Related papers: When are dynamical systems learned from time serie…

Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where…

We suggest a universal map capable to recover a behavior of a wide range of dynamical systems given by ODEs. The map is built as an artificial neural network whose weights encode a modeled system. We assume that ODEs are known and prepare…

Domain generalization is the problem of machine learning when the training data and the test data come from different data domains. We present a simple theoretical model of learning to generalize across domains in which there is a…

Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…

Generalization error (also known as the out-of-sample error) measures how well the hypothesis learned from training data generalizes to previously unseen data. Proving tight generalization error bounds is a central question in statistical…

We numerically show that a deep neural network (DNN) can learn macroscopic thermodynamic laws purely from microscopic data. Using molecular dynamics simulations, we generate the data of snapshot images of gas particles undergoing adiabatic…

A machine learning (ML) system must learn not only to match the output of a target function on a training set, but also to generalize to novel situations in order to yield accurate predictions at deployment. In most practical applications,…

Distributed learning facilitates the scaling-up of data processing by distributing the computational burden over several nodes. Despite the vast interest in distributed learning, generalization performance of such approaches is not well…

Learning multi-agent system dynamics has been extensively studied for various real-world applications, such as molecular dynamics in biology. Most of the existing models are built to learn single system dynamics from observed historical…

Dynamic graph neural networks (DGNNs) are increasingly pervasive in exploiting spatio-temporal patterns on dynamic graphs. However, existing works fail to generalize under distribution shifts, which are common in real-world scenarios. As…

Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. Identifying…

Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…

In this paper we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability…

The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…

Time series frequently manifest distribution shifts, diverse latent features, and non-stationary learning dynamics, particularly in open and evolving environments. These characteristics pose significant challenges for out-of-distribution…

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…

Understanding how the dynamics in biological and artificial neural networks implement the computations required for a task is a salient open question in machine learning and neuroscience. In particular, computations requiring complex memory…

Can a dynamical system paint masterpieces such as Da Vinci's Mona Lisa or Monet's Water Lilies? Moreover, can this dynamical system be chaotic in the sense that although the trajectories are sensitive to initial conditions, the same…

There has been an increasing interest in modeling continuous-time dynamics of temporal graph data. Previous methods encode time-evolving relational information into a low-dimensional representation by specifying discrete layers of neural…

Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs,…