Jing An

Bio

I am a tenure-track associate professor at Shanghai Jiao Tong University.

[CV]

Research Interests

I am broadly interested in the mathematical aspects of machine learning and data science problems, using tools from stochastic analysis and partial differential equations. I also study evolution equations including reaction diffusion equations. If you are interested in working in these fields, please contact me!

Papers

• Reaction enhancement by flux-limited chemotaxis, with Alexander Kiselev and Yao Yao. Submitted [arXiv]
• Convergence of two-timescale gradient descent ascent dynamics: finite-dimensional and mean-field perspectives, with Jianfeng Lu. Submitted [arXiv]
• Why does the two-timescale Q-learning converge to different mean field solutions? A unified convergence analysis, with Jianfeng Lu, Yue Wu, and Yang Xiang. Submitted [arXiv]
• Convergence of stochastic gradient descent under a local Lojasiewicz condition for deep neural networks, with Jianfeng Lu. J. Mach. Learn. [link]
• Front location determines convergence rate to traveling waves, with Christopher Henderson and Lenya Ryzhik. Annales de l'Institut Henri Poincaré C [link]
• Critical points and convergence analysis of generative deep linear networks trained with Bures-Wasserstein loss, with Pierre Brechet, Katerina Papagiannouli, and Guido Montufar. ICML [link]
• Voting models and semilinear parabolic equations, with Christopher Henderson and Lenya Ryzhik. Nonlinearity [link]
• Quantitative steepness, semi-FKPP reactions, and pushmi-pullyu fronts, with Christopher Henderson and Lenya Ryzhik. Arch. Ration. Mech. Anal. [link]
• Pushed, pulled and pushmi-pullyu fronts of the Burgers-FKPP equation, with Christopher Henderson and Lenya Ryzhik. J. Eur. Math. Soc. [link]
• Combining resampling and reweighting for faithful stochastic optimization, with Lexing Ying. Comm. Math. Sci. [link]
• Why resampling outperforms reweighting for correcting sampling bias with stochastic gradients, with Lexing Ying and Yuhua Zhu. ICLR [link]
• On the gradient flow structure of the isotropic Landau equation, with Lexing Ying. Comm. Math. Sci. [link]
• Global well-posedness for the Euler alignment system with mildly singular interactions, with Lenya Ryzhik. Nonlinearity [link]
• Stochastic modified equations for the asynchronous stochastic gradient descent, with Jianfeng Lu and Lexing Ying. Information and Inference: A Journal of the IMA [link]
• Fast algorithms for integral formulations of steady-state radiative transfer equation, with Yuwei Fan and Lexing Ying. Journal of Computational Physics [link]
• Image segmentation with dynamic artifacts detection and bias correction, with D. Zosso, J. Stevick, N. Takaki, M. Weiss, L. S. Slaughter, H. H. Cao, P. S. Weiss, and A. L. Bertozzi. AIMS Inverse Problems and Imaging [link]

Teaching

I am teaching Math 361S: Mathematical Numerical Analysis in Spring 2025 Canvas page