论文标题
反应扩散系统的深层对抗Koopman模型
Deep Adversarial Koopman Model for Reaction-Diffusion systems
论文作者
论文摘要
反应扩散系统本质和工程应用中都是无处不在的，并且通常是使用非线性的管理方程式建模的。尽管存在鲁棒的数值方法来解决它们，但基于深度学习的降低订单模型（ROM）正在使用线性化的动力学模型来及时促进解决方案，从而获得了吸引力。这样的算法系列基于库普曼理论，本文将这种数值模拟策略应用于反应扩散系统。引入了对抗性和梯度损失，并发现可以鲁棒化预测。提出的模型将扩展以处理缺失的培训数据，并从控制角度重新塑造问题。这些发展的功效已在两个不同的反应扩散问题上证明：（1）混乱的库拉莫托 - 西瓦辛斯基方程，以及（2）使用灰色 - 斯科特模型的图灵不稳定性。
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.
