Chandana Pati, S. M. Mallikarjunaiah
Neural networks can learn and internalize real physical laws: When trained on material behavior data, neural networks successfully captured established physics principles like the Mooney-Rivlin hyperelastic model and path-dependent plasticity, demonstrating that AI systems can discover genuine scientific relationships rather than just fitting patterns.
Explainability methods can verify AI trustworthiness in scientific applications: By applying techniques like SHAP and gradient-based attribution analysis, researchers confirmed the networks learned physically meaningful features (e.g., identifying plastic strain as the dominant predictor in elastoplasticity), providing concrete evidence that the "black box" was making decisions based on scientifically valid reasoning.
Different neural network architectures encode physics differently: Recurrent networks (LSTMs and GRUs) successfully captured time-dependent material behaviors by organizing information hierarchically across layers—with different layers encoding instantaneous versus delayed responses—showing that architecture choices matter for physics-consistent AI.
Validation frameworks are essential before deploying AI in engineering: This work demonstrates a systematic approach to validating that surrogate models don't just predict accurately but do so for the right physical reasons, which is critical before using AI to replace traditional physics-based simulations in real engineering applications.
Synthetic data combined with explainability can reduce validation costs: By training on synthetically generated data and then using XAI methods to confirm physical consistency, this approach offers a pathway to validate AI systems more efficiently than traditional methods, potentially accelerating responsible AI adoption in materials science.
This paper presents a Physics-\textit{Explainable AI} (XAI) framework to validate and interpret neural networks for the constitutive modeling of solid materials. The study bridges the gap between data-driven models and continuum mechanics by applying a suite of explainability methods to neural networks trained on three distinct material behaviors: hyperelasticity (\textit{Mooney-Rivlin}), elastoplasticity (\textit{Chaboche}), and viscoelasticity (\textit{Fractional Zener}). First, high-fidelity surrogate models, including dense feed-forward networks, LSTMs, and GRUs, are trained on synthetically generated data to accurately capture complex material responses. The core of the work then employs XAI techniques to "open the black box" and confirm that the networks learn physically meaningful principles. For hyperelasticity, gradient-based attributions (\textit{Grad Input} (GI)) successfully match the analytical tangent modulus, proving the network learned material stiffness. For elastoplasticity, \textit{SHapley Additive exPlanations} (SHAP) and \textit{Principal Component Analysis} (PCA) demonstrate the \textit{Recurrent Neural Network} (RNN) internalizes path-dependent memory, with SHAP identifying \textit{plastic strain} as the dominant feature governing the stress prediction. For viscoelasticity, latent-space and wavelet analyses of the \textit{Gated Recurrent Unit. } GRU layers reveal a clear temporal hierarchy, with different layers encoding instantaneous elastic response, intermediate relaxation, and long-term fractional memory. Ultimately, the study demonstrates that the XAI framework can verify that the neural networks are not merely curve-fitting but are, in fact, learning the underlying physical mechanisms of stiffness, history-dependence, and temporal damping.
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