Related papers: Dynamical reduced basis methods for Hamiltonian sy…
In this paper, Hamiltonian and energy preserving reduced-order models are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with the state-dependent Poisson matrix. The high fidelity…
We investigate a projection-based reduced-order model of the steady incompressible Navier-Stokes equations for moderate Reynolds numbers. In particular, we construct an "embedded" reduced basis space, by applying proper orthogonal…
This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
Recently, continuous-time dynamical systems have proved useful in providing conceptual and quantitative insights into gradient-based optimization, widely used in modern machine learning and statistics. An important question that arises in…
In this paper we introduce a new hierarchical model reduction framework for the Fokker-Planck equation. We reduce the dimension of the equation by a truncated basis expansion in the velocity variable, obtaining a hyperbolic system of…
This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with model…
We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many…
We consider a classical model of non-equilibrium statistical mechanics accounting for non-Markovian effects, which is referred to as the Generalized Langevin Equation in the literature. We derive reduced Markovian descriptions obtained…
The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result,…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
In this paper we extend the hierarchical model reduction framework based on reduced basis techniques for the application to nonlinear partial differential equations. The major new ingredient to accomplish this goal is the introduction of…
Classical model reduction techniques project the governing equations onto linear subspaces of the high-dimensional state-space. For problems with slowly decaying Kolmogorov-n-widths such as certain transport-dominated problems, however,…
In this paper we explore the nonholonomic Lagrangian setting of mechanical systems in local coordinates on finite-dimensional configuration manifolds. We prove existence and uniqueness of solutions by reducing the basic equations of motion…
We propose a reduced basis method to solve time-dependent partial differential equations based on the Laplace transform. Unlike traditional approaches, we start by applying said transform to the evolution problem, yielding a…
Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…
This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional spatiotemporal output quantities of interest, such as pressure, temperature and…
For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based…
This work investigates projection-based Reduced-Order Models (ROMs) formulated in the frequency domain, employing a space-time basis constructed with Spectral Proper Orthogonal Decomposition to efficiently represent dominant spatio-temporal…