Research Interests

1. Machine Learning for Multiscale Modeling

Data-driven methods for coarse-grained molecular dynamics, Mori–Zwanzig formulations, generalized Langevin equations, state-dependent memory, and model reduction.

2. Scientific Machine Learning and Numerical Algorithms

Deep mixed residual methods, deep-learning-based discontinuous Galerkin methods, reproducing activation functions, and high-dimensional scientific computing.

3. Gradient-Free Optimization and Sampling

Consensus-based optimization and sampling, stochastic optimal control, and gradient-free methods for complex multimodal problems.

Selected Publications

1. Liyao Lyu and Huan Lei, “On the Generalization Ability of Coarse-Grained Molecular Dynamics Models for Nonequilibrium Processes,” Multiscale Modeling & Simulation, 2025.

2. Liyao Lyu and Jingrun Chen, “Consensus Based Stochastic Optimal Control,” Proceedings of the 42nd International Conference on Machine Learning (ICML), 2025.

3. Senwei Liang, Liyao Lyu, Chunmei Wang, and Haizhao Yang, “Reproducing Activation Function for Deep Learning,” Communications in Mathematical Sciences, 2024.

4. Liyao Lyu and Huan Lei, “Construction of Coarse-Grained Molecular Dynamics with Many-Body Non-Markovian Memory,” Physical Review Letters 131, 177301, 2023.

5. Jingrun Chen, Shi Jin, and Liyao Lyu, “A Deep Learning Based Discontinuous Galerkin Method for Hyperbolic Equations with Discontinuous Solutions and Random Uncertainties,” Journal of Computational Mathematics, 2023.

6. Liyao Lyu, Zhen Zhang, Minxin Chen, and Jingrun Chen, “MIM: A Deep Mixed Residual Method for Solving High-order Partial Differential Equations,” Journal of Computational Physics, 2022.

Full publication list: https://lyuliyao.com/publication.html