POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium

Abstract

The numerical simulation of multiple scenarios easily becomes computationally prohibitive for cardiac electrophysiology (EP) problems 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 and 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 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 study, we show that performing a prior dimensionality reduction on FOM snapshots through randomized proper orthogonal decomposition (POD) enables to speed up training times and to decrease networks 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.

Few-shot Generation of Personalized Neural Surrogates for Cardiac Simulation via Bayesian Meta-Learning

“…Alternative neural surrogates of cardiac simulations [5,17,13] are also related, although existing works are either 2D on image grids or on atria [13]. Once learned, they all have to be separately optimized to a subject's data for personalized predictions -the latter we have not seen in published works.…”

“…In parallel, advances in deep learning (DL) have led to a surge of interests in developing efficient neural approximations of expensive scientific simulations [18]. Progress in building neural surrogates for cardiac electrophysiology simulations, however, has been relatively limited: initial successes have been mainly demonstrated in 2D settings [5,17] with a recent work reporting 3D results on the left atrium [13]. A significant challenge arises from the dependence of these simulations on various model parameters such as material properties, denoted here as θ.…”

Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models

“…With the same spirit, POD-DL-ROMs [30] enable a more efficient training stage and the use of much larger FOM dimensions, without affecting network complexity, thanks to a prior dimensionality reduction of FOM snapshots through randomized POD (rPOD) [31], and a multi-fidelity pretraining stage, where different models (exploiting, e.g., coarser discretizations or simplified physical models) can be combined to iteratively initialize network parameters. This latter strategy has proven to be effective for instance in the real-time approximation of cardiac electrophysiology problems [32,33] and problems in fluid dynamics [34].…”

A Cost-Efficient Approach towards Computational Fluid Dynamics Simulations on Quantum Devices

“…Truncation-based reduction techniques tend to preserve the input-output dynamics of a system for a certain set of output states while removing any unnecessary details of the system that are irrelevant for the calculation of that given output set [24]. Lastly, there is an increasing number of work towards enhancing deep-learning for model-order reduction where traditional MOR algorithms could be problematic in capturing the nonlinear input-output dynamics of the system due to the strong variability characterizing the solution set [25][26][27].…”