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We consider the problem of learning the dynamics of autonomous linear systems (i.e., systems that are not affected by external control inputs) from observations of multiple trajectories of those systems, with finite sample guarantees.…

We explore how to build a vector field from the various functions involved in a given mathematical program, and show that locally-stable equilibria of the underlying dynamical system are precisely the local solutions of the optimization…

We describe a computational method for constructing a coarse combinatorial model of some dynamical system in which the macroscopic states are given by elementary cycling motions of the system. Our method is in particular applicable to time…

This article describes some common issues encountered in the use of Direct Numerical Simulation (DNS) turbulent flow data for machine learning. We focus on two specific issues; 1) the requirements for a fair validation set, and 2) the…

In this note, we propose a novel approach for a class of autonomous dynamical systems that allows, given some observations of the solutions, to identify its parameters and reconstruct the state vector. This approach relies on proving the…

Behavior cloning of expert demonstrations can speed up learning optimal policies in a more sample-efficient way over reinforcement learning. However, the policy cannot extrapolate well to unseen states outside of the demonstration data,…

Data-driven models of dynamical systems require extensive amounts of training data. For many practical applications, gathering sufficient data is not feasible due to cost or safety concerns. This work uses the Subset Extended Kalman Filter…

Emerging vehicular systems with increasing proportions of automated components present opportunities for optimal control to mitigate congestion and increase efficiency. There has been a recent interest in applying deep reinforcement…

The vast majority of systems of practical interest are characterised by nonlinear dynamics. This renders the control and optimization of such systems a complex task due to their nonlinear behaviour. Additionally, standard methods such as…

Koopman spectral theory has provided a new perspective in the field of dynamical systems in recent years. Modern dynamical systems are becoming increasingly non-linear and complex, and there is a need for a framework to model these systems…

Clustering of time series is a well-studied problem, with applications ranging from quantitative, personalized models of metabolism obtained from metabolite concentrations to state discrimination in quantum information theory. We consider a…

This paper studies how to find compact state embeddings from high-dimensional Markov state trajectories, where the transition kernel has a small intrinsic rank. In the spirit of diffusion map, we propose an efficient method for learning a…

A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to…

The current trend in next-generation exascale systems goes towards integrating a wide range of specialized (co-)processors into traditional supercomputers. However, the integration of different specialized devices increases the degree of…

We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian)…

A properly designed controller can help improve the quality of experimental measurements or force a dynamical system to follow a completely new time-evolution path. Recent developments in deep reinforcement learning have made steep advances…

We study the identification of continuous-time vector fields from irregularly sampled trajectories. We introduce spectral flow learning, which learns in a windowed flow space using a lag-linear label operator that aggregates lagged Koopman…

Humans have a strong intuitive understanding of physical processes such as fluid falling by just a glimpse of such a scene picture, i.e., quickly derived from our immersive visual experiences in memory. This work achieves such a…

We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior…

Self-supervised representation learning is able to learn semantically meaningful features; however, much of its recent success relies on multiple crops of an image with very few objects. Instead of learning view-invariant representation…