一种推断复杂系统中非互惠相互作用和局部驱动的简单重建方法
A simple reconstruction method to infer nonreciprocal interactions and local driving in complex systems
AI总结：
本文提出一种结合马尔可夫状态模型与有向信息论度量的方法，从含噪时间序列中推断复杂系统的非互惠相互作用和局部驱动，并验证于伊辛链和时滞线性随机过程，具有广泛适用性。
摘要：
基于数据的复杂动力系统中定向相互作用的推断是许多科学学科共同面临的问题。在本工作中，我们研究了空间分离的动力实体网络，这些实体可以代表通过互惠或非互惠、瞬时或时滞相互作用相互作用的物理系统。我们提出了一种简单的方法，将马尔可夫状态模型与用于因果推断的有向信息论度量相结合，该方法可以仅从动力系统状态的含噪时间序列中准确推断潜在的相互作用。值得注意的是，尽管采用了马尔可夫假设的内置简化以及在概率估计层面选择了非常粗糙的离散化，这一点仍然可以实现。我们的测试系统是一个具有非互惠耦合的伊辛链，该耦合由单个自旋的局部驱动施加，以及一个由时滞耦合的线性随机过程组成的系统。脱离物理系统，该方法可推断因果关系，或更一般地，推断相互或单向影响的方向。所提出的方法对相互作用实体的数量和动力学细节不敏感，因此广泛适用于各个领域的问题。
英文摘要：
Data-based inference of directed interactions in complex dynamical systems is a problem common to many disciplines of science. In this work, we study networks of spatially separate dynamical entities, which could represent physical systems that interact with each other by reciprocal or nonreciprocal, instantaneous or time-delayed interactions. We present a simple approach that combines Markov state models with directed information-theoretical measures for causal inference that can accurately infer the underlying interactions from noisy time series of the dynamical system states alone. Remarkably, this is possible despite the built-in simplification of a Markov assumption and the choice of a very coarse discretization at the level of probability estimation. Our test systems are an Ising chain with nonreciprocal coupling imposed by local driving of a single spin, and a system of delay-coupled linear stochastic processes. Stepping away from physical systems, the approach infers cause-effect relationships, or more generally, the direction of mutual or one-way influence. The presented method is agnostic to the number of interacting entities and details of the dynamics, so that it is widely applicable to problems in various fields.
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