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We consider a stochastic partial differential equation close to bifurcation of pitchfork type, where a one-dimensional space changes its stability. For finite-time Lyapunov exponents we characterize regions depending on the distance from…
In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This…
In this paper, we present a framework for Stability Analysis of Systems of Coupled Linear Partial-Differential Equations. The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichelet,…
This paper presents an improved Matlab routine, FO_LE, for the numerical computation of Lyapunov exponents of fractional-order systems modeled by Caputo's derivative. It is conceived as an enhanced version of the former FO_Lyapunov and…
Computer assisted procedures of Lyapunov functions defined in given neighborhoods of fixed points for flows and maps are discussed. We provide a systematic methodology for constructing explicit ranges where quadratic Lyapunov functions…
We present a novel way of generating Lyapunov functions for proving linear convergence rates of first-order optimization methods. Our approach provably obtains the fastest linear convergence rate that can be verified by a quadratic Lyapunov…
Automated text scoring (ATS) tasks, such as automated essay scoring and readability assessment, are important educational applications of natural language processing. Due to their interpretability of models and predictions, traditional…
The aim of this paper is to give a presentation of the Python toolbox YALTAPy dedicated to the stability study of standard and fractional delay systems as well as its online version YALTAPy_Online. Both toolboxes are derived from YALTA…
This paper introduces Dynamic Embeddings with Task-Oriented prompting (DETOT), a novel approach aimed at improving the adaptability and efficiency of machine learning models by implementing a flexible embedding layer. Unlike traditional…
We introduce new features in the MathPartner service that have recently become available to users. We highlight the functions for calculating both arithmetic-geometric mean and geometric-harmonic mean. They allow calculating complete…
This paper provides a first example of constructing Lyapunov functions in a class of piecewise linear systems with limit cycles. The method of construction helps analyze and control complex oscillating systems through novel geometric means.…
In this article we investigate model order reduction of large-scale systems using time-limited balanced truncation, which restricts the well known balanced truncation framework to prescribed finite time intervals. The main emphasis is on…
We provide algorithms for computing a Lyapunov function for a class of systems where the state trajectories are constrained to evolve within a closed convex set. The dynamical systems that we consider comprise a differential equation which…
The stability analysis of possibly time varying positive semigroups on non necessarily compact state spaces, including Neumann and Dirichlet boundary conditions is a notoriously difficult subject. These crucial questions arise in a variety…
This paper studies the continuous-time dynamics of primal-dual algorithms for linearly constrained convex optimization problems and provides a quantitative convergence analysis using the Lyapunov functions. With the growing prevalence of…
The fast simulation of dynamical systems is a key challenge in many scientific and engineering applications, such as weather forecasting, disease control, and drug discovery. With the recent success of deep learning, there is increasing…
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…
PyPOTS is an open-source Python library dedicated to data mining and analysis on multivariate partially-observed time series with missing values. Particularly, it provides easy access to diverse algorithms categorized into five tasks:…
pdepath 2.0 is an upgrade of the continuation/bifurcation package pde2path for elliptic systems of PDEs over bounded 2D domains, based on the Matlab pdetoolbox. The new features include a more efficient use of FEM, easier switching between…
Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces. However, despite their remarkable early promise,…