Stochastic Solutions for the Two-Dimensional Advection-Diffusion Equation. - Xiaoliang Wan; Dongbin Xiu; George E. Karniadakis (SIAM J. Sci. Comput., 2004)

A sharp error estimate for the fast Gauss transform. - Xiaoliang Wan; George E. Karniadakis (J. Comput. Phys., 2006)

Beyond Wiener-Askey Expansions: Handling Arbitrary PDFs. - Xiaoliang Wan; George E. Karniadakis (J. Sci. Comput., 2006)

Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures. - Xiaoliang Wan; George E. Karniadakis (SIAM J. Sci. Comput., 2006)

Stochastic Computational Fluid Mechanics. - Guang Lin 001; Xiaoliang Wan; Chau-Hsing Su; George E. Karniadakis (Comput. Sci. Eng., 2007)

The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications. - Jasmine Foo; Xiaoliang Wan; George E. Karniadakis (J. Comput. Phys., 2008)

An adaptive high-order minimum action method. - Xiaoliang Wan (J. Comput. Phys., 2011)

A minimum action method for small random perturbations of two-dimensional parallel shear flows. - Xiaoliang Wan (J. Comput. Phys., 2013)

Hybrid parallel computing of minimum action method. - Xiaoliang Wan; Guang Lin 001 (Parallel Comput., 2013)

The Wick-Malliavin Approximation of Elliptic Problems with Log-Normal Random Coefficients. - Xiaoliang Wan; Boris L. Rozovskii (SIAM J. Sci. Comput., 2013)

A dynamic-solver-consistent minimum action method: With an application to 2D Navier-Stokes equations. - Xiaoliang Wan; Haijun Yu (J. Comput. Phys., 2017)

Convergence Analysis of a Finite Element Approximation of Minimum Action Methods. - Xiaoliang Wan; Haijun Yu; Jiayu Zhai (SIAM J. Numer. Anal., 2018)

Asymptotically Efficient Simulation of Elliptic Problems with Small Random Forcing. - Xiaoliang Wan; Xiang Zhou 001 (SIAM J. Sci. Comput., 2018)

VAE-KRnet and its applications to variational Bayes. - Xiaoliang Wan; Shuangqing Wei (CoRR, 2020)

Coupling the reduced-order model and the generative model for an importance sampling estimator. - Xiaoliang Wan; Shuangqing Wei (J. Comput. Phys., 2020)

Augmented KRnet for density estimation and approximation. - Xiaoliang Wan; Kejun Tang (CoRR, 2021)

DAS: A deep adaptive sampling method for solving partial differential equations. - Kejun Tang; Xiaoliang Wan; Chao Yang 002 (CoRR, 2021)

A Minimum Action Method for Dynamical Systems with Constant Time Delays. - Xiaoliang Wan; Jiayu Zhai (SIAM J. Sci. Comput., 2021)

Adaptive deep density approximation for Fokker-Planck equations. - Kejun Tang; Xiaoliang Wan; Qifeng Liao (J. Comput. Phys., 2022)

Dimension-reduced KRnet maps for high-dimensional Bayesian inverse problems. - Yani Feng; Kejun Tang; Xiaoliang Wan; Qifeng Liao (CoRR, 2023)

Bounded KRnet and its applications to density estimation and approximation. - Li Zeng; Xiaoliang Wan; Tao Zhou (CoRR, 2023)

Adaptive importance sampling for Deep Ritz. - Xiaoliang Wan; Tao Zhou; Yuancheng Zhou (CoRR, 2023)

DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations. - Kejun Tang; Xiaoliang Wan; Chao Yang 002 (J. Comput. Phys., 2023)

Adaptive Deep Density Approximation for Fractional Fokker-Planck Equations. - Li Zeng; Xiaoliang Wan; Tao Zhou (J. Sci. Comput., 2023)

Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs. - Kejun Tang; Jiayu Zhai; Xiaoliang Wan; Chao Yang 002 (ICLR, 2024)

A hybrid FEM-PINN method for time-dependent partial differential equations. - Xiaodong Feng; Haojiong Shangguan; Tao Tang; Xiaoliang Wan; Tao Zhou (CoRR, 2024)

Deep Adaptive Sampling for Surrogate Modeling Without Labeled Data. - Xili Wang; Kejun Tang; Jiayu Zhai; Xiaoliang Wan; Chao Yang 002 (J. Sci. Comput., 2024)

Estimating Committor Functions via Deep Adaptive Sampling on Rare Transition Paths. - Yueyang Wang; Kejun Tang; Xili Wang; Xiaoliang Wan; Weiqing Ren; Chao Yang (CoRR, 2025)

Integral regularization PINNs for evolution equations. - Xiaodong Feng; Haojiong Shangguan; Tao Tang; Xiaoliang Wan (CoRR, 2025)

Adaptive Deep Density Approximation for Stochastic Dynamical Systems. - Junjie He; Qifeng Liao; Xiaoliang Wan (J. Sci. Comput., 2025)

LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian process. - Xiaodong Feng; Ling Guo; Xiaoliang Wan; Hao Wu; Tao Zhou; Wenwen Zhou (CoRR, 2025)