Related papers: PIETOOLS: A Matlab Toolbox for Manipulation and Op…
PIETOOLS 2022 manual is a document that describes all the features of the MATLAB toolbox for the analysis and control of Partial Integral Equations (PIEs). The manual is aimed to guide, with examples, the first time users to three…
The PIETOOLS 2025 User Manual describes all the features of version 2025 of the MATLAB toolbox PIETOOLS for the analysis and control of Partial Integral Equations (PIEs). The manual is aimed to guide, with examples, first-time users to four…
Linear operators and optimisation are at the core of many algorithms used in signal and image processing, remote sensing, and inverse problems. For small to medium-scale problems, existing software packages (e.g., MATLAB, Python numpy and…
Operator-splitting methods are widespread in the numerical solution of differential equations, especially the initial-value problems in ordinary differential equations that arise from a method-of-lines discretization of partial differential…
Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…
We present a MATLAB toolbox for five different classes of exponential integrators for solving (mildly) stiff ordinary differential equations or time-dependent partial differential equations. For the efficiency of such exponential…
Solving partial differential equations (PDEs) by learning the solution operators has emerged as an attractive alternative to traditional numerical methods. However, implementing such architectures presents two main challenges: flexibility…
This study is an attempt at generalizing the class of partially hypoelliptic differential operators to a class of pseudodifferential operators, Symbol ideals are formed on the set of lineality and we discuss suitable topologies that allow…
PENLAB is an open source software package for nonlinear optimization, linear and nonlinear semidefinite optimization and any combination of these. It is written entirely in MATLAB. PENLAB is a young brother of our code PENNON \cite{pennon}…
We present a new Partial Integral Equation (PIE) representation of Partial Differential Equations (PDEs) in which it is possible to use convex optimization to perform stability analysis with little or no conservatism. The first result gives…
In this paper, we present a new method for estimating the $L_2$-gain of systems governed by 2nd order linear Partial Differential Equations (PDEs) in two spatial variables, using semidefinite programming. It has previously been shown that,…
Let us denote ${\cal V}$, the finite dimensional vector spaces of functions of the form $\psi(x) = p_n(x) + f(x) p_m(x)$ where $p_n(x)$ and $p_m(x)$ are arbitrary polynomials of degree at most $n$ and $m$ in the variable $x$ while $f(x)$…
We present a MATLAB package called the Pha-sorArray Toolbox that has been developed to make harmonic analysis and control methods both practical and user-friendly. The toolbox adopts an object-oriented architecture that enables intuitive…
We develop an algorithm for computing the solution of a large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to computing the action of a certain matrix function on the vector…
This paper presents a new Matlab toolbox, aimed at facilitating the use of polynomial optimization for stability analysis of nonlinear systems. In the past decade several decisive contributions made it possible to recast this type of…
The $\Pi$-operator, also known as Ahlfors-Beurling transform, plays an important role in solving the existence of locally quasiconformal solutions of Beltrami equations. In this paper, we first construct the $\Pi$-operator on a general…
Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable…
In this report, we present a new programming model based on Pipelines and Operators, which are the building blocks of programs written in PiCo, a DSL for Data Analytics Pipelines. In the model we propose, we use the term Pipeline to denote…
Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate models for the…
We prove a general black box result which produces algebras of pseudodifferential operators (ps.d.o.s) on noncompact manifolds, together with a precise principal symbol calculus. Our construction (which also applies in parameter-dependent…