Integrating Isogeometric Analysis and Kolmogorov–Arnold Networks for Efficient Cardiac Simulation
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Heart muscle tissue shows highly nonlinear, dynamic thermo-mechanical behaviour. To advance cardiac simulation and personalised medicine, developing accurate and yet computationally efficient models is of great necessity. While traditional phenomenological models, such as the Holzapfel-Ogden framework, remain prevalent, they require extensive manual calibration and face limitations in dynamic, multi-physics scenarios. Recently, data-driven approaches—particularly neural networks—have appeared as promising tools for capturing constitutive relations directly from data. Nevertheless, most current frameworks are either restricted to quasi-static, isotropic problems or are built upon black-box deep neural networks, of which transparency is low. Recently, the newly proposed Kolmogorov–Arnold Networks (KANs) have emerged as a compelling alternative. KANs facilitate the discovery of interpretable mathematical relationships by decomposing a multivariate function into learnable univariate ones. This work evaluates the suitability of KANs for learning the constitutive laws governing the dynamic thermo-mechanical behaviour of the myocardium. To test this, we simulate a simplified model of heart muscle mechanics to generate a high-fidelity dataset. The computation is performed within an Isogeometric Analysis (IGA) framework to enhance geometric approximation. A KAN is then trained as a surrogate model based on these numerical data to assess its capacity for constitutive law discovery. This study demonstrates the potential of KANs as fast, interpretable surrogates for the complex, dynamic thermo-mechanical behaviour of heart muscle tissue.
