论文标题
从嘈杂和部分观察的识别和重建混乱和随机动力学系统的差异深度学习
Variational Deep Learning for the Identification and Reconstruction of Chaotic and Stochastic Dynamical Systems from Noisy and Partial Observations
论文作者
论文摘要
动力学系统的数据驱动的恢复尚未恢复，最近引起了越来越多的兴趣。但是，在处理嘈杂和部分观察时，管理方程式的识别仍然具有挑战性。在这里，我们应对这一挑战并研究变分深度学习方案。在拟议的框架内，我们共同学习一个推理模型，以从一系列嘈杂和部分数据中重建系统的真实状态以及这些状态的管理法律。这样，这个框架桥接了经典数据同化和最先进的机器学习技术。我们还证明了它概括了最先进的方法。重要的是，推理模型和管理模型都嵌入了随机组件，以说明随机变化，模型误差和重建不确定性。关于混乱和随机动力学系统的各种实验支持我们方案W.R.T.的相关性。最先进的方法。
The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial observations. Here, we address this challenge and investigate variational deep learning schemes. Within the proposed framework, we jointly learn an inference model to reconstruct the true states of the system and the governing laws of these states from series of noisy and partial data. In doing so, this framework bridges classical data assimilation and state-of-the-art machine learning techniques. We also demonstrate that it generalises state-of-the-art methods. Importantly, both the inference model and the governing model embed stochastic components to account for stochastic variabilities, model errors, and reconstruction uncertainties. Various experiments on chaotic and stochastic dynamical systems support the relevance of our scheme w.r.t. state-of-the-art approaches.
