Related papers: Optimal renormalization of multi-scale systems
In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…
Many reduced order models are neither robust with respect to the parameter changes nor cost-effective enough for handling the nonlinear dependence of complex dynamical systems. In this study, we put forth a robust machine learning framework…
In the context of simulation-based methods, multiple challenges arise, two of which are considered in this work. As a first challenge, problems including time-dependent phenomena with complex domain deformations, potentially even with…
Recent research in non-intrusive data-driven model order reduction (MOR) enabled accurate and efficient approximation of parameterized ordinary differential equations (ODEs). However, previous studies have focused on constant parameters,…
The 2D Euler equations are a simple but rich set of non-linear PDEs that describe the evolution of an ideal inviscid fluid, for which one dimension is negligible. Solving numerically these equations can be extremely demanding. Several…
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…
In this paper, a backward Euler method combined with finite element discretization in spatial direction is discussed for the equations of motion arising in the $2D$ Oldroyd model of viscoelastic fluids of order one with the forcing term…
In this paper, we develop low regularity theory for 3D Burgers equation perturbed by a linear multiplicative stochastic force. This method is new and essentially different from the deterministic partial differential equations(PDEs). Our…
Within the class of nonlinear hyperbolic balance laws posed on a curved spacetime (endowed with a volume form), we identify a hyperbolic balance law that enjoys the same Lorentz invariance property as the one satisfied by the Euler…
In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal…
Finite-dimensional state-space representations of unsteady aerodynamics implicitly assume a system with fading memory. However, the impulse response of the two-dimensional inviscid (Euler) equations is characterized by an asymptotic…
In this paper, we generalize existing frameworks for $\mathcal{H}_2\otimes\mathcal{L}_2$-optimal model order reduction to a broad class of parametric linear time-invariant systems. To this end, we derive first-order necessary ptimality…
The paper discusses extensions of the renormalization group (RG) formalism for 3D incompressible Euler equations, which can be used for describing singularities developing in finite (blowup) or infinite time from smooth initial conditions…
Computable estimates for the error of finite element discretisations of parabolic problems in the $L^\infty(0,T; L^2)$ norm are developed, which exhibit constant effectivities (the ratio of the estimated error to the true error) with…
In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…
In this article, we explore the feedback stabilization of a viscous Burgers equation around a non-constant steady state using localized interior controls and then develop error estimates for the stabilized system using finite element…
We study a 1D model for the 3D incompressible Euler equations in axisymmetric geometries, which can be viewed as a local approximation to the Euler equations near the solid boundary of a cylindrical domain. We prove the local well-posedness…
We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear…
In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to…