研究方向

1. 多尺度建模与机器学习

发展数据驱动方法以提升自下而上的多尺度建模能力，包括粗粒化分子动力学、Mori–Zwanzig 形式、广义朗之万方程和模型降阶。

2. 科学机器学习与数值算法

研究混合残差方法、深度学习辅助的不连续 Galerkin 方法、再现激活函数，以及偏微分方程的高维数值计算。

3. 无梯度优化与采样

研究基于共识的优化与采样、随机最优控制，以及适用于复杂多峰问题的无梯度计算方法。

代表性论文

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.

完整论文列表：https://lyuliyao.com/publication.html