论文标题
部分可观测时空混沌系统的无模型预测
Computing non-equilibrium trajectories by a deep learning approach
论文作者
论文摘要
在复杂系统中预测罕见事件和极端事件的发生是非平衡物理学中的一个众所周知的问题。这些事件可能会对人类社会产生巨大影响。在过去的十年中，新方法出现了，可以更好地估计尾巴分布。他们经常使用大型偏差概念，而无需执行重型直接合奏模拟。特别是，一种众所周知的方法是得出最低限度的动作原则并找到其最小化器。 在理论上和计算上，对没有详细平衡的非平衡系统中罕见的反应性事件的分析都是困难的。 Freidlin-Wentzell动作以小噪声的极限描述。我们在这里提出了一种新方法，该方法将几何作用最小化而不是使用神经网络：它称为深gmam。它依赖于经典GMAM方法的天然和简单的机器学习公式。我们详细描述了该方法以及许多示例。这些包括复杂随机（部分）微分方程，准电位估计值和汉堡湍流中极端事件的双峰开关。
Predicting the occurence of rare and extreme events in complex systems is a well-known problem in non-equilibrium physics. These events can have huge impacts on human societies. New approaches have emerged in the last ten years, which better estimate tail distributions. They often use large deviation concepts without the need to perform heavy direct ensemble simulations. In particular, a well-known approach is to derive a minimum action principle and to find its minimizers. The analysis of rare reactive events in non-equilibrium systems without detailed balance is notoriously difficult either theoretically and computationally. They are described in the limit of small noise by the Freidlin-Wentzell action. We propose here a new method which minimizes the geometrical action instead using neural networks: it is called deep gMAM. It relies on a natural and simple machine-learning formulation of the classical gMAM approach. We give a detailed description of the method as well as many examples. These include bimodal switches in complex stochastic (partial) differential equations, quasi-potential estimates, and extreme events in Burgers turbulence.
