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We present a supervised learning method to learn the propagator map of a dynamical system from partial and noisy observations. In our computationally cheap and easy-to-implement framework a neural network consisting of random feature maps…

We present a data-driven and interpretable approach for reducing the dimensionality of chaotic systems using spectral submanifolds (SSMs). Emanating from fixed points or periodic orbits, these SSMs are low-dimensional inertial manifolds…

In this paper we develop a new data-driven closure approximation method to compute the statistical properties of quantities of interest in high-dimensional stochastic dynamical systems. The new method relies on estimating conditional…

This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…

A novel approach to reduced-order modeling of high-dimensional time varying systems is proposed. It leverages the formalism of the Dynamic Mode Decomposition technique together with the concept of balanced realization. It is assumed that…

We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…

Given that observational and numerical climate data are being produced at ever more prodigious rates, increasingly sophisticated and automated analysis techniques have become essential. Deep learning is quickly becoming a standard approach…

Coherent X-ray scattering (CXS) techniques are capable of interrogating dynamics of nano- to mesoscale materials systems at time scales spanning several orders of magnitude. However, obtaining accurate theoretical descriptions of complex…

We construct a data-driven dynamical system model for a macroscopic variable the Reynolds number of a high-dimensionally chaotic fluid flow by training its scalar time-series data. We use a machine-learning approach, the reservoir computing…

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 study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The…

The surrogate process approximation (SPA) is applied to model the nonequilibrium dynamics of a reaction coordinate (RC) associated with the unfolding and refolding processes of a deca-alanine peptide at 300 K. The RC dynamics, which…

Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here…

Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…

Data-driven simulation of pedestrian dynamics is an incipient and promising approach for building reliable microscopic pedestrian models. We propose a methodology based on generalized regression neural networks, which does not have to deal…

We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is…

We present a new partially linearized mapping-based approach for approximating real-time quantum correlation functions in condensed-phase nonadiabatic systems, called spin-PLDM. Within a classical trajectory picture, partially linearized…

Abstractions of dynamical systems enable their verification and the design of feedback controllers using simpler, usually discrete, models. In this paper, we propose a data-driven abstraction mechanism based on a novel metric between Markov…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

We introduce the notion of descriptor embedding for nonlinear systems and use it for the data-driven design of stabilizing controllers. Specifically, we provide sufficient data-dependent LMI conditions which, if feasible, return a…