Related papers: Dynamic message-passing equations for models with …

We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the…

Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully…

Randomized experiments are a powerful methodology for data-driven evaluation of decisions or interventions. Yet, their validity may be undermined by network interference. This occurs when the treatment of one unit impacts not only its…

We investigate how the time evolution of different kinetic Ising models depends on the initial conditions of the dynamics. To this end we consider the simultaneous evolution of two identical systems subjected to the same thermal noise. We…

Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…

We consider classical spin systems evolving in continuous time with interactions given by a locally tree-like graph. Several approximate analysis methods have earlier been reported based on the idea of Belief Propagation / cavity method. We…

Dynamics of arbitrary communication system is analysed as unreduced interaction process. The applied generalised, universally nonperturbative method of effective potential reveals the phenomenon of dynamic multivaluedness of competing…

Molecular dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chemistry to engineering, life and medical science. In the last decade, the approach…

Discovering governing equations from data is crucial for understanding complex systems in many diverse fields from science to engineering. Yet, there still is a lack of versatile computational toolbox to deal with this long standing…

This paper presents a computational framework that generates ensemble predictive mechanics models with uncertainty quantification (UQ). We first develop a causal discovery algorithm to infer causal relations among time-history data measured…

We study a simple model of how social behaviors, like trends and opinions, propagate in networks where individuals adopt the trend when they are informed by threshold $T$ neighbors who are adopters. Using a dynamic message-passing…

Accurate trajectory prediction is crucial for autonomous driving, yet uncertainty in agent behavior and perception noise makes it inherently challenging. While multi-modal trajectory prediction models generate multiple plausible future…

Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…

Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…

This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to…

Many of today's most pressing issues require a more robust understanding of how information spreads in populations. Current models of information spread can be thought of as falling into one of two varieties: epidemiologically-inspired…

We present a data-driven modeling strategy to overcome improperly modeled dynamics for systems exhibiting complex spatio-temporal behaviors. We propose a Deep Learning framework to resolve the differences between the true dynamics of the…

We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from…

Although the notion of diagnostic problem has been extensively investigated in the context of static systems, in most practical applications the behavior of the modeled system is significantly variable during time. The goal of the paper is…

We develop a new quantifier for forward time uncertainty for trajectories that are solutions of models generated from data sets. Our uncertainty quantifier is defined on the phase space in which the trajectories evolve and we show that it…