non-standard preconditioning strategy for the numerical approximation of the classical elliptic equations with log-normal random coefficients. In \cite{…
Convergence analysis of a finite element approximation of minimum action methods
Xiaoliang Wan, Haijun Yu, Jiayu Zhai
In this work, we address the convergence of a finite element approximation of the minimizer of the Freidlin-Wentzell (F-W) action functional for non-gradient dynamical systems pert…
A General Framework for Enhancing Sparsity of Generalized Polynomial Chaos Expansions
Xiu Yang, Xiaoliang Wan, Lin Lin +1
Compressive sensing has become a powerful addition to uncertainty quantification when only limited data is available. In this paper we provide a general framework to enhance the sp…