The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying the full-field heterogeneous elastic properties of soft materials using traditional computational and engineering approaches is fundamentally challenging due to difficulties in estimating local stress fields. Recently, there has been a growing interest in using data-driven models to learn full-field mechanical responses such as displacement and strain from experimental or synthetic data. However, research studies on inferring the full-field elastic properties of materials, a more challenging problem, are scarce, particularly for large deformation, hyperelastic materials. Here, we propose a novel approach to identify the elastic modulus distribution in nonlinear, large deformation hyperelastic materials utilizing physics-informed neural networks (PINNs). We evaluate the prediction accuracies and computational efficiency of PINNs, informed by mechanic features and principles, across three synthetic materials with structural complexity that closely resemble real tissue patterns, such as brain tissue and tricuspid valve tissue. Our improved PINN architecture accurately estimates the full-field elastic properties, with relative errors of less than 5% across all examples. This research has significant potential for advancing our understanding of micromechanical behaviors in biological materials, impacting future innovations in engineering and medicine.

翻译：生物组织的非均匀微力学特性在医学与工程等多个领域具有深远影响。然而，由于局部应力场估算困难，利用传统计算与工程方法识别软材料的全场非均匀弹性特性面临根本性挑战。近年来，基于数据驱动的模型从实验或合成数据中学习全场力学响应（如位移与应变）的研究日益受到关注。然而，关于推断材料全场弹性特性（一个更具挑战性的问题）的研究仍十分稀少，尤其是在大变形超弹性材料领域。本文提出了一种新方法，利用物理信息神经网络（PINNs）识别非线性大变形超弹性材料中的弹性模量分布。通过力学特征与原理的约束，我们评估了PINNs在三种结构复杂度接近真实组织模式（如脑组织与三尖瓣组织）的合成材料中的预测精度与计算效率。改进后的PINN架构能够准确估算全场弹性特性，所有示例的相对误差均低于5%。本研究在深化对生物材料微力学行为的理解方面具有重要潜力，并将影响未来工程与医学领域的创新。