Effective Data Sampling Strategies and Boundary Condition Constraints of Physics-Informed Neural Networks for Identifying Material Properties in Solid Mechanics

TL;DR

This paper enhances physics-informed neural networks for material property identification in solid mechanics by developing nonuniform data sampling strategies and boundary condition enforcement methods, achieving high accuracy across various material models.

Contribution

The paper introduces novel data sampling and boundary condition enforcement techniques to improve PINNs' accuracy and efficiency in identifying nonlinear material properties.

Findings

Relative errors less than 1% in parameter estimation

Effective handling of diverse solid mechanics problems

Improved PINN performance with proposed strategies

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 developed efficient strategies to nonuniformly sample observational data. We also investigated different approaches to enforce Dirichlet boundary conditions 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.