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Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the…

This work introduces a formulation of model predictive control (MPC) which adaptively reasons about the complexity of the model based on the task while maintaining feasibility and stability guarantees. Existing MPC implementations often…

Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…

Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…

We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…

Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…

We consider continuous-time dynamics for distributed optimization with set constraints in the paper. To handle the computational complexity of projection-based dynamics due to solving a general quadratic optimization subproblem with…

We provide a comprehensive study of the convergence of the forward-backward algorithm under suitable geometric conditions, such as conditioning or {\L}ojasiewicz properties. These geometrical notions are usually local by nature, and may…

In this paper one first shows that the slow flow of a mechanical system with one unstable mode coupled to a Nonlinear Energy Sink (NES) can be reduced, in the neighborhood of a fold point of its critical manifold, to a normal form of the…

Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…

Estimation and inference in dynamic discrete choice models often relies on approximation to lower the computational burden of dynamic programming. Unfortunately, the use of approximation can impart substantial bias in estimation and results…

Model-free and model-based reinforcement learning are two ends of a spectrum. Learning a good policy without a dynamic model can be prohibitively expensive. Learning the dynamic model of a system can reduce the cost of learning the policy,…

The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…

This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional spatiotemporal output quantities of interest, such as pressure, temperature and…

This work develops a functional analytic framework for making computer assisted arguments involving transverse heteroclinic connecting orbits between hyperbolic periodic solutions of ordinary differential equations. We exploit a…

This work presents the application of a recently developed parametric, non-intrusive, and multi-fidelity reduced-order modeling method on high-dimensional displacement and stress fields arising from the structural analysis of geometries…

Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…

Reservoir computing has been shown to be a useful framework for predicting critical transitions of a dynamical system if the bifurcation parameter is also provided as an input. Its utility is significant because in real-world scenarios, the…

We aim to study a finite volume scheme to solve the two dimensional inviscid primitive equations of the atmosphere with humidity and saturation, in presence of topography and subject to physically plausible boundary conditions to the system…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…