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Computational modeling and experimental/clinical prediction of the complex signals during cardiac arrhythmias have the potential to lead to new approaches for prevention and treatment. Machine-learning (ML) and deep-learning approaches can be used for time-series forecasting and have recently been applied to cardiac electrophysiology. While the high spatiotemporal nonlinearity of cardiac electrical dynamics has hindered application of these approaches, the fact that cardiac voltage time series are not random suggests that reliable and efficient ML methods have the potential to predict future action potentials. This work introduces and evaluates an integrated architecture in which a long short-term memory autoencoder (AE) is integrated into the echo state network (ESN) framework. In this approach, the AE learns a compressed representation of the input nonlinear time series. Then, the trained encoder serves as a feature-extraction component, feeding the learned features into the recurrent ESN reservoir. The proposed AE-ESN approach is evaluated using synthetic and experimental voltage time series from cardiac cells, which exhibit nonlinear and chaotic behavior. Compared to the baseline and physics-informed ESN approaches, the AE-ESN yields mean absolute errors in predicted voltage 6–14 times smaller when forecasting approximately 20 future action potentials for the datasets considered. The AE-ESN also demonstrates less sensitivity to algorithmic parameter settings. Furthermore, the representation provided by the feature-extraction component removes the requirement in previous work for explicitly introducing external stimulus currents, which may not be easily extracted from real-world datasets, as additional time series, thereby making the AE-ESN easier to apply to clinical data. 

The electrical signals triggering the heart's contraction are governed by non-linear processes that can produce complex irregular activity, especially during or preceding the onset of cardiac arrhythmias. Forecasts of cardiac voltage time series in such conditions could allow new opportunities for intervention and control but would require efficient computation of highly accurate predictions. Although machine-learning (ML) approaches hold promise for delivering such results, non-linear time-series forecasting poses significant challenges. In this manuscript, we study the performance of two recurrent neural network (RNN) approaches along with echo state networks (ESNs) from the reservoir computing (RC) paradigm in predicting cardiac voltage data in terms of accuracy, efficiency, and robustness. We show that these ML time-series prediction methods can forecast synthetic and experimental cardiac action potentials for at least 15–20 beats with a high degree of accuracy, with ESNs typically two orders of magnitude faster than RNN approaches for the same network size. 

In this work, we introduce an interval formulation that accounts for uncertainty in supporting conditions of structural systems. Uncertainty in structural systems has been the focus of a wide range of research. Different models of uncertain parameters have been used. Conventional treatment of uncertainty involves probability theory, in which uncertain parameters are modeled as random variables. Due to specific limitation of probabilistic approaches, such as the need of a prior knowledge on the distributions, lack of complete information, and in addition to their intensive computational cost, the rationale behind their results is under debate. Alternative approaches such as fuzzy sets, evidence theory, and intervals have been developed. In this work, it is assumed that only bounds on uncertain parameters are available and intervals are used to model uncertainty. Here, we present a new approach to treat uncertainty in supporting conditions. Within the context of Interval Finite Element Method (IFEM), all uncertain parameters are modeled as intervals. However, supporting conditions are considered in idealized types and described by deterministic values without accounting for any form of uncertainty. In the current developed approach, uncertainty in supporting conditions is modeled as bounded range of values, i.e., interval value that capture any possible variation in supporting condition within a given interval. Extreme interval bounds can be obtained by analyzing the considered system under the conditions of the presence and absence of the specific supporting condition. A set of numerical examples is presented to illustrate and verify the accuracy of the proposed approach.