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.

Data-driven methods in multiscale modeling

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, Jeff Calder, Attraction-Repulsion Swarming: A Generalized Framework of t-SNE via Force Normalization and Tunable Interactions, arXiv:2411.10617

Jingcheng Lu, Kunlun Qi, Li Wang, Jeff Calder, Continuous data assimilation for hydrodynamics: consistent discretization and application to moment recovery, arXiv:2409.03872

Jingcheng Lu, Eitan Tadmor, Anil Zenginoglu, Swarm-Based Gradient Descent Method for Non-Convex Optimization, Communications of the AMS (2024).

We developed a novel swarm-based approach for non-convex optimizations. The key idea is to introduce cross-individual communications such that the best agent would progressively dominate the search, helping the crowd escape from local minima.

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

We revisited the theoretical TVD stability of the smooth van Albada slope limiter.

Jingcheng Lu, Eitan Tadmor, Hydrodynamic Alignment with Pressure II. Multi-species, Quarterly of Applied Mathematics.

We provide the very first proof of hydrodynamic alignment of multi-species systems without assuming specific closure of entropic pressures.

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

We proposed a (nominally) unconditionally non-oscillatory Limited-DIRK3 scheme for conservation laws and convection-diffusion equations.