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Scientific Machine Learning

  • X. Feng, H. Shangguan, T. Tang, X. Wan and T. Zhou, A hybrid FEM-PINN method for time-dependent partial differential equations, (2024), arXiv:2409.02810. [link]
  • J. Yuan, J.-H. Liang, E. P. Chassignet, O. Zavala-Romero, X. Wan and M. F. Cronin, The K-profile parameterization augmented by deep neural networks (KPP_DNN) in the general ocean turbulence model (GOTM), Journal of Advances in Modeling Earth Systems, 16 (2024), e2024MS004405. [pdf]
  • J. He, Q. Liao and X. Wan, Adaptive deep density approximation for stochastic dynamical systems, (2024), arXiv:2405.02810v1. [Link]
  • X. Wang, K. Tang, J. Zhai, X. Wan and C. Yang, Deep adaptive sampling for surrogate modeling without labeled data, Journal of Scientific Computing, (2024) 101:77. [pdf]
  • K. Tang, J. Zhai, X. Wan and C. Yang, Adversarial adaptive sampling: Unify PINN and optimal transport for the approximation of PDEs, 12th International Conference on Learning Representations (ICLR 2024). [link]
  • X. Wan, T. Zhou and Y. Zhou, Adaptive importance sampling for Deep Ritz, Communications on Applied Mathematics and Computation, (2024). [link]
  • L. Zeng, X. Wan and T. Zhou, Bounded KRnet and its applications to density estimation and approximation, (2023), arXiv:2305.09063. [link]
  • Y. Feng, K. Tang, X. Wan and Q. Liao, Dimension-reduced KRnet maps for high-dimensional inverse problems, (2023), arXiv:2303.00573. [link]
  • K. Tang, X. Wan and C. Yang, DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations, Journal of Computational Physics, 476 (2023), 111868. [pdf]
  • L. Zeng, X. Wan and T. Zhou, Adaptive deep density approximation for fractional Fokker-Planck equations, Journal of Scientific Computing, 97:68 (2023). [pdf]
  • J.-H. Liang, J. Yuan, X. Wan, J. Liu, B. Liu, H. Jang, and M. Tyagi, Exploring the use of machine learning to parameterize vertical mixing in the ocean surface boundary layer, Ocean Modelling, 176, (2022), 102059. [link]
  • X. Wan and S. Wei, VAE-KRnet and its applications to variational Bayes, Communications in Computational Physics, 31 (2022), pp. 1049-1082. [pdf]
  • K. Tang, X. Wan and Q. Liao, Adaptive deep density approximation for Fokker-Planck equations, Journal of Computational Physics, 457 (2022), 111080. [pdf]
  • X. Wan and K. Tang, Augmented KRnet for density estimation and approximation, (2021), arXiv:2105.12866v2. [pdf]
  • K. Tang, X. Wan and Q. Liao, Deep density estimation via invertible block-triangular mapping, Theoretical & Applied Mechanics Letters, 10 (2020), 000-5. [pdf]
  • X. Wan and S. Wei, Coupling the reduced-order model and the generative model for an importance sampling estimator, Journal of Computational Physics, 408(2020), 109281. [pdf]

Minimum action method

  • X. Wan and J. Zhai, A minimum action method for dynamical systems with constant time delays, SIAM Journal on Scientific Computing, 43(1) (2021), pp. A541-A565. [pdf]

  • X. Wan, H. Yu and J. Zhai, Convergence analysis of a finite element approximation of minimum action method, SIAM Journal on Numerical Analysis, 56(3) (2018), pp. 1597-1620. [pdf]

  • X. Wan and X. Zhou, Asymptotically efficient simulation of elliptic problems with small random forcing, SIAM Journal on Scientific Computing, 40(1) (2018), pp. A548-A572. [pdf]

  • X. Wan, B. Zheng and G. Lin, An hp adaptive minimum action method based on a posteriori error estimate, Communications in Computational Physics, 23(2) (2018), pp. 408-439. [pdf]

  • X. Wan, A minimum action method with optimal linear time scaling, Communications in Computational Physics, 18(5) (2015), pp. 1352-1379. [pdf]

  • X. Wan and G. Lin, Hybrid parallel computing of minimum action method, Parallel Computing, 39 (2013), pp. 638-651. [pdf]

  • X. Wan, An adaptive high-order minimum action method, Journal of Computational Physics, 230 (2011), pp. 8669-8682. [pdf]

  • X. Wan, X. Zhou and W. E, Study of the noise-induced transition and the exploration of the configuration space for the Kuramoto-Sivashinsky equation using the minimum action method, Nonlinearity, 23 (2010), pp. 475-493. [pdf]

Small random perturbations of Navier-Stokes equations
  • X. Wan ahd H. Yu, A dynamic-solver-consistent minimum action method: With an application to 2D Navier-Stokes equations, Journal of Computational Physics 331 (2017), pp. 209-226. [pdf]

  • X. Wan, H. Yu and W. E, Model the nonlinear instability of wall-bounded shear flows as a rare event: A study on two-dimensional Poiseuille flow, Nonlinearity, 28 (2015), pp. 1409-1440. [pdf]

  • X. Wan, A minimum action method for small random perturbations of two-dimensional parallel shear flows, Journal of Computational Physics, 235 (2013), pp. 497-514. [pdf]

Numerical methods of SPDEs

  • X. Wan and B. Rozovskii, The Wick-Malliavin approximation of elliptic problems with log-normal random coefficients, SIAM Journal on Scientific Computing, 35(5) (2013), pp. A2370-A2392. [pdf]

  • D. Venturi, X. Wan, R. Mikulevicius, B. Rozovskii and G. Karniadakis, Wick-Malliavin approximation to nonlinear stochastic PDEs: analysis and simulations, Proceedings of the Royal Society A, 469 (2013), 20130001. [pdf]

  • X. Wan, A discussion on two stochastic elliptic modeling strategies, Communications in Computational Physics, 11 (2012), pp. 775-796. [pdf]

  • X. Wan, A note on stochastic elliptic models, Computer Methods in Applied Mechanics and Engineering, 199(45-48) (2010), pp. 2987-2995. [pdf]

  • S. V. Lototsky, B. L. Rozovskii and X. Wan, Elliptic equations of higher stochastic order, ESAIM: Mathematical Modeling and Numerical Analysis, 5/4 (2010), pp. 1135-1153. [pdf]

  • X. Wan, B. Rozovskii and G. E. Karniadakis, A stochastic modeling methodology based on weighted Wiener chaos and Malliavin calculus, Proceedings of the National Academy of Sciences, 106 (2009), pp. 14189-14194. [pdf]

Uncertainty Quantification

  • X. Wan and H. Yu, Numerical approximaiton of elliptic problems with log-normal random coefficients, International Journal for Uncertainty Quantification, 9(2) (2019), pp. 161-186. [pdf]
  • X. Yang, X. Wan, L. Lin and H. Lei, A general framework of enhancing sparsity of generalized polynomial chaos expansion, arXiv:1707.02688, International Journal for Uncertainty Quantification, 9(3) (2019), pp. 221-243.
  • M. Zheng, X. Wan and G. Karniadakis, Adaptive multi-element polynomial chaos with discrete measure: Algorithms and applications to SPDEs, Applied Numerical Mathematics, 90 (2015), pp. 91-110. [pdf]

  • H. Babaee, X. Wan and S. Acharya, Effect of uncertainty in blowing ratio on film cooling effectiveness, ASME Journal of Heat Transfer, 136(3) (2014), pp. 031701. [pdf]

  • G. Lin, M. Elizondo, S. Lu and X. Wan, Uncertainty quantification in dynamic simulations of large-scale power system models using the high-order probabilistic collocation method on sparse grids, International Journal for Uncertainty Quantification, 4(3) (2014), pp. 185-204. [pdf]

  • D. Venturi, X. Wan and G. E. Karniadakis, Stochastic bifurcation and stability of natural convective flows in bidimensional square enclosures, Journal of Fluid Mechanics, 650 (2010), pp. 391-413. [pdf]

  • X. Wan and G. E. Karniadakis, Solving elliptic problems with non-Gaussian spatially-dependent random coefficients: algorithms, error analysis and applications, Computer Methods in Applied Mechanics and Engineering, 198/21-26 (2009), pp. 1985-1995. [pdf]

  • X. Wan and G. E. Karniadakis, Error control in multi-element polynomial chaos method for elliptic problems with random coefficients, Communications in Computational Physics, 5/2-4 (2009), pp. 793-820. [pdf]

  • J. Foo, X. Wan and G. E. Karniadakis, The multi-element probabilistic collocation method: analysis and simulation, Journal of Computational Physics, 227 (2008), pp. 9572-9595. [pdf]

  • D. Venturi, X. Wan and G. E. Karniadakis, Stochastic low dimensional modeling of random laminar wake past a circular cylinder, Journal of Fluid Mechanics, 606 (2008), pp. 339-367. [pdf]

  • G. Lin, X. Wan, C.-H. Su and G. E. Karniadakis, Stochastic computational fluid mechanics, IEEE Computing in Science and Engineering Journal (CiSE), 9 (2007), pp. 21-29. [pdf]

  • X. Wan and G. E. Karniadakis, Stochastic heat transfer in a grooved channel, Journal of Fluid Mechanics, 565 (2006), pp. 255-278. [pdf]

  • X. Wan and G. E. Karniadakis, Long-term behavior of polynomial chaos in stochastic flow simulations, Computer Methods in Applied Mechanics and Engineering, 195 (2006), pp. 5582-5596. [pdf]

  • X. Wan and G. E. Karniadakis, Multi-element generalized polynomial chaos for arbitrary probability measures, SIAM Journal on Scientific Computing, 28 (2006), pp. 901-928. [pdf]

  • X. Wan and G. E. Karniadakis, Beyond Wiener-Askey expansions: handling arbitrary PDFs, Journal of Scientific Computing, 27 (2006), pp. 455-464. [pdf]

  • X. Wan and G. E. Karniadakis, An adaptive multi-element generalized polynomial chaos method for stochastic differential equations, Journal of Computational Physics, 209 (2005), pp. 617-642. [pdf]

  • X. Wan, D. Xiu and G. E. Karniadakis, Stochastic solutions for the two-dimensional advection-diffusion equation, SIAM Journal on Scientific Computing, 26 (2004), pp. 578-590. [pdf]

Miscellaneous topics

  • J.-H. Liang, X. Wan, K. Rose, P. Sullivan and J. McWilliams, Horizontal dispersion of buoyant materials in the ocean surface boundary layer, Journal of Physical Oceanography, 48 (2018), pp. 2103-2125. [pdf]

  • L. Zhu, Q. Chen and X. Wan, Optimization of non-hydrostatic Euler model for water waves, Coastal Engineering, 91 (2014), pp. 191-199. [pdf]

  • H. Babaee, S. Acharya and X. Wan, Optimization of forcing parameters of film cooling effectiveness, ASME Journal of Turbomachinery, ASME Journal of Turbomachinery, 136 (2014), 021016. [pdf]

  • X. Wan, Some improvements to the flux-type a posteriori error estimators, Computer Methods in Applied Mechanics and Engineering, 197/6-8 (2008), pp. 567-576. [pdf]

  • X. Wan and G. E. Karniadakis, A sharp error estimate for the Fast Gauss Transform [Short Note], Journal of Computational Physics, 219 (2006), pp. 7-12. [pdf]