Bridging Scientific Machine Learning methods with physics-based models in Computational Cardiology
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The development of computational models in the cardiovascular field is a challenging research area, where the need for accurate responses in short timeframes conflicts with the complexity of the underlying physical processes and the great anatomical and functional variability among patients. In this context, physics-based models require long times and computational resources for the numerical discretization of multi-scale and multi-physics systems of differential equations, while standard data-driven methods rarely achieve high accuracy and generalization capabilities. In this talk, we present scientific machine learning methods that integrate physical knowledge with data-driven techniques to accelerate the evaluation of differential models and address many-query problems - such as sensitivity analysis, robust parameter estimation, and uncertainty quantification - in cardiovascular applications. To speed up input-output evaluations, we develop emulators of time-dependent processes capable of predicting spatial outputs and accounting for geometric variability from patient to patient. Our methods also enable data-driven learning of mathematical models for the slow-scale remodeling associated with processes whose fast scale is well characterized by physics-based models. Numerical results demonstrate that these scientific machine learning methods enhance efficiency and accuracy in approximating quantities of interest, as well as in solving parameter estimation and uncertainty quantification problems.
