Related papers: Data-based stochastic model reduction for the Kura…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

We present a novel continuous time trajectory representation based on a Chebyshev polynomial basis, which when governed by known dynamics models, allows for full trajectory and robot dynamics estimation, particularly useful for…

One of the challenges in model-based control of stochastic dynamical systems is that the state transition dynamics are involved, and it is not easy or efficient to make good-quality predictions of the states. Moreover, there are not many…

The problem of estimating the constant parameters of the Kuramoto-Sivashinsky (KS) equation from observed data has received attention from researchers in physics, applied mathematics and statistics. This is motivated by the various physical…

In this paper, we study stochastic constrained minimax optimization problems with nonconvex-nonconcave structure, a central problem in modern machine learning, for which reliable and efficient algorithms remain largely unexplored due to its…

High-dimensional panels of time series often arise in finance and macroeconomics, where co-movements within groups of panel components occur. Extracting these groupings from the data provides a coarse-grained description of the complex…

We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…

The Kuramoto-Sivashinsky equations (KSE) arise in many diverse scientific areas, and are of much mathematical interest due in part to their chaotic behavior, and their similarity to the Navier-Stokes equations. However, very little is known…

We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…

While Koopman-based techniques like extended Dynamic Mode Decomposition are nowadays ubiquitous in the data-driven approximation of dynamical systems, quantitative error estimates were only recently established. To this end, both sources of…

A stochastic mode reduction strategy is applied to multiscale models with a deterministic energy-conserving fast sub-system. Specifically, we consider situations where the slow variables are driven stochastically and interact with the fast…

Data-driven reduced-order models often fail to make accurate forecasts of high-dimensional nonlinear dynamical systems that are sensitive along coordinates with low-variance because such coordinates are often truncated, e.g., by proper…

We propose a data-driven approach for propagating uncertainty in stochastic power grid simulations and apply it to the estimation of transmission line failure probabilities. A reduced-order equation governing the evolution of the observed…

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 consider multiscale stochastic dynamical systems. In this article an \emph{intermediate} reduced model is obtained for a slow-fast system with fast mode driven by white noise. First, the reduced stochastic system on exponentially…

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

Spatiotemporal chaos (STC) exhibited by the Kuramoto-Sivashinsky (KS) equation is investigated analytically and numerically. An effective stochastic equation belonging to the KPZ universality class is constructed by incorporating the…

We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretic extension of a renormalization group technique using a modified maximum entropy principle. We obtain a rigorous dimensionally…

In this document, some novel theoretical and computational techniques for constrained approximation of data-driven systems, are presented. The motivation for the development of these techniques came from structure-preserving matrix…

This paper studies a stochastic algorithm for linearly constrained nonconvex optimization, where the objective function is smooth but only unbiased stochastic gradients with bounded variance are available. We propose a momentum-based…