Cold Spring Harbor Laboratory, Cold Spring Harbor, NY, USA.
University of Michigan, Ann Arbor, MI, USA.
Nat Commun. 2021 Oct 13;12(1):5986. doi: 10.1038/s41467-021-26202-1.
Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their function. However, dynamics are often inaccessible directly and can be only gleaned through a stochastic observation process, which makes the inference challenging. Here we present a non-parametric framework for inferring the Langevin equation, which explicitly models the stochastic observation process and non-stationary latent dynamics. The framework accounts for the non-equilibrium initial and final states of the observed system and for the possibility that the system's dynamics define the duration of observations. Omitting any of these non-stationary components results in incorrect inference, in which erroneous features arise in the dynamics due to non-stationary data distribution. We illustrate the framework using models of neural dynamics underlying decision making in the brain.
许多远离平衡态的复杂系统表现出随机动力学，可以用朗之万方程来描述。从数据中推断朗之万方程可以揭示这些系统的瞬态动力学如何产生它们的功能。然而，动力学通常无法直接访问，只能通过随机观测过程来获取，这使得推断具有挑战性。在这里，我们提出了一种从数据中推断朗之万方程的非参数框架，该框架明确地对随机观测过程和非平稳潜在动力学进行建模。该框架考虑了观测系统的非平衡初始和最终状态，以及系统动力学定义观测持续时间的可能性。省略任何这些非平稳分量都会导致不正确的推断，因为非平稳数据分布会导致动力学中出现错误特征。我们使用大脑中决策的神经动力学模型来说明该框架。
