Related papers: Universal Learning of Nonlinear Dynamics
We address the problem of learning to control an unknown nonlinear dynamical system through sequential interactions. Motivated by high-stakes applications in which mistakes can be catastrophic, such as robotics and healthcare, we study…
An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It…
Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…
This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by…
This paper presents an algorithm for the unsupervised learning of latent variable models from unlabeled sets of data. We base our technique on spectral decomposition, providing a technique that proves to be robust both in theory and in…
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…
A methodology is developed to learn a feedback linearization (i.e., nonlinear change of coordinates and input transformation) using a data-driven approach for a single input control-affine nonlinear system with unknown dynamics. We employ…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
This paper studies the learning-to-control problem under process and sensing uncertainties for dynamical systems. In our previous work, we developed a data-based generalization of the iterative linear quadratic regulator (iLQR) to design…
Kalman filter is a key tool for time-series forecasting and analysis. We show that the dependence of a prediction of Kalman filter on the past is decaying exponentially, whenever the process noise is non-degenerate. Therefore, Kalman filter…
A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical…
Recently, a general data driven numerical framework has been developed for learning and modeling of unknown dynamical systems using fully- or partially-observed data. The method utilizes deep neural networks (DNNs) to construct a model for…
Model-based control requires an accurate model of the system dynamics for precisely and safely controlling the robot in complex and dynamic environments. Moreover, in the presence of variations in the operating conditions, the model should…
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…
Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
Modal methods are a long-standing approach to physical modelling synthesis. Extensions to nonlinear problems are possible, leading to coupled nonlinear systems of ordinary differential equations. Recent work in scalar auxiliary variable…
Unsupervised mixture learning (UML) aims at identifying linearly or nonlinearly mixed latent components in a blind manner. UML is known to be challenging: Even learning linear mixtures requires highly nontrivial analytical tools, e.g.,…
Koopman spectral analysis has attracted attention for understanding nonlinear dynamical systems by which we can analyze nonlinear dynamics with a linear regime by lifting observations using a nonlinear function. For analysis, we need to…