Research

Research Interests

  • Numerical methods for multiscale kinetic equations.
  • Deep learning for solving differential equations.
  • Generative models for Scientific computing.


Publications

  • Xu, W., Lu, Y. and Wang, L. Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations. The 37th AAAI conference on Artificial Intelligence (2023). Link., Code.

  • Lu, Y., Wang, L. and Xu, W. Solving multiscale steady radiative transfer equation using neural networks with uniform stability. Res Math Sci 9, 45 (2022). Link., Code.

  • Xu, W. and Wang, L. An asymptotic preserving scheme for Lévy-Fokker-Planck equation with fractional diffusion limit. Comm Math Sci, 23, 1-23, (2023). Link., Code.

  • Carrillo, J., Wang, L., Xu, W. and Yan, M. Variational asymptotic preserving scheme for the Vlasov–Poisson–Fokker–Planck system, Multiscale Modeling & Simulation 19(1), 478–505. Link. Code.

  • Carrillo, J., Shu, R., Wang, L. and Xu, W. To blow-up or not to blow-up for a granular kinetic equation, Physica D: Nonlinear Phenomena, 470, 134410 (2024). Link., [Code will be available soon]

  • Lu, Y. and Xu, W. Generative downscaling of PDE solvers with physics-guided diffusion models, Journal of Scientific Computing, 101(3), 71 (2024). Link., Code.