Related papers: Upper limits on the robustness of Turing models an…
Multiplicative and additive $D$-stability, diagonal stability, Schur $D$-stability, $H$-stability are classical concepts which arise in studying linear dynamical systems. We unify these types of stability, as well as many others, in one…
This Ph.D. thesis contains original contributions to several areas within the disciplines of disordered systems, numerical linear algebra, and scientific computing: (1) Theoretical and numerical study of the errors caused by using certain…
Recent work have shown how the optimal state-feedback, obtained as the solution to the Hamilton-Jacobi-Bellman equations, can be approximated for several nonlinear, deterministic systems by deep neural networks. When imitation (supervised)…
In this paper we propose a new method to detect and classify coexisting solutions in nonlinear systems. We focus on mechanical and structural systems where we usually avoid multistability for safety and reliability. We want to be sure that…
The Turing instability is a paradigmatic route to patterns formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a…
This paper considers the robustness of an uncertain nonlinear system along a finite-horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients.…
We present a nonlinear stabilized Lagrange-Galerkin scheme for the Oseen-type Peterlin viscoelastic model. Our scheme is a combination of the method of characteristics and Brezzi-Pitk\"aranta's stabilization method for the conforming linear…
The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on…
Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…
An hyperelastic biphasic model is presented. For slow-draining problems (permeability less than 1\times10-2 mm4 N-1 s-1), numerical instabilities in the form of non-physical oscillations in the pressure field are observed in 3D problems…
This paper presents a generalized robust stability analysis for bearing-based formation control and network localization systems. For an undirected network, we provide a robust stability analysis in the presence of time-varying exogenous…
We study filtering of multiscale dynamical systems with model error arising from unresolved smaller scale processes. The analysis assumes continuous-time noisy observations of all components of the slow variables alone. For a linear model…
We study the problem of identification of linear dynamical system from a single trajectory, via excitations of isotropic Gaussian. In stark contrast with previously reported results, Ordinary Least Squares (OLS) estimator for even…
The fastest known algorithms for dealing with structured matrices, in the sense of the displacement rank measure, are randomized. For handling classical displacement structures, they achieve the complexity bounds…
This is the second part of our error analysis of the stabilized Lagrange-Galerkin scheme applied to the Oseen-type Peterlin viscoelastic model. Our scheme is a combination of the method of characteristics and Brezzi-Pitk\"aranta's…
A new Bayesian approach to linear system identification has been proposed in a series of recent papers. The main idea is to frame linear system identification as predictor estimation in an infinite dimensional space, with the aid of…
A linear PDE problem for randomly perturbed domains is considered in an adaptive Galerkin framework. The perturbation of the domain's boundary is described by a vector valued random field depending on a countable number of random variables…
The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of…
We study systems on time scales that are generalizations of classical differential or difference equations. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of…
While empirical scaling laws for LLM reasoning are well-documented, the theoretical mechanisms governing out-of-distribution (OOD) generalization remain elusive. We formalize reasoning via optimal transport, projecting discrete trajectories…