Note on coefficient matrices from stochastic Galerkin methods for random diffusion equations. - Tao Zhou 010; Tao Tang 003 (J. Comput. Phys., 2010)

Galerkin Methods for Stochastic Hyperbolic Problems Using Bi-Orthogonal Polynomials. - Tao Zhou 010; Tao Tang 003 (J. Sci. Comput., 2012)

On Discrete Least-Squares Projection in Unbounded Domain with Random Evaluations and its Application to Parametric Uncertainty Quantification. - Tao Tang 003; Tao Zhou 010 (SIAM J. Sci. Comput., 2014)

New Kinds of High-Order Multistep Schemes for Coupled Forward Backward Stochastic Differential Equations. - Weidong Zhao; Yu Fu; Tao Zhou 010 (SIAM J. Sci. Comput., 2014)

Multivariate Discrete Least-Squares Approximations with a New Type of Collocation Grid. - Tao Zhou 010; Akil Narayan 001; Zhiqiang Xu (SIAM J. Sci. Comput., 2014)

A multilevel finite element method for Fredholm integral eigenvalue problems. - Hehu Xie; Tao Zhou 010 (J. Comput. Phys., 2015)

Weighted discrete least-squares polynomial approximation using randomized quadratures. - Tao Zhou 010; Akil Narayan 001; Dongbin Xiu (J. Comput. Phys., 2015)

Multistep Schemes for Forward Backward Stochastic Differential Equations with Jumps. - Yu Fu; Weidong Zhao; Tao Zhou 010 (J. Sci. Comput., 2016)

Fast parareal iterations for fractional diffusion equations. - Shu-Lin Wu; Tao Zhou 010 (J. Comput. Phys., 2017)

A Christoffel function weighted least squares algorithm for collocation approximations. - Akil Narayan 001; John D. Jakeman; Tao Zhou 010 (Math. Comput., 2017)

An Efficient Gradient Projection Method for Stochastic Optimal Control Problems. - Bo Gong; Wenbin Liu; Tao Tang 003; Weidong Zhao; Tao Zhou 010 (SIAM J. Numer. Anal., 2017)

Stochastic Collocation Methods via ℓ1 Minimization Using Randomized Quadratures. - Ling Guo; Akil Narayan 001; Tao Zhou 010; Yuhang Chen (SIAM J. Sci. Comput., 2017)

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions. - John D. Jakeman; Akil Narayan 001; Tao Zhou 010 (SIAM J. Sci. Comput., 2017)

A gradient enhanced ℓ1-minimization for sparse approximation of polynomial chaos expansions. - Ling Guo; Akil Narayan 001; Tao Zhou 010 (J. Comput. Phys., 2018)

Parareal algorithms with local time-integrators for time fractional differential equations. - Shu-Lin Wu; Tao Zhou 010 (J. Comput. Phys., 2018)

Explicit theta-Schemes for Mean-Field Backward Stochastic Differential Equations. - Yabing Sun; Weidong Zhao; Tao Zhou 010 (SIAM J. Numer. Anal., 2018)

Weighted Approximate Fekete Points: Sampling for Least-Squares Polynomial Approximation. - Ling Guo; Akil Narayan 001; Liang Yan 002; Tao Zhou 010 (SIAM J. Sci. Comput., 2018)

An adaptive surrogate modeling based on deep neural networks for large-scale Bayesian inverse problems. - Liang Yan 002; Tao Zhou 010 (CoRR, 2019)

Data-driven polynomial chaos expansions: A weighted least-square approximation. - Ling Guo; Yongle Liu; Tao Zhou 010 (J. Comput. Phys., 2019)

Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems. - Liang Yan 002; Tao Zhou 010 (J. Comput. Phys., 2019)

Efficient Stochastic Galerkin Methods for Maxwell's Equations with Random Inputs. - Zhiwei Fang; Jichun Li 001; Tao Tang 003; Tao Zhou 010 (J. Sci. Comput., 2019)

Explicit Deferred Correction Methods for Second-Order Forward Backward Stochastic Differential Equations. - Jie Yang; Weidong Zhao; Tao Zhou 010 (J. Sci. Comput., 2019)

On Energy Dissipation Theory and Numerical Stability for Time-Fractional Phase-Field Equations. - Tao Tang 003; Haijun Yu; Tao Zhou 010 (SIAM J. Sci. Comput., 2019)

Analysis of the second order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection. - Hong-lin Liao; Xuehua Song; Tao Tang 003; Tao Zhou 010 (CoRR, 2020)

Sparse approximation of data-driven Polynomial Chaos expansions: an induced sampling approach. - Ling Guo; Akil Narayan 001; Yongle Liu; Tao Zhou 010 (CoRR, 2020)

Positive definiteness of real quadratic forms resulting from the variable-step approximation of convolution operators. - Hong-lin Liao; Tao Tang 003; Tao Zhou 010 (CoRR, 2020)

A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations. - Hong-lin Liao; Tao Tang 003; Tao Zhou 010 (J. Comput. Phys., 2020)

On Energy Stable, Maximum-Principle Preserving, Second-Order BDF Scheme with Variable Steps for the Allen-Cahn Equation. - Hong-lin Liao; Tao Tang 003; Tao Zhou 010 (SIAM J. Numer. Anal., 2020)

A Unified Probabilistic Discretization Scheme for FBSDEs: Stability, Consistency, and Convergence Analysis. - Jie Yang; Weidong Zhao; Tao Zhou 010 (SIAM J. Numer. Anal., 2020)

Constructing Least-Squares Polynomial Approximations. - Ling Guo; Akil Narayan 001; Tao Zhou 010 (SIAM Rev., 2020)

Rational Spectral Methods for PDEs Involving Fractional Laplacian in Unbounded Domains. - Tao Tang 003; Li-Lian Wang; Huifang Yuan; Tao Zhou 010 (SIAM J. Sci. Comput., 2020)

A new discrete energy technique for multi-step backward difference formulas. - Hong-Lin Liao; Tao Tang 003; Tao Zhou 010 (CoRR, 2021)

Stein variational gradient descent with local approximations. - Liang Yan 002; Tao Zhou 010 (CoRR, 2021)

An acceleration strategy for randomize-then-optimize sampling via deep neural networks. - Liang Yan 002; Tao Zhou 010 (CoRR, 2021)

Optimal design for kernel interpolation: Applications to uncertainty quantification. - Akil Narayan 001; Liang Yan 002; Tao Zhou 010 (J. Comput. Phys., 2021)

Parallel implementation for the two-stage SDIRK methods via diagonalization. - Shu-Lin Wu; Tao Zhou 010 (J. Comput. Phys., 2021)

An Energy Stable and Maximum Bound Preserving Scheme with Variable Time Steps for Time Fractional Allen-Cahn Equation. - Hong-lin Liao; Tao Tang 003; Tao Zhou 010 (SIAM J. Sci. Comput., 2021)

Discrete energy analysis of the third-order variable-step BDF time-stepping for diffusion equations. - Hong-lin Liao; Tao Tang 003; Tao Zhou 010 (CoRR, 2022)

Failure-informed adaptive sampling for PINNs, Part II: combining with re-sampling and subset simulation. - Zhiwei Gao; Tao Tang; Liang Yan 002; Tao Zhou 010 (CoRR, 2023)

Failure-Informed Adaptive Sampling for PINNs. - Zhiwei Gao; Liang Yan 002; Tao Zhou 010 (SIAM J. Sci. Comput., 2023)

A class of refined implicit-explicit Runge-Kutta methods with robust time adaptability and unconditional convergence for the Cahn-Hilliard model. - Hong-lin Liao; Tao Tang 003; Xuping Wang; Tao Zhou 010 (CoRR, 2024)

Adaptive Operator Learning for Infinite-Dimensional Bayesian Inverse Problems. - Zhiwei Gao; Liang Yan 002; Tao Zhou 010 (SIAM/ASA J. Uncertain. Quantification, 2024)

Convergence Analysis of the Parareal Algorithm with Nonuniform Fine Time Grid. - Shu-Lin Wu; Tao Zhou 010 (SIAM J. Numer. Anal., 2024)

Deep learning-enhanced reduced-order ensemble Kalman filter for efficient Bayesian data assimilation of parametric PDEs. - Yanyan Wang; Liang Yan 002; Tao Zhou 010 (Comput. Phys. Commun., 2025)