Related papers: Invariance Proximity: Closed-Form Error Bounds for…

It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem…

The modeling of nonlinear dynamics based on Koopman operator theory, which is originally applicable only to autonomous systems with no control, is extended to non-autonomous control system without approximation to input matrix B. Prevailing…

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…

In this work we study two Riemannian distances between infinite-dimensional positive definite Hilbert-Schmidt operators, namely affine-invariant Riemannian and Log-Hilbert-Schmidt distances, in the context of covariance operators associated…

Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…

Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional framework. These functionals impose a generalized piecewise…

We provide a direct, intersection theoretic, argument that the Jordan models of an operator of class C_{0}, of its restriction to an invariant subspace, and of its compression to the orthogonal complement, satisfy a multiplicative form of…

We introduce an inhomogeneous variant of Kaufman's measure, with applications to diophantine approximation. In particular, we make progress towards a problem related to Littlewood's conjecture.

In [R. J. Baraldi and D. P. Kouri, Math. Program., 201:1 (2023), pp. 559-598], the authors introduced a trust-region method for minimizing the sum of a smooth nonconvex and a nonsmooth convex function, the latter of which has an analytical…

Models based on approximation capabilities have recently been studied in the context of Optimal Recovery. These models, however, are not compatible with overparametrization, since model- and data-consistent functions could then be…

The mathematical models used to represent physical phenomena are generally known to be imperfect representations of reality. Model inadequacies arise for numerous reasons, such as incomplete knowledge of the phenomena or computational…

Finite-precision floating point arithmetic unavoidably introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be…

This paper studies the convergence properties of the inexact Jordan-Kinderlehrer-Otto (JKO) scheme and proximal-gradient algorithm in the context of Wasserstein spaces. The JKO scheme, a widely-used method for approximating solutions to…

We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…

We rigorously derive novel error bounds for extended dynamic mode decomposition (EDMD) to approximate the Koopman operator for discrete- and continuous time (stochastic) systems; both for i.i.d. and ergodic sampling under non-restrictive…

In many contexts the modal properties of a structure change, either due to the impact of a changing environment, fatigue, or due to the presence of structural damage. For example during flight, an aircraft's modal properties are known to…

As robots are being increasingly used in close proximity to humans and objects, it is imperative that robots operate safely and efficiently under real-world conditions. Yet, the environment is seldom known perfectly. Noisy sensors and…

Orthogonal projection-based reduced order models (PROM) are the output of widely-used model reduction methods. In this work, a novel product form is derived for the reduction error system of these reduced models, and it is shown that any…

Gromov-Wasserstein distance has found many applications in machine learning due to its ability to compare measures across metric spaces and its invariance to isometric transformations. However, in certain applications, this invariance…

Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense…