報告承辦單位: 數學與統計學院
報告內容: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.
報告人姓名:喬中華
報告人所在單位:香港理工大學
報告人職稱/職務及學術頭銜: 教授, 博士生導師
報告時間:2025年5月10日下午14:30—18:30
報告地點:云塘校區理科樓A212
報告人簡介:香港理工大學應用數學系講座教授，國家級高層次人才，中科院數學與系統科學研究院--香港理工大學應用數學聯合實驗室港方副主任，中國工業與應用數學學會理事，中國數學會計算數學分會副理事長。主要從事微分方程數值算法設計及分析，近年來的研究工作集中在相場方程的數值模擬及計算流體力學的高效算法。至今在SIAM Rev.，SIAM J. Numer. Anal.，SIAM J. Sci. Comp.，Math Comp.，J. Comp. Phys.，等計算數學頂級期刊上發表學術論文80余篇，文章被合計引用3000余次。2013年獲香港研究資助局杰出青年學者獎，2018年獲得香港數學會青年學者獎，2020年獲得香港研究資助局研究學者獎。