Enhancing Computational Efficiency in Multiscale Systems Using Deep Learning of Coordinates and Flow Maps
This addresses the problem of computationally unmanageable simulations for researchers studying complex systems like neurons or fluid dynamics, though it appears incremental as it builds on existing deep learning techniques for multiscale modeling.
The paper tackled the computational challenge of simulating multiscale systems with wide spatiotemporal scales by developing a deep learning-based time-stepping approach that jointly discovers coordinates and flow maps, achieving state-of-the-art predictive accuracy with reduced computational costs, as demonstrated on the Fitzhugh Nagumo neuron model and 1D Kuramoto-Sivashinsky equation.
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.