AI for PDEs in solid mechanics: A review

WANG Yizheng; ZHUANG Xiaoying; TIMON Rabczuk; LIU Yinghua

doi:10.6052/1000-0992-24-016

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Article Navigation > Advances in Mechanics > 2024 > Accepted Manuscript

Wang Y Z, Zhuang X Y, Timon R, Liu Y H. AI for PDEs in solid mechanics: A review. Advances in Mechanics, 2024, 54(4): 1-57 doi: 10.6052/1000-0992-24-016

Citation:

Wang Y Z, Zhuang X Y, Timon R, Liu Y H. AI for PDEs in solid mechanics: A review. Advances in Mechanics, 2024, 54(4): 1-57 doi: 10.6052/1000-0992-24-016

Wang Y Z, Zhuang X Y, Timon R, Liu Y H. AI for PDEs in solid mechanics: A review. Advances in Mechanics, 2024, 54(4): 1-57 doi: 10.6052/1000-0992-24-016

Citation:

Wang Y Z, Zhuang X Y, Timon R, Liu Y H. AI for PDEs in solid mechanics: A review. Advances in Mechanics, 2024, 54(4): 1-57 doi: 10.6052/1000-0992-24-016

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AI for PDEs in solid mechanics: A review

doi: 10.6052/1000-0992-24-016 cstr: 32046.14.1000-0992-24-016

1.
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
2.
Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China
3.
Chair of Computational Mechanics, Institute of Structural Mechanics, Bauhaus University Weimar, Weimar 99423, Germany

More Information

Corresponding author: yhliu@mail.tsinghua.edu.cn
Received Date: 2024-05-06
Accepted Date: 2024-06-26

Available Online: 2024-07-09

Abstract

Abstract

In recent years, deep learning has become ubiquitous and is empowering various fields. In particular, the combination of artificial intelligence and traditional science (AI for science, AI4Science) has attracted widespread attention. In the field of AI4Science, the use of artificial intelligence algorithms to solve partial differential equations (AI4PDEs) has become the focus of computational mechanics research. The core of AI4PDEs is to fuse data with equations and can solve almost any PDEs. Due to the advantages of AI4PDEs in data fusion, computational efficiency using AI4PDEs is usually increased by tens of thousands of times compared to traditional algorithms. Therefore, this article comprehensively reviews the research on AI4PDEs, summarizes the existing AI4PDEs algorithms and theories, discusses its application in solid mechanics, including forward and inverse problems, and outlines future research directions, especially the foundation model of computational mechanics. Existing algorithms of AI4PDEs include physics-informed neural networks (PINNs), deep energy methods (DEM), operator learning, and (physics-informed neural operator, PINO). AI4PDEs has numerous applications in scientific computing, and this paper focuses on application of AI4PDEs in the forward and inverse problems of solid mechanics. The forward problems include linear elasticity, elasto-plasticity, hyperelasticity, and fracture mechanics; while the inverse problems encompass the identification of material parameters, constitutive laws, defect recognition, and topology optimization. AI4PDEs represents a novel method of scientific simulation, which offers approximate solutions for specific problems by leveraging large datasets and then fine-tunes according to the specific physical equations, avoiding the need to start calculations from scratch as traditional algorithms do. Thus, AI4PDEs is a prototype for the foundation model of computational mechanics in the future, capable of significantly accelerating traditional numerical methods. We believe that utilizing artificial intelligence to empower scientific computing is not only a vital direction for the future of computation but also a dawn of humanity in scientific research, laying the foundation for mankind to reach new heights in scientific development.
- PINNs,
- operator learning,
- computational mechanics,
- AI for PDEs,
- solid mechanics

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