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We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier-Stokes equations. Our algorithm is based on an approximated…

Numerical Analysis · Mathematics 2021-04-07 Luca Pegolotti , Martin Pfaller , Alison Marsden , Simone Deparis

We consider an optimal flow control problem in a patient-specific coronary artery bypass graft with the aim of matching the blood flow velocity with given measurements as the Reynolds number varies in a physiological range. Blood flow is…

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

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when…

Fluid Dynamics · Physics 2021-12-15 Shady E. Ahmed , Omer San , Adil Rasheed , Traian Iliescu

In this contribution we investigate in mathematical modeling and efficient simulation of biological cells with a particular emphasis on effective modeling of structural properties that originate from active forces generated from…

Numerical Analysis · Mathematics 2021-11-02 Tobias Leibner , Maja Matis , Mario Ohlberger , Stephan Rave

We develop a convolutional regularized least squares ($\texttt{CRLS}$) framework for reduced-order modeling of transonic flows with shocks. Conventional proper orthogonal decomposition (POD) based reduced models are attractive because of…

Fluid Dynamics · Physics 2025-11-27 Muhammad Bilal , Ashwin Renganathan

We introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients based on model order reduction techniques and the Laplace…

Numerical Analysis · Mathematics 2026-01-06 Fernando Henríquez , Jan S. Hesthaven

Predictive modeling of blood flow and pressure have numerous applications ranging from non-invasive assessment of functional significance of disease to planning invasive procedures. While several such predictive modeling techniques have…

We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…

Numerical Analysis · Mathematics 2026-04-16 Enrico Ballini , Marco Gambarini , Alessio Fumagalli , Luca Formaggia , Anna Scotti , Paolo Zunino

While proper orthogonal decomposition (POD) is widely used for model reduction, its standard form does not take into account any parametric model structure. Extensions to POD have been proposed to address this, but these either require…

Numerical Analysis · Mathematics 2025-08-13 Sebastiaan P. C. van Schie , Boris Kramer , John T. Hwang

We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition (KPOD) for the generation of a reduced-order space and…

Numerical Analysis · Mathematics 2021-04-01 Matteo Salvador , Luca Dede' , Andrea Manzoni

The numerical tools to simulate the bidomain model in cardiac electrophysiology are constantly developing due to the great clinical interest and scientific advances in mathematical models and computational power. The bidomain model consists…

Numerical Analysis · Mathematics 2025-11-03 Gopika P B , Peter Bastian , Nagaiah Chamakuri

This paper presents a new technique for developing reduced-order models (ROMs) for nonlinear radiative transfer problems in high-energy density physics. The proper orthogonal decomposition (POD) of photon intensities is applied to obtain…

Numerical Analysis · Mathematics 2026-03-18 Joseph M. Coale , Dmitriy Y. Anistratov

In feedback flow control, one of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A…

Optimization and Control · Mathematics 2015-05-13 Zhanhua Ma , Sunil Ahuja , Clarence W. Rowley

In this paper, we present a projection-based model-order reduction (MOR) technique for smoothed particle hydrodynamics (SPH) simulations, which is a mesh-free approach within the Lagrangian framework. Our approach utilizes the proper…

Computational Physics · Physics 2025-07-29 Lidong Fang , Zilong Song , Kirk Fraser , Faisal Habib , Christopher Drummond , Huaxiong Huang

In this paper, a non-intrusive reduced-order model (ROM) for parametric reactor kinetics simulations is presented. Time-dependent ROMs are notoriously data intensive and difficult to implement when nonlinear multiphysics phenomena are…

Numerical Analysis · Mathematics 2023-03-17 Zachary K. Hardy , Jim. E. Morel

A non-intrusive model order reduction (MOR) method for solving parameterized electromagnetic scattering problems is proposed in this paper. A database collecting snapshots of high-fidelity solutions is built by solving the parameterized…

Numerical Analysis · Mathematics 2022-07-19 Xiao-Feng He , Liang Li , Stephane Lanteri , Kun Li

A large number of theoretically predicted waveforms are required by matched-filtering searches for the gravitational-wave signals produced by compact binary coalescence. In order to substantially alleviate the computational burden in…

General Relativity and Quantum Cosmology · Physics 2018-06-11 Dániel Barta , Mátyás Vasúth

We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental…

Numerical Analysis · Mathematics 2023-08-08 Maria Strazzullo , Francesco Ballarin , Renzo Mosetti , Gianluigi Rozza

The definition of partial differential equation (PDE) models usually involves a set of parameters whose values may vary over a wide range. The solution of even a single set of parameter values may be quite expensive. In many cases, e.g.,…

Numerical Analysis · Mathematics 2016-11-17 Max Gunzburger , Nan Jiang , Michael Schneier