핵심 개념
Physics-informed neural networks can accurately estimate the full-field heterogeneous elastic properties of complex biological tissues undergoing large deformations.
초록
This study proposes a physics-informed machine learning approach to identify the elastic modulus distribution in nonlinear, large deformation hyperelastic materials. The authors evaluate the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) on inferring the heterogeneous material parameter maps across three nonlinear materials with structural complexity that closely resemble real tissue patterns, such as brain tissue and tricuspid valve tissue.
The key highlights and insights are:
The authors introduced a physics-informed machine learning approach to discovering the elastic modulus distribution in complex heterogeneous hyperelastic materials that have traditionally been challenging and mathematically ill-posed.
An improved PINN architecture accurately estimates the full-field elastic properties of three hyperelastic constitutive models, with relative errors of less than 5% across all examples.
PINNs have remarkable potential for providing highly accurate parameter estimations using just one data sample, even when there is a high level of noise in training data.
The proposed approach provides a promising method for studying the effect of material heterogeneity in their macroscopic behaviors and the evolution of material micromechanical properties in response to mechanical load, which is highly applicable to studying tissue growth, remodeling, and detecting early mechanical markers of diseases.
Among the 20 network architectures tested, the network architecture IIB, which partitions output variables into separate independent networks based on their shared features, provided the most accurate estimates of the elastic moduli, with average L2 relative errors below 5% across the three examples, while also being the fastest in terms of computational time.
The selected PINN architecture IIB was found to be robust to noise in the reference strain data, maintaining high accuracy even with up to 10% white Gaussian noise.
The PINN architecture IIB was also able to accurately estimate the full-field material parameters for different material constitutive models, including plane stress Neo-Hookean, incompressible Mooney Rivlin, and incompressible Gent, as well as varying levels of biaxial stretch.
통계
The relative errors of the estimated full-field elastic modulus were less than 5% across all three examples.
The maximum pointwise error of the estimated full-field elastic modulus maps was up to 0.32.
인용구
"Physics-informed neural networks have remarkable potential for providing highly accurate parameter estimations using just one data sample, even when there is a high level of noise in training data."
"The proposed approach provides a promising method for studying the effect of material heterogeneity in their macroscopic behaviors and the evolution of material micromechanical properties in response to mechanical load, which is highly applicable to studying tissue growth, remodeling, and detecting early mechanical markers of diseases."