LS-RJF for Inverse Thermal Homogenization: Identification of Material Parameters in Fiber-Reinforced Composites

Abstract

Identifying the constituent thermal conductivities of fiber-reinforced composites from macroscopic measurements is a fundamental inverse problem in materials science, with direct applications in thermal management and non-destructive characterization. We present the first neural network-based framework for inverse thermal homogenization of fiber-reinforcedcomposites. The Residual–Jacobian Framework for Lippmann–Schwinger equation (LS-RJF), originally introduced by the authors for direct homogenization [1], is extended here to the inverse problem of simultaneously identifying the thermal conductivities of the fiber (kf ) and matrix (km) phases from observed effective conductivity tensors Kobseff . The inverse LS-RJF formulates the identification as a physics-informed residual system coupling the Lippmann–Schwinger equation with neural networks, where the Jacobian with respect to the material parameters is derived analytically, yielding exact quadratic convergence without automatic differentiation for the material parameter columns, thereby avoiding memory explosion. To resolve the under determination inherent to single-microstructure identification, two Representative Volume Elements (RVEs) with distinct fiber volume fractions are employed simultaneously, providing an overdetermined system of six equations for two unknowns.Observed data are generated from three independent sources Fast Fourier Transform (FFT, Moulinec–Suquet), Finite ElementMethod (FEniCS), and Mori–Tanaka (Eshelby)—demonstrating robustness of the identified parameters with respect to thedata source. Nine parametric series reveal the capabilities and limitations of the framework across a broad range of microstruc-ture configurations. Comparison with a FEM-based inverse identification using an analytical Jacobian—itself inspired bythe RJF framework—with observed data from both FFT and Mori–Tanaka (Eshelby) shows that LS-RJF and FEniCS exhibitcomplementary accuracy depending on the data source: LS-RJF achieves superior identification of kf from FFT observations,while FEniCS outperforms from Mori–Tanaka observations. To the best of our knowledge, this is the first neural network framework to simultaneously identify constituent conductivities kf and km by directly minimizing the residual of the Lippmann–Schwinger integral equation, without labeled training data or a separate outer optimization loop.