Federated Scientific Machine Learning Framework for Multi-Scale Inverse Parameter Identification: Application to Nonlocal Strain Gradient Plasticity
Abstract
Abstract Size-dependent plasticity in micro-scale experiments cannot be adequately described by classical plasticity, while calibration of nonlocal strain gradient plasticity (SGP) models remains challenging due to sparse and geometry-dependent experimental data. In this study, we develop, for the first time, an inverse federated scientific machine learning (I-FedSciML) framework for identifying parameters of a size-dependent nonlocal SGP model without centralizing raw experimental data. Each experimental curve is treated as an independent client characterized by its own geometry, microstructural length scale, loading mode, and measured response. A geometry-conditioned inverse neural network maps client descriptors to the SGP parameter vector, which is then embedded in differentiable micro-bending and micro-torsion SGP forward models. We validated the framework using micro-scale experimental datasets for annealed nickel beams, LIGA nickel foils, aluminum beams, and copper wires. The identified client-specific parameters accurately reproduce experimental moment–curvature and torque–twist responses, with R 2 values of 0.982–0.990 for annealed nickel, 0.925–0.974 for LIGA nickel, 0.898–0.904 for aluminum, and 0.985–0.997 for copper torsion. Noise sensitivity analysis at 1%, 2.5%, 5%, and 10% showed that although parameter bias, prediction uncertainty, and the final loss plateau increase with noise level, the framework maintains reliable predictive capability even at 10% noise.…
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