We present a new, computationally efficient framework to perform forward uncertainty quantification (UQ) in cardiac electrophysiology. We consider the monodomain model to describe the electrical activity in the cardiac tissue, coupled with the Aliev-Panfilov model to characterize the ionic activity through the cell membrane. We address a complete forward UQ pipeline, including both: (i) a variance-based global sensitivity analysis for the selection of the most relevant input parameters, and (ii) a way to perform uncertainty propagation to investigate the impact of intra-subject variability on outputs of interest depending on the cardiac potential. Both tasks exploit stochastic sampling techniques, thus implying overwhelming computational costs because of the huge amount of queries to the high-fidelity, full-order computational model obtained by approximating the coupled monodomain/Aliev-Panfilov system through the finite element method. To mitigate this computational burden, we replace the full-order model with computationally inexpensive projection-based reduced-order models (ROMs) aimed at reducing the state-space dimensionality. Resulting approximation errors on the outputs of interest are finally taken into account through artificial neural network (ANN)-based models, enhancing the accuracy of the whole UQ pipeline. Numerical results show that the proposed physics-based ROMs outperform regression-based emulators relying on ANNs built with the same amount of training data, in terms of both numerical accuracy and overall computational efficiency.

中文翻译：

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通过降阶建模和机器学习在心脏电生理学中实现前向不确定性量化和灵敏度分析

我们提出了一个新的、计算效率高的框架来在心脏电生理学中执行前向不确定性量化 (UQ)。我们考虑使用单域模型来描述心脏组织中的电活动，结合 Aliev-Panfilov 模型来表征通过细胞膜的离子活动。我们解决了一个完整的前向 UQ 管道，包括：（i）用于选择最相关输入参数的基于方差的全局敏感性分析，以及（ii）一种执行不确定性传播的方法，以根据心脏电位研究受试者内部变异性对感兴趣输出的影响。这两个任务都利用了随机采样技术，因此，由于对通过有限元方法逼近耦合的单域/Aliev-Panfilov 系统而获得的高保真全阶计算模型的大量查询，这意味着压倒性的计算成本。为了减轻这种计算负担，我们用计算成本低廉的基于投影的降阶模型（ROM）替换全阶模型，旨在降低状态空间维度。最终通过基于人工神经网络 (ANN) 的模型将感兴趣的输出产生的近似误差考虑在内，从而提高整个 UQ 管道的准确性。