Research

Research Interests

  • Deep learning for PDEs and optimal control.
  • Generative models for scientific computing.
  • Numerical methods for multiscale kinetic equations.


Preprints

  • Xu, W. Han, J., and Lai, R. Self-Supervised Amortized Neural Operators for Optimal Control: Scaling Laws and Applications. Submitted. Link., Code.

Journal Publications

  • Cole, F., Lu, Y., Xu, W. and Zhang, T. In-Context Learning of Linear Systems: Generalization theory and Application to Operator Learning. Accepted by SIAM Journal on Mathematics of Data Science, (2026). arXiv Link., Code.

  • Xu, W. Lu, Y., Shen, L., Xuan, A. and Barzegari, A. Diffusion-based Models for Unpaired Super-resolution in Fluid Dynamics. Accepted by SIAM Journal on Scientific Computing, (2026). arXiv Link., Code.

  • Xu, W. Lu, Y., Wang, S. and Liu, T. Improving Data Fidelity via Diffusion Model-based Correction and Super-Resolution. Journal of Computational Physics 559, 114883 (2026). Link., Code.

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

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

  • Lu, Y., Wang, L. and Xu, W. Solving multiscale steady radiative transfer equation using neural networks with uniform stability. Research in the Mathematical Sciences 9, 45 (2022). 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. (2021). Link. Code.

Peer-Reviewed Conference 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.