A simple reconstruction method to infer nonreciprocal interactions and local driving in complex systems

Abstract: 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.