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Related papers: Reduced-Order Modeling Of Hidden Dynamics

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We propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for a Leray model. For the implementation of the model, we combine a two-step algorithm called Evolve-Filter (EF) with a computationally efficient…

Numerical Analysis · Mathematics 2021-04-14 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

Systems may depend on parameters which one may control, or which serve to optimise the system, or are imposed externally, or they could be uncertain. This last case is taken as the ``Leitmotiv'' for the following. A reduced order model is…

Machine Learning · Computer Science 2025-02-17 Hermann G. Matthies

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

To describe non-equilibrium transport processes in a quantum device with infinite baths, we propose to formulate the problems as a reduced-order problem. Starting with the Liouville-von Neumann equation for the density-matrix, the…

Mesoscale and Nanoscale Physics · Physics 2019-11-04 Weiqi Chu , Xiantao Li

We consider linear dynamical systems consisting of ordinary differential equations with high dimensionality. The aim of model order reduction is to construct an approximating system of a much lower dimension. Therein, the reduced system may…

Numerical Analysis · Mathematics 2017-11-09 Roland Pulch

We present a low-order modeling technique for actuated flows based on the regularization of an inverse problem. The inverse problem aims at minimizing the error between the model predictions and some reference simulations. The parameters to…

Fluid Dynamics · Physics 2009-11-13 Jessie Weller , Edoardo Lombardi , Angelo Iollo

This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order…

Systems and Control · Computer Science 2015-05-20 Răzvan Ştefănescu , Adrian Sandu , Ionel Michael Navon

In a real life process evolving over time, the relationship between its relevant variables may change. Therefore, it is advantageous to have different inference models for each state of the process. Asymmetric hidden Markov models fulfil…

Machine Learning · Computer Science 2023-05-16 Carlos Puerto-Santana , Pedro Larrañaga , Concha Bielza

We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution…

Numerical Analysis · Mathematics 2019-09-11 Marie Billaud-Friess , Anthony Nouy

Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…

Machine Learning · Computer Science 2021-10-29 Abhishek Sharma , Catherine Zeng , Sanjana Narayanan , Sonali Parbhoo , Finale Doshi-Velez

The proper orthogonal decomposition reduced-order models (POD-ROMs) have been widely used as a computationally efficient surrogate models in large-scale numerical simulations of complex systems. However, when it is applied to a Hamiltonian…

Numerical Analysis · Mathematics 2017-03-08 Yuezheng Gong , Qi Wang , Zhu Wang

We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden…

Probability · Mathematics 2017-05-09 Thomas Krak , Jasper De Bock , Arno Siebes

We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier-Stokes equations in the stream function-vorticity formulation. Unlike previous…

Numerical Analysis · Mathematics 2022-01-04 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

This paper considers the reduction of the Langevin equation arising from bio-molecular models. To facilitate the construction and implementation of the reduced models, the problem is formulated as a reduced-order modeling problem. The…

Numerical Analysis · Mathematics 2019-10-04 Lina Ma , Xiantao Li , Chun Liu

This paper deals with model order reduction of parametrical dynamical systems. We consider the specific setup where the distribution of the system's trajectories is unknown but the following two sources of information are available:…

Methodology · Statistics 2017-05-10 Patrick Héas , Cédric Herzet

An adaptive scheme to generate reduced-order models for parametric nonlinear dynamical systems is proposed. It aims to automatize the POD-Greedy algorithm combined with empirical interpolation. At each iteration, it is able to adaptively…

Numerical Analysis · Mathematics 2021-10-13 Sridhar Chellappa , Lihong Feng , Peter Benner

We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier--Stokes equations (NSE). In the proposed approach, the presence of simulated…

Fluid Dynamics · Physics 2022-09-08 Saddam Hijazi , Melina Freitag , Niels Landwehr

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

Numerical Analysis · Mathematics 2023-01-18 Mengwu Guo , Shane A. McQuarrie , Karen E. Willcox

This paper introduces a reduced order modeling technique based on Koopman operator theory that gives confidence bounds on the model's predictions. It is based on a data-driven spectral decomposition of the Koopman operator. The reduced…

Dynamical Systems · Mathematics 2025-03-31 Ryan Mohr , Maria Fonoberova , Igor Mezic

In the present work, we investigate a cut finite element method for the parameterized system of second-order equations stemming from the splitting approach of a fourth order nonlinear geometrical PDE, namely the Cahn-Hilliard system. We…

Numerical Analysis · Mathematics 2021-08-10 Efthymios N. Karatzas , Gianluigi Rozza