Robust Inverse Identification of Heterogeneous Hyperelastic Materials Under Large Deformation via Residual-Adaptive Physics-Informed Neural Networks

Characterizing heterogeneous inclusions in hyperelastic materials is critical for diverse fields ranging from soft robotics to medical diagnostics. However, this inverse problem remains challenging as traditional engineering approaches struggle to resolve sharp material interface and strong nonlinearity, while data-driven approaches typically require prior geometric assumptions or accurate stress measurements. To address these limitations, we propose a robust framework based on physics-informed neural networks equipped with residual-based adaptive refinement (AR-PINN). By dynamically appending collocation points according to governing-equation residuals, our method autonomously resolves both the complex inclusion topologies and the relative shear modulus distributions using only sparse Green–Lagrange strain measurements, requiring no prior knowledge regarding the shape or size of inclusions. Extensive numerical studies demonstrate accurate identification and remarkable robustness under large nonlinear deformation, including uniaxial stretching up to (Formula presented.), as well as resistance to measurement noise levels up to 30%. These results firmly establish AR-PINN as a data-efficient, assumption-free, and practical tool for nondestructive characterization and inverse design of heterogeneous soft materials in experimental settings.