POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium - Fresca, Stefania; Manzoni, Andrea; Dedè, Luca; Quarteroni, Alfio (Frontiers in Physiology, 2021)
The numerical simulation of multiple scenarios easily become computationally prohibitive for cardiac electrophysiology (EP) problems may become infeasible if relying on usual high-fidelity, full order models (FOMs). Likewise, the use of traditional reduced order models (ROMs) for parametrized PDEs to speed up the solution of the aforementioned problems can be problematic. This is primarily due to the strong variability characterizing the solution set, as well as to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To enhance ROM efficiency, we proposed a new generation of non-intrusive, nonlinear ROMs, based on deep learning (DL) algorithms, such as convolutional, feedforward and autoencoder neural networks. In the proposed DL-ROM, both the nonlinear solution manifold and the nonlinear reduced dynamics used to model the system evolution on that manifold, can be learnt in a non-intrusive way thanks to DL algorithms trained on a set of full order model (FOM) snapshots. DL-ROMs were shown to be able to accurately capture complex front propagation processes, both in physiological and pathological cardiac EP, very rapidly once neural networks were trained, however at the expense of huge training costs. In this work, we show that performing a prior dimensionality reduction on FOM snapshots through randomized proper orthogonal decomposition (POD) enables to speed up training times, and decrease the network complexity. Accuracy and efficiency of this strategy, which we refer to as POD-DL-ROM, are assessed in the context of cardiac EP on an idealized left atrium (LA) geometry and considering snapshots arising from a NURBS (non-uniform rational B-splines)-based Isogeometric Analysis (IGA) discretization. Once the ROMs have been trained, POD-DL-ROMs can efficiently solve, both physiological and pathological cardiac EP problems, for any new scenario, in real-time, even in extremely challenging contexts such as those featuring circuit re-entries, that are among the factors triggering cardiac arrhythmias.