MD-PINNs: a domain decomposition strategy for inverse identification of property distributions in heterogeneous composites

Accurately characterizing the spatial property distributions of heterogeneous materials remains a formidable challenge in both theoretical and engineering science. To address this issue, the present work proposes a multiple domain physics-informed neural network (MD-PINNs) framework that leverages prior physics-constrained optimization procedures. The method simultaneously determines the property distributions of heterogeneous composites, namely, the longitudinal and transverse moduli, in-plane shear modulus, and major Poisson’s ratio, by establishing a mapping from spatial coordinates (input) to the corresponding full-field stresses (output). The framework incorporates a domain decomposition strategy, partitioning the calculation domain according to the material geometry and assigning independent subnetworks to each subdomain. Additional regularization terms (interface continuity conditions) are employed to describe the connecting relations between different materials. A physics-augmented multi-objective loss function is constructed, incorporating equilibrium equations, constitutive relations, boundary conditions, and interface constraints. Using full-field strain measurements from one single experiment, the proposed approach enables coupled material property identification and full-field stress reconstruction through minimizing a shared loss function. Validation through simulated tensile experiments on an anisotropic composite open-hole lamina demonstrates the accuracy and reliability of MD-PINNs, yielding remarkably low errors below 0.75%. Comparative evaluation against existing models shows that the proposed approach achieves a mean relative error of merely 0.438%, which represents reductions in identification errors by approximately 18.7-fold and 10.2-fold relative to the general PINN-driven framework (8.191%) and the FEMU-based technique (4.470%), respectively. Furthermore, the framework exhibits strong robustness against Gaussian noise and variations in initial parameter values, with minimal sensitivity to network configurations (error < 3.1%). The proposed MD-PINNs framework is inherently generic, robust, stable, and can be readily extended to other anisotropic heterogeneous systems (e.g., soils, concretes, and biomaterials) beyond the case validated herein, establishing itself as a powerful computational tool for advanced material characterization, damage evolution, and structure-integrity assessment.