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Deep Adversarial Koopman Model for Reaction-Diffusion systems

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Document pages: 16 pages

Abstract: Reaction-diffusion systems are ubiquitous in nature and in engineeringapplications, and are often modeled using a non-linear system of governingequations. While robust numerical methods exist to solve them, deeplearning-based reduced ordermodels (ROMs) are gaining traction as they uselinearized dynamical models to advance the solution in time. One such family ofalgorithms is based on Koopman theory, and this paper applies this numericalsimulation strategy to reaction-diffusion systems. Adversarial and gradientlosses are introduced, and are found to robustify the predictions. The proposedmodel is extended to handle missing training data as well as recasting theproblem from a control perspective. The efficacy of these developments aredemonstrated for two different reaction-diffusion problems: (1) theKuramoto-Sivashinsky equation of chaos and (2) the Turing instability using theGray-Scott model.

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