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In this paper, we put forth an evolve-then-correct reduced order modeling approach that combines intrusive and nonintrusive models to take hidden physical processes into account. Specifically, we split the underlying dynamics into known and…

Computational Physics · Physics 2019-11-07 Suraj Pawar , Shady E. Ahmed , O. San , A. Rasheed

We consider linear first-order systems of ordinary differential equations (ODEs) in port-Hamiltonian (pH) form. Physical parameters are remodelled as random variables to conduct an uncertainty quantification. A stochastic Galerkin…

Numerical Analysis · Mathematics 2023-08-15 Roland Pulch , Olivier Sète

Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…

Dynamical Systems · Mathematics 2023-09-27 Samuel E. Otto , Gregory R. Macchio , Clarence W. Rowley

In the Reduced Basis approximation of Stokes and Navier-Stokes problems, the Galerkin projection on the reduced spaces does not necessarily preserved the inf-sup stability even if the snapshots were generated through a stable full order…

Numerical Analysis · Mathematics 2023-08-08 Shafqat Ali , Francesco Ballarin , Gianluigi Rozza

In this work, Galerkin projection is used to build Reduced Order Models (ROM) for two-dimensional Rayleigh-B\'enard (RB) convection with no-slip walls. We compare an uncoupled projection approach that uses separate orthonormal bases for…

Fluid Dynamics · Physics 2025-04-07 Enrique Flores-Montoya , André V. G. Cavalieri

A new Bayesian approach to linear system identification has been proposed in a series of recent papers. The main idea is to frame linear system identification as predictor estimation in an infinite dimensional space, with the aid of…

Machine Learning · Statistics 2015-07-03 Diego Romeres , Gianluigi Pillonetto , Alessandro Chiuso

Reduced Order Models (ROMs) have gained a great attention by the scientific community in the last years thanks to their capabilities of significantly reducing the computational cost of the numerical simulations, which is a crucial objective…

Numerical Analysis · Mathematics 2024-06-05 Guglielmo Padula , Michele Girfoglio , Gianluigi Rozza

We introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, the optimal control problems require a huge…

Numerical Analysis · Mathematics 2023-08-08 Maria Strazzullo , Zakia Zainib , Francesco Ballarin , Gianluigi Rozza

In this work we present a Reduced Order Model which is specifically designed to deal with turbulent flows in a finite volume setting. The method used to build the reduced order model is based on the idea of merging/combining…

Numerical Analysis · Mathematics 2025-12-04 Saddam Hijazi , Giovanni Stabile , Andrea Mola , Gianluigi Rozza

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

Numerical Analysis · Mathematics 2021-05-27 Cecilia Pagliantini

This paper explores an iterative coupling approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order…

Numerical Analysis · Mathematics 2024-01-08 Francesco Ballarin , Sanghyun Lee , Son-Young Yi

This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…

Numerical Analysis · Mathematics 2025-09-05 Antonio Blanco-Casares , Vishal Kumar , Daniel Mira , Oriol Lehmkuhl

In this paper, a dynamic closure modeling approach has been derived to stabilize the projection-based reduced order models in the long-term evolution of forced-dissipative dynamical systems. To simplify our derivation without losing…

Fluid Dynamics · Physics 2019-02-21 Sk. Mashfiqur Rahman , Shady E. Ahmed , Omer San

We investigate linear dynamical systems consisting of ordinary differential equations with high dimensionality. Model order reduction yields alternative systems of much lower dimensions. However, a reduced system may be unstable, although…

Numerical Analysis · Mathematics 2018-08-14 Roland Pulch

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…

Computational Physics · Physics 2018-12-05 Xuping Xie , Guannan Zhang , Clayton G. Webster

In this paper, we consider the learning of a Reduced-Order Linear Parameter-Varying Model (ROLPVM) of a nonlinear dynamical system based on data. This is achieved by a two-step procedure. In the first step, we learn a projection to a lower…

Systems and Control · Electrical Eng. & Systems 2024-05-21 Patrick J. W. Koelewijn , Rajiv Sing , Peter Seiler , Roland Tóth

The modeling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control are discussed. The structure is ideal for automated network-based modeling since it is invariant under power-conserving…

Dynamical Systems · Mathematics 2022-01-19 Volker Mehrmann , Benjamin Unger

We present two different reduced order strategies for incompressible parameterized Navier-Stokes equations characterized by varying Reynolds numbers. The first strategy deals with low Reynolds number (laminar flow) and is based on a…

Numerical Analysis · Mathematics 2023-08-08 Saddam Hijazi , Shafqat Ali , Giovanni Stabile , Francesco Ballarin , Gianluigi Rozza

Non-intrusive reduced-order modeling techniques are necessary for systems that are simulated using black-box solvers or known only from data. For systems exhibiting large transients and operating far away from equilibria, current…

Numerical Analysis · Mathematics 2026-03-24 Cole J. Errico , Alberto Padovan , Daniel J. Bodony

Model-based controllers can offer strong guarantees on stability and convergence by relying on physically accurate dynamic models. However, these are rarely available for high-dimensional mechanical systems such as deformable objects or…

Robotics · Computer Science 2026-02-10 Katharina Friedl , Noémie Jaquier , Seungyeon Kim , Jens Lundell , Danica Kragic