Enhancing Computational Efficiency in Multiscale Systems Using Deep Learning of Coordinates and Flow Maps
<|reference_start|>Enhancing Computational Efficiency in Multiscale Systems Using Deep Learning of Coordinates and Flow Maps: Complex systems often show macroscopic coherent behavior due to the interactions of microscopic agents like molecules, cells, or individuals in a population with their environment. However, simulating such systems poses several computational challenges during simulation as the underlying dynamics vary and span wide spatiotemporal scales of interest. To capture the fast-evolving features, finer time steps are required while ensuring that the simulation time is long enough to capture the slow-scale behavior, making the analyses computationally unmanageable. This paper showcases how deep learning techniques can be used to develop a precise time-stepping approach for multiscale systems using the joint discovery of coordinates and flow maps. While the former allows us to represent the multiscale dynamics on a representative basis, the latter enables the iterative time-stepping estimation of the reduced variables. The resulting framework achieves state-of-the-art predictive accuracy while incurring lesser computational costs. We demonstrate this ability of the proposed scheme on the large-scale Fitzhugh Nagumo neuron model and the 1D Kuramoto-Sivashinsky equation in the chaotic regime.<|reference_end|>
@article{hamid2024enhancing,
    title={Enhancing Computational Efficiency in Multiscale Systems Using Deep
  Learning of Coordinates and Flow Maps},
    author={Asif Hamid, Danish Rafiq, Shahkar Ahmad Nahvi, Mohammad Abid Bazaz},
    journal={arXiv preprint arXiv:2407.00011},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.00011},
    primaryClass={cs.DC cs.LG cs.NE nlin.CD}
}