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Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…

In complex systems, information propagation can be defined as diffused or delocalized, weakly localized, and strongly localized. This study investigates the application of graph neural network models to learn the behavior of a linear…

To explore the mechanistic relationships between ageing, frailty and mortality, we developed a computational model in which possible health attributes are represented by the nodes of a complex network. Each node can be either damaged (i.e.…

A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model…

While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…

We introduce a simple network formation model for social networks. Agents are nodes, connecting to another agent by building a directed edge (or accepting a connection from another agent) has a cost, and reaching (or being reached by) other…

Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…

This study presents a method, along with its algorithmic and computational framework implementation, and performance verification for dynamical system identification. The approach incorporates insights from phase space structures, such as…

We consider a general class of translation-invariant systems with a specific category of output nonlinearities motivated by biological sensing. We show that no dynamic output feedback can stabilize this class of systems to an isolated…

State-space models have gained popularity in sequence modelling due to their simple and efficient network structures. However, the absence of nonlinear activation along the temporal direction limits the model's capacity. In this paper, we…

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and…

We introduce and study a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to reconstruct all the main features of the original…

Trajectory optimization methods have achieved an exceptional level of performance on real-world robots in recent years. These methods heavily rely on accurate analytical models of the dynamics, yet some aspects of the physical world can…

Generative models such as diffusion models, excel at capturing high-dimensional distributions with diverse input modalities, e.g. robot trajectories, but are less effective at multi-step constraint reasoning. Task and Motion Planning (TAMP)…

To help mitigate road congestion caused by the unrelenting growth of traffic demand, many transportation authorities have implemented managed lane policies, which restrict certain freeway lanes to certain types of vehicles. It was…

Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…

Terracettes, striking, step-like landforms that stripe steep, vegetated hillslopes, have puzzled scientists for more than a century. Competing hypotheses invoke either slow mass-wasting or the relentless trampling of grazing animals, yet no…

Exact numerical simulations of dynamics of open quantum systems often require immense computational resources. We demonstrate that a deep artificial neural network comprised of convolutional layers is a powerful tool for predicting…

One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and…

Coherent, large scale dynamics in many nonequilibrium physical, biological, or information transport networks are driven by small-scale local energy input. Here, we introduce and explore an analytically tractable nonlinear model for…