Deep Adversarial Koopman Model for Reaction-Diffusion systems
Deep Adversarial Koopman Model for Reaction-Diffusion systems
复制标题
反应扩散系统的深度对抗库普曼模型
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
D. Upadhyay
中科院分区：
文献类型：
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作者：
K. Balakrishnan;D. Upadhyay
反应扩散系统在自然界和工程应用中普遍存在，并且通常使用非线性控制方程组来建模。虽然存在强大的数值方法来解决它们，但基于深度学习的降阶模型（ROM）正在获得吸引力，因为它们使用线性化的动态模型来及时推进解决方案。这样的家庭的算法是基于Koopman理论，本文将这种数值模拟策略的反应扩散系统。对抗和梯度损失的介绍，并发现robustify的预测。所提出的模型扩展到处理丢失的训练数据，以及从控制的角度重铸的问题。这些发展的有效性证明了两个不同的反应扩散问题：（1）Kuramoto-Sivashinsky方程的混沌和（2）图灵不稳定性使用的Gray-Scott模型。
Reaction-diffusion systems are ubiquitous in nature and in engineering applications, and are often modeled using a non-linear system of governing equations. While robust numerical methods exist to solve them, deep learning-based reduced ordermodels (ROMs) are gaining traction as they use linearized dynamical models to advance the solution in time. One such family of algorithms is based on Koopman theory, and this paper applies this numerical simulation strategy to reaction-diffusion systems. Adversarial and gradient losses are introduced, and are found to robustify the predictions. The proposed model is extended to handle missing training data as well as recasting the problem from a control perspective. The efficacy of these developments are demonstrated for two different reaction-diffusion problems: (1) the Kuramoto-Sivashinsky equation of chaos and (2) the Turing instability using the Gray-Scott model.