Deep learning model for spiral defect chaos (SDC): Prediction of wave dynamics and faithful capture of the self-termination time statistics
POSTER
Abstract
Spiral Defect Chaos (SDC) is a complex dynamical state observed in certain extended physical and biological systems, characterized by the continuous creation and annihilation of spiral waves, or phase singularities (PS). In cardiac tissue, the formation of single or multiple spiral waves is essential to sustaining fatal cardiac arrhythmias. In cardiac tissue models, SDC takes the form of transient chaos where multiple spiral wave patterns eventually self-terminate, with termination times (τ) following an exponential distribution and mean termination time (τmean) scaling exponentially with the area of the tissue.
In this work, we train a deep learning (DL) model using limited data to learn the creation and annihilation of PS, deliberately withholding information about self-termination within SDC. We show that, despite this restricted input, the trained model extrapolates effectively, calculating key SDC characteristics. Our findings reveal that: (i) the model accurately forecasts PS locations and wave dynamics up to a few Lyapunov times, capturing the system’s short-term behavior; (ii) it reproduces the self-termination time distribution, including τmean; and (iii) it generalizes to larger tissue domains than used in training, extending predictive capabilities.
This DL-based approach offers two significant advantages over traditional PDE models: it uses a single variable to represent SDC dynamics rather than requiring multi-variable PDE, and it enables wave dynamics modeling with a time step (∆tDL = 10 ms) 100 times larger than that of standard PDE solvers (∆tPDE = 0.1 ms), achieving notable computational efficiency. Remarkably, even without explicit self-termination events in the training data, the model autonomously identified this behavior, highlighting its ability to capture intrinsic SDC properties. Additionally, a model trained on smaller domain sizes successfully replicates self-termination statistics in larger domains, which further enhances computational savings, making this approach applicable to realistic cardiac electrophysiology models.
In this work, we train a deep learning (DL) model using limited data to learn the creation and annihilation of PS, deliberately withholding information about self-termination within SDC. We show that, despite this restricted input, the trained model extrapolates effectively, calculating key SDC characteristics. Our findings reveal that: (i) the model accurately forecasts PS locations and wave dynamics up to a few Lyapunov times, capturing the system’s short-term behavior; (ii) it reproduces the self-termination time distribution, including τmean; and (iii) it generalizes to larger tissue domains than used in training, extending predictive capabilities.
This DL-based approach offers two significant advantages over traditional PDE models: it uses a single variable to represent SDC dynamics rather than requiring multi-variable PDE, and it enables wave dynamics modeling with a time step (∆tDL = 10 ms) 100 times larger than that of standard PDE solvers (∆tPDE = 0.1 ms), achieving notable computational efficiency. Remarkably, even without explicit self-termination events in the training data, the model autonomously identified this behavior, highlighting its ability to capture intrinsic SDC properties. Additionally, a model trained on smaller domain sizes successfully replicates self-termination statistics in larger domains, which further enhances computational savings, making this approach applicable to realistic cardiac electrophysiology models.
Publication: https://arxiv.org/abs/2409.00278
Presenters
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Mahesh K Mulimani
University of California, San Diego
Authors
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Mahesh K Mulimani
University of California, San Diego