Research

Research Interests

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

Preprints

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

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

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

Journal Publications

• 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 . arXiv 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.]

• 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.

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.