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Abstract This study presents a data-driven framework for modeling complex systems, with a specific emphasis on traffic modeling. Traditional methods in traffic modeling often rely on assumptions regarding vehicle interactions. Our approach comprises two steps: first, utilizing information- theoretic (IT) tools to identify interaction directions and candidate variables thus eliminating assumptions, and second, employing the sparse identification of nonlinear systems (SINDy) tool to establish functional relationships. We validate the framework’s efficacy using synthetic data from two distinct traffic models, while considering measurement noise. Results show that IT tools can reliably detect directions of interaction as well as instances of no interaction. SINDy proves instrumental in creating precise functional relationships and determining coefficients in tested models. The innovation of our framework lies in its ability to use data-driven approach to model traffic dynamics without relying on assumptions, thus offering applications in various complex systems beyond traffic. 

Many problems in the study of dynamical systems—including identification of effective order, detection of nonlinearity or chaos, and change detection—can be reframed in terms of assessing the similarity between dynamical systems or between a given dynamical system and a reference. We introduce a general metric of dynamical similarity that is well posed for both stochastic and deterministic systems and is informative of the aforementioned dynamical features even when only partial information about the system is available. We describe methods for estimating this metric in a range of scenarios that differ in respect to contol over the systems under study, the deterministic or stochastic nature of the underlying dynamics, and whether or not a fully informative set of variables is available. Through numerical simulation, we demonstrate the sensitivity of the proposed metric to a range of dynamical properties, its utility in mapping the dynamical properties of parameter space for a given model, and its power for detecting structural changes through time series data. 

Social animals exhibit collective behavior whereby they negotiate to reach an agreement, such as the coordination of group motion. Bats are unique among most social animals, since they use active sensory echolocation by emitting ultrasonic waves and sensing echoes to navigate. Bats’ use of active sensing may result in acoustic interference from peers, driving different behavior when they fly together rather than alone. The present study explores quantitative methods that can be used to understand whether bats flying in pairs move independently of each other or interact. The study used field data from bats in flight and is based on the assumption that interactions between two bats are evidenced in their flight patterns. To quantify pairwise interaction, we defined the strength of coupling using model-free methods from dynamical systems and information theory. We used a control condition to eliminate similarities in flight path due to environmental geometry. Our research question is whether these data-driven methods identify directed coupling between bats from their flight paths and, if so, whether the results are consistent between methods. Results demonstrate evidence of information exchange between flying bat pairs, and, in particular, we find significant evidence of rear-to-front coupling in bats’ turning behavior when they fly in the absence of obstacles.