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Estimation of parameters in differential equation models can be achieved by applying learning algorithms to quantitative time-series data. However, sometimes it is only possible to measure qualitative changes of a system in response to a…

Machine Learning · Computer Science 2021-10-28 Gregory Szep , Neil Dalchau , Attila Csikasz-Nagy

This work presents a data-driven Koopman operator-based modeling method using a model averaging technique. While the Koopman operator has been used for data-driven modeling and control of nonlinear dynamics, it is challenging to accurately…

Optimization and Control · Mathematics 2024-12-05 Daisuke Uchida , Karthik Duraisamy

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

In this work, we investigate a model order reduction scheme for polynomial parametric systems. We begin with defining the generalized multivariate transfer functions for the system. Based on this, we aim at constructing a reduced-order…

Numerical Analysis · Mathematics 2019-04-29 Peter Benner , Pawan Goyal

Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics…

Dynamical Systems · Mathematics 2024-02-22 Jan-Hendrik Niemann , Stefan Klus , Nataša Djurdjevac Conrad , Christof Schütte

Determining the proper level of details to develop and solve physical models is usually difficult when one encounters new engineering problems. Such difficulty comes from how to balance the time (simulation cost) and accuracy for the…

Artificial Intelligence · Computer Science 2022-02-03 Randi Wang , Morad Behandish

We propose a method for the construction of preconditioners of parameter-dependent matrices for the solution of large systems of parameter-dependent equations. The proposed method is an interpolation of the matrix inverse based on a…

Numerical Analysis · Mathematics 2016-10-26 Olivier Zahm , Anthony Nouy

Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-03-22 Dániel Berényi , András Leitereg , Gábor Lehel

We present a component-based model order reduction procedure to efficiently and accurately solve parameterized incompressible flows governed by the Navier-Stokes equations. Our approach leverages a non-overlapping optimization-based domain…

Numerical Analysis · Mathematics 2023-11-01 Tommaso Taddei , Xuejun Xu , Lei Zhang

Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…

Numerical Analysis · Mathematics 2017-04-05 Howard C. Elman , Virginia Forstall

Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications…

Numerical Analysis · Mathematics 2026-01-14 Pascal den Boef , Diana Manvelyan , Joseph Maubach , Wil Schilders , Nathan van de Wouw

This paper presents a block-structured formulation of Operator Inference as a way to learn structured reduced-order models for multiphysics systems. The approach specifies the governing equation structure for each physics component and the…

Computational Engineering, Finance, and Science · Computer Science 2026-02-20 Benjamin G. Zastrow , Anirban Chaudhuri , Karen E. Willcox , Anthony Ashley , Michael Chamberlain Henson

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…

Numerical Analysis · Mathematics 2020-07-02 Thomas Simpson , Nikolaos Dervilis , Eleni Chatzi

We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…

Numerical Analysis · Mathematics 2017-08-08 Robert O'Connor

Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…

Machine Learning · Computer Science 2024-03-13 Soo Min Kwon , Zekai Zhang , Dogyoon Song , Laura Balzano , Qing Qu

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

This paper discusses a non-intrusive data-driven model order reduction method that learns low-dimensional dynamical models for a parametrized shallow water equation. We consider the shallow water equation in non-traditional form (NTSWE). We…

Numerical Analysis · Mathematics 2020-08-06 Süleyman Yıldız , Pawan Goyal , Peter Benner , Bülent Karasözen

In this contribution, we develop an efficient surrogate modeling framework for simulation-based optimization of enhanced oil recovery, where we particularly focus on polymer flooding. The computational approach is based on an adaptive…

Numerical Analysis · Mathematics 2022-03-04 Tim Keil , Hendrik Kleikamp , Rolf J Lorentzen , Micheal B Oguntola , Mario Ohlberger

In this paper, we investigate projection-based intrusive and data-driven non-intrusive model order reduction methods in numerical simulation of rotating thermal shallow water equation (RTSWE) in parametric and non-parametric form.…

Numerical Analysis · Mathematics 2023-07-19 Süleyman Yıldız , Murat Uzunca , Bülent Karasözen

This paper introduces a novel two-stage machine learning-based surrogate modeling framework to address inverse problems in scientific and engineering fields. In the first stage of the proposed framework, a machine learning model termed the…

Machine Learning · Computer Science 2024-01-05 Farhad Pourkamali-Anaraki , Jamal F. Husseini , Evan J. Pineda , Brett A. Bednarcyk , Scott E. Stapleton