Enhancing Computational Efficiency in Multiscale Systems Using Deep Learning of Coordinates and Flow Maps

• URL: http://arxiv.org/abs/2407.00011v1
• Date: Sun, 28 Apr 2024 14:05:13 GMT
• Title: Enhancing Computational Efficiency in Multiscale Systems Using Deep Learning of Coordinates and Flow Maps
• Authors: Asif Hamid, Danish Rafiq, Shahkar Ahmad Nahvi, Mohammad Abid Bazaz,
• Abstract summary: This paper showcases how deep learning techniques can be used to develop a precise time-stepping approach for multiscale systems. The resulting framework achieves state-of-the-art predictive accuracy while incurring lesser computational costs.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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