Related papers: Structure-preserving Interpolatory Model Reduction…
We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected…
We consider the discretization and subsequent model reduction of a system of partial differential-algebraic equations describing the propagation of pressure waves in a pipeline network. Important properties like conservation of mass,…
The aim of this work is to design implicit and semi-implicit high-order well-balanced finite-volume numerical methods for 1D systems of balance laws. The strategy introduced by two of the authors in a previous paper for explicit schemes…
A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating…
Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…
In this work we propose a high-order structure-preserving discretization of the cold plasma model which describes the propagation of electromagnetic waves in magnetized plasmas. By utilizing B-Splines Finite Elements Exterior Calculus, we…
We focus on the numerical modelling of water waves by means of depth averaged models. We consider in particular PDE systems which consist in a nonlinear hyperbolic model plus a linear dispersive perturbation involving an elliptic operator.…
Distributed Port-Hamiltonian (dPHS) theory provides a powerful framework for modeling physical systems governed by partial differential equations and has enabled a broad class of boundary control methodologies. Their effectiveness, however,…
This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for…
We present a framework for constructing a structured realization of a linear time-invariant dynamical system solely from a discrete sampling of an input and output trajectory of the system. We estimate the transfer function of the original…
There is developed a differential-algebraic approach to studying the representations of commuting differentiations in functional differential rings under nonlinear differential constraints. An example of the differential ideal with the only…
The parareal in time algorithm allows to efficiently use parallel computing for the simulation of time-dependent problems. It is based on a decomposition of the time interval into subintervals, and on a predictor-corrector strategy, where…
The problem of reducing a Hidden Markov Model (HMM) to one of smaller dimension that exactly reproduces the same marginals is tackled by using a system-theoretic approach. Realization theory tools are extended to HMMs by leveraging suitable…
We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to {iteratively} train a…
Many dynamical systems -- from robots interacting with their surroundings to large-scale multiphysics systems -- involve a number of interacting subsystems. Toward the objective of learning composite models of such systems from data, we…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
We propose a rigorous, conservative invariant-domain preserving (IDP) projection technique for hierarchical discretizations that enforces membership in physics-implied convex sets when mapping between solution spaces. When coupled with…
In this note, we consider port-Hamiltonian structures in numerical optimal control of ordinary differential equations. By introducing a novel class of nonlinear monotone port-Hamiltonian (pH) systems, we show that the primal-dual gradient…
There is a growing interest in the conservation of invariants when numerically solving a system of ordinary differential equations. Methods that exactly preserve these quantities in time are known as geometric integrators. In this paper we…
The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural…