报告题目：Machine Learning based solutions of PDE with applications in engineering and mechanics

报 告 人：Timon Rabczuk, Professor

报告人所在单位：Bauhaus University Weimar

报告日期：2025年5月26日

报告时间：14:00

报告地点：光华楼东辅楼 103会议室

报告摘要：This presentation highlights recent advancements in Scientific Machine Learning (SciML) for modeling physical systems governed by partial differential equations (PDEs). It will first compare and present an overview of SciML approaches including Physics-Informed Neural Networks (PINNs), Deep Energy Methods (DEMs) and Neural Operators for analyzing mechanical problems. Then, two advanced neural operator frameworks will be introduced: one for static problems and one for dynamic problems. For static PDEs, the Variational Physics-Informed Neural Operator (VINO) combines the generalization power of neural operators with the accuracy and stability of energy-based formulations. VINO minimizes the variational form of PDEs rather than pointwise residuals, enabling training without labeled data and significantly improving performance over existing machine learning methods, particularly as mesh resolution increases. Its element-based discretization enhances scalability and physical fidelity, addressing key limitations in existing physics-informed models. For dynamic problems, we present the so-called Step Aware Neural Operator (SANO), designed for efficient multi-step predictions in time-dependent PDEs. SANO incorporates time-step-specific projections and message-passing mechanisms, capturing long-term dependencies while avoiding error accumulation, and demonstrates strong performance across a range of phase field models. Finally, a hybrid approach will be proposed that uses the output of neural operators as an initial guess for iterative solvers, significantly improving the computational time for Challenging problems by combining data-driven prediction with the robustness of numerical methods.

个人简介：Timon Rabczuk is the Chair Professor of Computational Mechanics at Bauhaus University Weimar. He is a member of the European Academy of Sciences and Art, Academia Europea and Europe Academy of Science. His key research area is computational mechanics, Al for mechanics and advanced computational materials design. Prof. Rabczuk obtained his doctoral degree from Karlsruhe Institute of Technology (KIT) in Germany in 2002 which is followed by his postdoctoral research with Prof. Ted Belytschko in University of Northwestern. He became the Chair Professor in Computational Mechanics in his current institution in 2009. He has published so far 3 academic monographs, over 700 SCI papers, with H-Index of 120, attracting over 50000 times citations in Web of Science core collection. He has been awarded with the ERC Consolidator Grant from European Union, Feodor-Lynen Fellow from Humboldt Foundation and was listed as Highly Cited Researcher in both ‘Engineering' and ‘Computer Science’ in ISI Web of Science.

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