English
Related papers

Related papers: Efficient and certified solution of parametrized o…

200 papers

For a nonlinear dynamical system that depends on parameters, the paper introduces a novel tensorial reduced-order model (TROM). The reduced model is projection-based, and for systems with no parameters involved, it resembles proper…

Numerical Analysis · Mathematics 2023-11-16 Alexander V. Mamonov , Maxim A. Olshanskii

We investigate new developments of the combined Reduced-Basis and Empirical Interpolation Methods (RB-EIM) for parametrized nonlinear parabolic problems. In many situations, the cost of the EIM in the offline stage turns out to be…

Numerical Analysis · Mathematics 2018-04-23 Amina Benaceur , Alexandre Ern , Virginie Ehrlacher , Sébastien Meunier

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…

Numerical Analysis · Mathematics 2026-04-13 Elise Bonnet-Weill , Virginie Ehrlacher , Luca Nenna

Accurate simulations are essential for engineering applications, and intricate continuum mechanical material models are constructed to achieve this goal. However, the increasing complexity of the material models and geometrical properties…

Computational Engineering, Finance, and Science · Computer Science 2023-11-30 Steffen Kastian , Jannick Kehls , Tim Brepols , Stefanie Reese

We present a reduced order modeling (ROM) technique for subsurface multi-phase flow problems building on the recently introduced deep residual recurrent neural network (DR-RNN) [1]. DR-RNN is a physics aware recurrent neural network for…

Computational Engineering, Finance, and Science · Computer Science 2018-10-25 J. Nagoor Kani , Ahmed H. Elsheikh

In this paper, we introduce the neural empirical interpolation method (NEIM), a neural network-based alternative to the discrete empirical interpolation method for reducing the time complexity of computing the nonlinear term in a reduced…

Numerical Analysis · Mathematics 2025-05-13 Max Hirsch , Federico Pichi , Jan S. Hesthaven

The Poisson-Boltzmann equation (PBE) is a nonlinear elliptic PDE that arises in biomolecular modeling and is a fundamental tool for structural biology. It is used to calculate electrostatic potentials around an ensemble of fixed charges…

Numerical Analysis · Mathematics 2017-10-12 Cleophas Kweyu , Lihong Feng , Matthias Stein , Peter Benner

This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin…

Numerical Analysis · Mathematics 2023-12-05 Nicholas Mueller , Santiago Badia

We propose an efficient hyper-reduced order model (HROM) designed for segregated finite-volume solvers in geometrically parametrized problems. The method follows a discretize-then-project strategy: the full-order operators are first…

Numerical Analysis · Mathematics 2026-01-13 Valentin Nkana Ngan , Giovanni Stabile , Andrea Mola , Gianluigi Rozza

Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…

Optimization and Control · Mathematics 2025-05-16 Matteo Tomasetto , Andrea Manzoni , Francesco Braghin

This contribution presents a model order reduction strategy for fast parametric modelling of problems with cracks formulated on spline discretizations. In the context of damage detection, parametric reduced order models (ROMs) are well…

Computational Engineering, Finance, and Science · Computer Science 2026-03-30 Margarita Chasapi

This paper presents and evaluates an approach for coupling together subdomain-local reduced order models (ROMs) constructed via non-intrusive operator inference (OpInf) with each other and with subdomain-local full order models (FOMs),…

Numerical Analysis · Mathematics 2024-10-15 Ian Moore , Christopher Wentland , Anthony Gruber , Irina Tezaur

We apply reduced-order modeling (ROM) techniques to single-phase flow in faulted porous media, accounting for changing rock properties and fault geometry variations using a radial basis function mesh deformation method. This approach…

Numerical Analysis · Mathematics 2024-03-07 Enrico Ballini , Luca Formaggia , Alessio Fumagalli , Anna Scotti , Paolo Zunino

Bayesian statistical inverse problems are often solved with Markov chain Monte Carlo (MCMC)-type schemes. When the problems are governed by large-scale discrete nonlinear partial differential equations (PDEs), they are computationally…

Numerical Analysis · Mathematics 2019-09-06 Howard C. Elman , Akwum Onwunta

An adaptive parametric reduced-order modeling method based on interpolating poles of reduced-order models is proposed in this paper. To guarantee correct interpolation, a pole-matching process is conducted to determine which poles of two…

Numerical Analysis · Mathematics 2019-08-05 Yao Yue , Lihong Feng , Peter Benner

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

The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE solvers using reduced-order modeling (ROM). Whereas prior ROM approaches reduce…

Reduced Order Models (ROMs) have been regarded as an efficient alternative to conventional high-fidelity Computational Fluid Dynamics (CFD) for accelerating the design and optimization processes in engineering applications. Many industrial…

Numerical Analysis · Mathematics 2026-01-15 Shenhui Ruan , Andreas G. Class , Gianluigi Rozza

Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PDE) by properly combining the high-fidelity solutions of the problem obtained for several…

Numerical Analysis · Mathematics 2023-08-08 M. Girfoglio , L. Scandurra , F. Ballarin , G. Infantino , F. Nicolò , A. Montalto , G. Rozza , R. Scrofani , M. Comisso , F. Musumeci

A comprehensive approach for real-time computations using a database of parameterized linear reduced-order models (ROMs) is proposed. The method proceeds by sampling offline ROMs for specific values of the parameters and interpolating…

Numerical Analysis · Mathematics 2015-06-24 David Amsallem , Radek Tezaur , Charbel Farhat