Reconstructing in-depth activity for chaotic 3D spatiotemporal excitable media models based on surface data

Motivated by potential applications in cardiac research, we consider the task of reconstructing the dynamics within a spatiotemporal chaotic 3D excitable medium from partial observations at the surface. Three artificial neural network methods (a spatiotemporal convolutional long-short-term-memory, an autoencoder, and a diffusion model based on the U-Net architecture) are trained to predict the dynamics in deeper layers of a cube from observational data at the surface using data generated by the Barkley model on a 3D domain. The results show that despite the high-dimensional chaotic dynamics of this system, such cross-prediction is possible, but non-trivial and as expected, its quality decreases with increasing prediction depth.