I am an Associate Professor in the Department of Computational Mathematics, Science, and Engineering at Michigan State University, with a joint appointment in the Department of Statistics and Probability. I received my Ph.D. in Applied Mathematics from Brown University under supervision of Prof. George Karniadakis.

My research lies at the intersection of scientific machine learning, multiscale modeling, and numerical analysis. I develop mathematical and computational methods for constructing partial differential equations (PDEs) and stochastic models of multiscale or high-dimensional problems from microscopic first-principles descriptions. In particular, my work focuses on the characterization of admissible model classes that preserve conservation laws, dissipative structure, and physical constraints. I construct representations that enable fast numerical algorithms and develop learning methods for identifying their parametric form from microscopic laws and data. The central goal is to construct physically interpretable reduced models that retain microscopic model fidelity and admit stable, efficient numerical approximation. My recent work includes multiscale fluid dynamics, kinetic transport and coarse-grained molecular systems, particularly in regimes where conventional closures shows limitations.

Research Interests

• Multi-scale and stochastic modeling
• Numerical methods for PDEs
• Scientific machine-learning
• Kinetic equations
• Fluid physics

Selected publications

• Y. Zhao and H. Lei. Fast spectral separation method for kinetic equation with anisotropic non-stationary collision operator retaining micro-model fidelity, Journal of Computational Physics, 565, 115205, 2026 [link].

• L. Lyu and H. Lei. Consensus-Based Adaptive Sampling and Approximation for High-Dimensional Energy Landscapes. SIAM Journal on Scientific Computing, 48(5): B751-B775, 2026 [link].

• Y. Zhao, J. Burby, A. Christlieb and H. Lei. Data-Driven Construction of a Generalized Kinetic Collision Operator from Molecular Dynamics. Phys. Rev. Lett., 135, 185101, 2025 [link].

• L. Lyu and H. Lei. On the generalization ability of coarse-grained molecular dynamics models for non-equilibrium processes. SIAM Multiscale Model. Simul., 23 (2): 816-837, 2025 [link].

• P. Ge, Z. Zhang, and H. Lei. Data-driven learning of the generalized Langevin equation with state-dependent memory. Phys. Rev. Lett. 133:077301, 2024. [link].

• W. E, H. Lei, P. Xie, and L. Zhang. Machine learning-assisted multi-scale modeling. Journal of Mathematical Physics, 64(7):071101, 2023 [link].

• H. Lei, N. A. Baker, and X. Li. Data-driven parameterization of the generalized Langevin equation. Proc. Natl. Acad. Sci. 113 (50):14183–14188, 2016 [link].