Elastoplasticity Informed Kolmogorov–Arnold Networks Using Chebyshev Polynomials

ABSTRACT Multilayer perceptron (MLP) networks are predominantly used to develop data‐driven constitutive models for granular materials. They offer a compelling alternative to traditional physics‐based constitutive models in predicting non‐linear responses of these materials, for example, elastoplasticity, under various loading conditions. To attain the necessary accuracy, MLPs often need to be sufficiently deep or wide, owing to the curse of dimensionality inherent in these problems. To overcome this limitation, we present an elastoplasticity informed Chebyshev‐based Kolmogorov–Arnold network (EPi‐cKAN) in this study. This architecture leverages the benefits of KANs and augmented Chebyshev polynomials, as well as integrates physical principles within both the network structure and the loss function. The primary objective of EPi‐cKAN is to provide an accurate and generalizable function approximation for non‐linear stress‐strain relationships, using fewer parameters compared to standard MLPs. To evaluate the efficiency, accuracy, and generalization capabilities of EPi‐cKAN in modeling complex elastoplastic behavior, we initially compare its performance with other cKAN‐based models, which include purely data‐driven parallel and serial architectures. Furthermore, to differentiate EPi‐cKAN's distinct performance, we also compare it against purely data‐driven and physics‐informed MLP‐based methods. Lastly, we test EPi‐cKAN's ability to predict blind strain‐controlled loading paths that extend beyond the training data distribution to gauge its generalization and predictive capabilities. EPi‐cKAN achieves superior accuracy in predicting stress components and generalizes well under blind strain‐controlled loading paths. It maintains robustness to noise, achieving only 1.52% error in deviatoric stress predictions with 5% noisy data, outperforming MLP models.