报告承办单位: 数学与统计学院

报告内容:Neural network (NN) solvers for partial differential equations (PDE) have been widely used in simulating complex systems in various scientific and engineering fields. However, most existing NN solvers mainly focus on satisfying the given PDEs, without explicitly considering intrinsic physical properties such as mass conservation or energy dissipation. This limitation can result in unstable or nonphysical solutions, particularly in long-term simulations. To address this issue, we propose Sidecar, a novel framework that enhances the accuracy and physical consistency of existing NN solvers by incorporating structure-preserving knowledge. This framework builds upon our previously proposed TDSR-ETD method for solving gradient flow problems, which satisfies discrete analogues of the energy-dissipation laws by introducing a time-dependent spectral renormalization (TDSR) factor. Inspired by this approach, our Sidecar framework parameterizes the TDSR factor using a small copilot network, which is trained to guide the existing NN solver in preserving physical structure. This design allows flexible integration of the structure-preserving knowledge into various NN solvers and can be easily extended to different types of PDEs. Our experimental results on a set of benchmark PDEs demonstrate that it improves the existing neural network solvers in terms of accuracy and consistency with structure-preserving properties.

报告人姓名:乔中华

报告人所在单位:香港理工大学

报告人职称/职务及学术头衔: 教授, 博士生导师

报告时间:2025年5月10日下午14:30—18:30

报告地点:云塘校区理科楼A212

报告人简介:香港理工大学应用数学系讲座教授，国家级高层次人才，中科院数学与系统科学研究院--香港理工大学应用数学联合实验室港方副主任，中国工业与应用数学学会理事，中国数学会计算数学分会副理事长。主要从事微分方程数值算法设计及分析，近年来的研究工作集中在相场方程的数值模拟及计算流体力学的高效算法。至今在SIAM Rev.，SIAM J. Numer. Anal.，SIAM J. Sci. Comp.，Math Comp.，J. Comp. Phys.，等计算数学顶级期刊上发表学术论文80余篇，文章被合计引用3000余次。2013年获香港研究资助局杰出青年学者奖，2018年获得香港数学会青年学者奖，2020年获得香港研究资助局研究学者奖。