张瑞丽 博士 (北京交通大学)

唐贻发 研究员

Learning symplectic model reduction based on an approximation theorem of symplectic embeddings

9月24日（周四）16:00-17:00，南楼202

High-dimensional Hamiltonian systems play a central role in many scientific and engineering disciplines, with dynamics that evolve on symplectic manifolds. Although deep learning provides powerful tools for constructing its low-dimensional surrogates from data, the intrinsic symplectic structure is easily destroyed during model reduction. As a result, a standard autoencoder may produce latent coordinates that do not support a Hamiltonian flow, leading to unstable long-time prediction. In this paper, we first establish a universal approximation theorem for symplectic embeddings. And based on the theory, we propose symplecticity-preserving autoencoders (SpAE), in which the decoder is parameterized as a symplectic embedding and the encoder is constructed as the corresponding symplectic projection. This architecture is expressive enough to approximate nonlinear symplectic embeddings and the corresponding symplectic projection, preserves the symplectic structure exactly by construction, and can be trained by standard unconstrained optimization, thereby improving both reconstruction and prediction accuracy. Extensive experiments on high-dimensional lattice and particle systems demonstrate the effectiveness of the proposed method.

报告人简介：张瑞丽，北京交通大学副教授，博士生导师。博士毕业于中国科学院数学与系统科学研究院，长期从事动力系统保结构算法和保结构神经网络的理论与应用研究。已在JCP、PRE、POP、JSC等期刊发表论文30余篇，先后主持中国博士后基金、国家自然科学基金青年和面上项目、主持和参与多个国家重点研发ITER专项。担任中国仿真学会仿真算法委员会委员、中国仿真学会青年工作委员会委员。