Research Interests

Collective Dynamics of Self-Organized Systems

I am interested in the models describing the collective behavior of self-propelled particles, such as the Cucker-Smale dynamics and p-alignment systems.

I'm also interested in the interplays between collective dynamics and data analysis, including the swarm-based algorithms for non-convex global optimizations and the applications to dimension reduction algorithms for data visualization.

Multiscale modeling and optimal control of plasma

I am interested in the data-driven methods for multiscale reduced-order modeling. In particular, I'm interested in the hydrodynamic moment recovery/closure problems assisted with data arising from plasma physics and the potential applications to instability control.

Numerical Methods for PDEs

I am interested in the numerical methods for nonlinear conservation laws & convection-diffusion equations arising from computational fluid dynamics.

Publications

Jingcheng Lu, Li Wang, Jeff Calder, Dynamical feedback control with operator learning for the Vlasov-Poisson system, in preparation

Jingcheng Lu, Li Wang, Jeff Calder, Controlling instability in the Vlasov-Poisson system through moment-based optimization, [arxiv]

Jingcheng Lu, Kunlun Qi, Li Wang, Jeff Calder, Continuous data assimilation for hydrodynamics: consistent discretization and application to moment recovery, Journal of Computational Physics, page 114199, 2025. [arxiv], [journal]

Jingcheng Lu, Jeff Calder, Attraction-Repulsion Swarming: A Generalized Framework of t-SNE via Force Normalization and Tunable Interactions, Philosophical Transactions of the Royal Society A, 383(2298):20240234, 2025. [arxiv], [journal]

Jingcheng Lu, Eitan Tadmor, Anil Zenginoglu, Swarm-Based Gradient Descent Method for Non-Convex Optimization, Communications of the American Mathematical Society, 2024, 4(17): 787-822. [journal]

Jingcheng Lu, Eitan Tadmor, Revisiting High-Resolution Schemes with van-Albada Slope Limiter, Communications on Applied Mathematics and Computation (2024): 1-30. [arxiv], [journal]

Jingcheng Lu, Eitan Tadmor, Hydrodynamic Alignment with Pressure II. Multi-species, Quarterly of Applied Mathematics 81.2 (2023): 259-279. [arxiv], [journal]

Jingcheng Lu, James D.Baeder, The High Resolution L-DIRK3 Scheme for Conservation Laws, AIAA SCITECH 2022 Forum, 2022, p. 1075. [arxiv], [conference]