Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

doi:10.1007/s10483-023-2995-8

Applied Mathematics and Mechanics (English Edition) ›› 2023, Vol. 44 ›› Issue (7): 1039-1068.doi: https://doi.org/10.1007/s10483-023-2995-8

Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

W. WU^1,2, M. DANEKER³, M. A. JOLLEY^1,2, K. T. TURNER⁴, L. LU³

1. Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, PA 19104, U.S.A.;
2. Division of Pediatric Cardiology, Children's Hospital of Philadelphia, Philadelphia, PA 19104, U.S.A.;
3. Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104, U.S.A.;
4. Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, U.S.A.

收稿日期:2022-11-28 修回日期:2023-05-09 出版日期:2023-07-01 发布日期:2023-07-05
通讯作者: L. LU, E-mail:lulu1@seas.upenn.edu

Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

W. WU^1,2, M. DANEKER³, M. A. JOLLEY^1,2, K. T. TURNER⁴, L. LU³

1. Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, PA 19104, U.S.A.;
2. Division of Pediatric Cardiology, Children's Hospital of Philadelphia, Philadelphia, PA 19104, U.S.A.;
3. Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104, U.S.A.;
4. Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, U.S.A.

Received:2022-11-28 Revised:2023-05-09 Online:2023-07-01 Published:2023-07-05
Contact: L. LU, E-mail:lulu1@seas.upenn.edu

摘要/Abstract

摘要： Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the material is highly nonlinear in nature, as is common in biological tissue. In this work, we identify unknown material properties in continuum solid mechanics via physics-informed neural networks (PINNs). To improve the accuracy and efficiency of PINNs, we develop efficient strategies to nonuniformly sample observational data. We also investigate different approaches to enforce Dirichlet-type boundary conditions (BCs) as soft or hard constraints. Finally, we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space. The estimated material parameters achieve relative errors of less than 1%. As such, this work is relevant to diverse applications, including optimizing structural integrity and developing novel materials.

关键词: solid mechanics, material identification, physics-informed neural network (PINN), data sampling, boundary condition (BC) constraint

Abstract: Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the material is highly nonlinear in nature, as is common in biological tissue. In this work, we identify unknown material properties in continuum solid mechanics via physics-informed neural networks (PINNs). To improve the accuracy and efficiency of PINNs, we develop efficient strategies to nonuniformly sample observational data. We also investigate different approaches to enforce Dirichlet-type boundary conditions (BCs) as soft or hard constraints. Finally, we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space. The estimated material parameters achieve relative errors of less than 1%. As such, this work is relevant to diverse applications, including optimizing structural integrity and developing novel materials.

Key words: solid mechanics, material identification, physics-informed neural network (PINN), data sampling, boundary condition (BC) constraint

中图分类号:

W. WU, M. DANEKER, M. A. JOLLEY, K. T. TURNER, L. LU. Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(7): 1039-1068.

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Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

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