Related papers: Resolvent-Type Data-Driven Learning of Generators …

Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep…

Dynamical semigroups have become the key structure for describing open system dynamics in all of physics. Bounded generators are known to be of a standard form, due to Gorini, Kossakowski, Sudarshan and Lindblad. This form is often used…

Experimental progress in qubit manufacturing calls for the development of new theoretical tools to analyze quantum data. We show how an unsupervised machine-learning technique can be used to understand short-range entangled many-qubit…

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

This paper proposes a data-driven control framework to regulate an unknown, stochastic linear dynamical system to the solution of a (stochastic) convex optimization problem. Despite the centrality of this problem, most of the available…

We propose an alternating optimization algorithm to the nonconvex Koopman operator learning problem for nonlinear dynamic systems. We show that the proposed algorithm will converge to a critical point with rate $O(1/T)$ and $O(\frac{1}{\log…

This paper proposes a novel formulation of frequency response for nonlinear systems in the Koopman operator framework. This framework is a promising direction for the analysis and synthesis of systems with nonlinear dynamics based on…

This paper studies the cooperative training of two generative models for image modeling and synthesis. Both models are parametrized by convolutional neural networks (ConvNets). The first model is a deep energy-based model, whose energy…

As a kind of generative self-supervised learning methods, generative adversarial nets have been widely studied in the field of anomaly detection. However, the representation learning ability of the generator is limited since it pays too…

Koopman operators provide tractable means of learning linear approximations of non-linear dynamics. Many approaches have been proposed to find these operators, typically based upon approximations using an a-priori fixed class of models.…

Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic…

Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often…

We develop a class of data-driven generative models that approximate the solution operator for parameter-dependent partial differential equations (PDE). We propose a novel probabilistic formulation of the operator learning problem based on…

Learning parameters of latent graphical models (GM) is inherently much harder than that of no-latent ones since the latent variables make the corresponding log-likelihood non-concave. Nevertheless, expectation-maximization schemes are…

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…

Stochastic generators are essential to produce synthetic realizations that preserve target statistical properties. We propose GenFormer, a stochastic generator for spatio-temporal multivariate stochastic processes. It is constructed using a…

This survey presents recent research on determining control-theoretic properties and designing controllers with rigorous guarantees using semidefinite programming and for nonlinear systems for which no mathematical models but measured…

We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven…

Stability analysis of a power network and its characterization (voltage or angle) is an important problem in the power system community. However, these problems are mostly studied using linearized models and participation factor analysis.…

Motivated by the goal of learning controllers for complex systems whose dynamics change over time, we consider the problem of designing control laws for systems that switch among a finite set of unknown discrete-time linear subsystems under…