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 focuses on computational mathematics and scientific computing. A central aspect of my work is integrating scientific machine learning with numerical analysis to construct accurate and physically interpretable partial differential equation (PDE) and stochastic differential equation (SDE) models of multi-scale or high-dimensional problems directly from first-principle descriptions, where conventional approaches often show limitations. In particular, I am interested in designing learning algorithms that preserve essential mathematical properties of the constructed PDE and SDE models, such as conservation laws, variational structures, and physical constraints.

Research Interests

• Multi-scale and stochastic modeling
• Numerical methods for PDEs
• Scientific machine-learning

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].