Dynamical maximum entropy approach to flocking

Abstract

We derive a new method to infer from data the out-of-equilibrium alignment dynamics of collectively moving animal groups, by considering the maximum entropy model distribution consistent with temporal and spatial correlations of flight direction. When bird neighborhoods evolve rapidly, this dynamical inference correctly learns the parameters of the model, while a static one relying only on the spatial correlations fails. When neighbors change slowly and the detailed balance is satisfied, we recover the static procedure. We demonstrate the validity of the method on simulated data. The approach is applicable to other systems of active matter.

Short-range interactions versus long-range correlations in bird flocks

“…We note that the ME approach is not bound to produce static Boltzmann-like measures. If we consider as input observables time dependent quantities (such as multi-point time correlation functions), the resulting ME model will consist in a time dependent distribution [40,[42][43][44]. Computations and inference of effective interactions can be in this case much more complicated.…”

“…This method was originally established by E. T. Jaynes in 1957 [24] and has strong connections with classical statistical physics. In the last decade, it has been widely used to describe the collective behavior of biological networks, from neural assemblies, to amino acids in proteins, biochemical and genetic networks and flocks of birds [26,27,[30][31][32][34][35][36][37][38][39][40][41].…”

A Truncation Scheme for the BBGKY2 Equation

“…In particular, the MaxEnt-based characterization of complex systems presented in [3] paved the way to applications in a variety of fields ranging from linguistics to biology [4][5][6][7][8]. First focussed on equilibrium situations, these works soon turned their attention to non-equilibrium properties as well [9][10][11][12].…”

Maximum Entropy Rate Reconstruction of Markov Dynamics

“…While originally devised in the context of statistical mechanics, the principle of maximum entropy (MaxEnt) found its way in many different research areas, from biology to linguistics, where it is now successfully employed [3][4][5][6][7]. More recently, several attempts to generalize this principle to dynamical situations have been proposed in different fields [8][9][10][11][12]. For instance, [11] studied the dynamical properties of starling flocks, while [12] tried the maximum entropy approach on financial time series, and [8] tackled the problem from the viewpoint of hidden Markov models (for completeness of the historical background, one should mention here the many pending controversies raised when extending the results of thermodynamics to non-equilibrium situations, but this topic is too far from our present concern).…”

“…More recently, several attempts to generalize this principle to dynamical situations have been proposed in different fields [8][9][10][11][12]. For instance, [11] studied the dynamical properties of starling flocks, while [12] tried the maximum entropy approach on financial time series, and [8] tackled the problem from the viewpoint of hidden Markov models (for completeness of the historical background, one should mention here the many pending controversies raised when extending the results of thermodynamics to non-equilibrium situations, but this topic is too far from our present concern). In all such attempts, nonetheless, one has to keep in mind that the relevance of maximum entropy methods depends tightly on the existence of sensible constraints that can be implemented easily.…”