Related papers: Bridging data science and dynamical systems theory

In this paper, we study connections between the classical model-based approach to nonlinear system theory, where systems are represented by equations, and the nonlinear behavioral approach, where systems are defined as sets of trajectories.…

We present a mathematical and computational framework for the problem of learning a dynamical system from noisy observations of a few trajectories and subject to side information. Side information is any knowledge we might have about the…

Attempts from different disciplines to provide a fundamental understanding of deep learning have advanced rapidly in recent years, yet a unified framework remains relatively limited. In this article, we provide one possible way to align…

Efficient skill acquisition, representation, and on-line adaptation to different scenarios has become of fundamental importance for assistive robotic applications. In the past decade, dynamical systems (DS) have arisen as a flexible and…

We consider the problem of learning a realization of a partially observed dynamical system with linear state transitions and bilinear observations. Under very mild assumptions on the process and measurement noises, we provide a finite time…

An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and…

Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…

Although there is a substantial body of literature on control and optimization problems for parabolic and hyperbolic systems, the specific problem of controlling and optimizing the coefficients of the associated operators within such…

Nudging is an empirical data assimilation technique that incorporates an observation-driven control term into the model dynamics. The trajectory of the nudged system approaches the true system trajectory over time, even when the initial…

This paper considers the problem of determining an optimal control action based on observed data. We formulate the problem assuming that the system can be modelled by a nonlinear state-space model, but where the model parameters, state and…

Bases, mappings, projections and metrics, natural for Neural network training, are introduced. Graph-theoretical interpretation is offered. Non-Gaussianity naturally emerges, even in relatively simple datasets. Training statistics,…

Information in the time distribution of points in a state space reconstructed from observed data yields a test for ``nonstationarity''. Framed in terms of a statistical hypothesis test, this numerical algorithm can discern whether some…

Data-driven model identification strategies can be used to obtain phenomenological models that capture the temporal evolution of observable data. While it is usually straightforward to obtain such a model from time series data, for instance…

We present the observation that the process of stochastic model predictive control can be formulated in the framework of iterated function systems. The latter has a rich ergodic theory that can be applied to study the system's long-run…

Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide sufficient performance across a large landscape…

Modeling dynamical systems is crucial for a wide range of tasks, but it remains challenging due to complex nonlinear dynamics, limited observations, or lack of prior knowledge. Recently, data-driven approaches such as Neural Ordinary…

Modern learning systems increasingly interact with data that evolve over time and depend on hidden internal state. We ask a basic question: when is such a dynamical system learnable from observations alone? This paper proposes a research…

This study concerns problems of time-series forecasting under the weakest of assumptions. Related results are surveyed and are points of departure for the developments here, some of which are new and others are new derivations of previous…

We consider several estimation and learning problems that networked agents face when making decisions given their uncertainty about an unknown variable. Our methods are designed to efficiently deal with heterogeneity in both size and…

We consider the problem of designing almost optimal predictors for dynamical systems from a finite sequence of noisy observations and incomplete knowledge of the dynamics and the noise. We first discuss the properties of the optimal (Bayes)…