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

arXiv 2407.00011 ↗First posted 28 Apr 2024cs.DC cs.LG cs.NEcited by 0

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Abstract (arXiv)

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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References · 18

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6 more
  1. 2020Hierarchical Deep Learning of Multiscale Differential Equation Time-Stepperscited by 37
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