Title: Koopman-based Deep Learning for Nonlinear System Estimation Show Chinese title

Title: 基于Koopman的深度学习用于非线性系统估计

Abstract: Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and invariably unmodeled dynamics present challenges in making precise predictions. In many cases the models exhibit extremely complicated behavior due to bifurcations and chaotic regimes. In this paper, we present a novel data-driven linear estimator that uses Koopman operator theory to extract finite-dimensional representations of complex nonlinear systems. The extracted model is used together with a deep reinforcement learning network that learns the optimal stepwise actions to predict future states of the original nonlinear system. Our estimator is also adaptive to a diffeomorphic transformation of the nonlinear system which enables transfer learning to compute state estimates of the transformed system without relearning from scratch. Show Chinese abstract

Abstract: 非线性微分方程作为流体流动、尖峰神经元和其他现实世界中感兴趣系统的模型被遇到。这些系统的共同特征是其行为难以准确描述，并且不可避免地存在未建模的动力学，这在进行精确预测时带来了挑战。在许多情况下，由于分岔和混沌区域，这些模型表现出极其复杂的行为。在本文中，我们提出了一种新颖的数据驱动线性估计器，该估计器使用Koopman算子理论来提取复杂非线性系统的有限维表示。提取的模型与一个深度强化学习网络一起使用，该网络学习最优的逐步动作以预测原始非线性系统的未来状态。我们的估计器还适应于非线性系统的微分同胚变换，这使得可以进行迁移学习，在不从头开始重新学习的情况下计算变换后系统的状态估计。