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Related papers: Multi-fidelity reduced-order surrogate modeling

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Partial differential equations (PDEs) are widely used for modeling various physical phenomena. These equations often depend on certain parameters, necessitating either the identification of optimal parameters or the solution of the…

Numerical Analysis · Mathematics 2025-10-17 Martina Bukač , Iva Manojlović , Boris Muha , Domagoj Vlah

Inverse problems governed by partial differential equations (PDEs) play a crucial role in various fields, including computational science, image processing, and engineering. Particularly, Darcy flow equation is a fundamental equation in…

Machine Learning · Statistics 2025-07-24 Hongji Wang , Hongqiao Wang , Jinyong Ying , Qingping Zhou

Multi-fidelity surrogate models combining dimensionality reduction and an intermediate surrogate in the reduced space allow a cost-effective emulation of simulators with functional outputs. The surrogate is an input-output mapping learned…

Computational Engineering, Finance, and Science · Computer Science 2024-12-17 Lucas Brunel , Mathieu Balesdent , Loïc Brevault , Rodolphe Le Riche , Bruno Sudret

The estimation of unknown values of parameters (or hidden variables, control variables) that characterise a physical system often relies on the comparison of measured data with synthetic data produced by some numerical simulator of the…

Machine Learning · Computer Science 2019-01-28 Xi Chen , Mike Hobson

In this paper, a reduced-order model (ROM) based on the proper orthogonal decomposition and the discrete empirical interpolation method is proposed for efficiently simulating time-fractional partial differential equations (TFPDEs). Both…

Numerical Analysis · Mathematics 2024-02-07 Hongfei Fu , Hong Wang , Zhu Wang

Many-query computations, in which a computational model for an engineering system must be evaluated many times, are crucial in design and control. For systems governed by partial differential equations (PDEs), typical high-fidelity…

Numerical Analysis · Mathematics 2024-02-09 Tomoki Koike , Elizabeth Qian

Neural networks can be used as surrogates for PDE models. They can be made physics-aware by penalizing underlying equations or the conservation of physical properties in the loss function during training. Current approaches allow to…

Machine Learning · Computer Science 2022-07-01 Raphael Leiteritz , Patrick Buchfink , Bernard Haasdonk , Dirk Pflüger

Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional…

Numerical Analysis · Mathematics 2019-05-22 Martin Hess , Alessandro Alla , Annalisa Quaini , Gianluigi Rozza , Max Gunzburger

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a…

Optimization and Control · Mathematics 2025-12-08 Ruanui Nicholson , Radoslav Vuchkov , Umberto Villa , Noemi Petra

Recent research in non-intrusive data-driven model order reduction (MOR) enabled accurate and efficient approximation of parameterized ordinary differential equations (ODEs). However, previous studies have focused on constant parameters,…

Dynamical Systems · Mathematics 2021-10-27 Jonas Kneifl , Julian Hay , Jörg Fehr

We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear…

Numerical Analysis · Mathematics 2020-11-24 Nikolaj T. Mücke , Sander M. Bohté , Cornelis W. Oosterlee

In this paper, we propose a deep learning based reduced order modeling method for stochastic underground flow problems in highly heterogeneous media. We aim to utilize supervised learning to build a reduced surrogate model from the…

Numerical Analysis · Mathematics 2022-07-27 Yiran Wang , Eric Chung , Shubin Fu

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

Data-driven surrogate modeling has emerged as a promising approach for reducing computational expenses of multiscale simulations. Recurrent Neural Network (RNN) is a common choice for modeling of path-dependent behavior. However, previous…

Computational Engineering, Finance, and Science · Computer Science 2023-12-29 Yangzi He , Shabnam J. Semnani

High-speed flight vehicles, which travel much faster than the speed of sound, are crucial for national defense and space exploration. However, accurately predicting their behavior under numerous, varied flight conditions is a challenge and…

Machine Learning · Computer Science 2024-11-07 Tyler E. Korenyi-Both , Nathan J. Falkiewicz , Matthew C. Jones

The need to rapidly solve PDEs in engineering design workflows has spurred the rise of neural surrogate models. In particular, neural operator models provide a discretization-invariant surrogate by retaining the infinite-dimensional,…

Machine Learning · Computer Science 2026-02-12 Yash Patel , Ambuj Tewari

Improving predictive understanding of Earth system variability and change requires data-model integration. Efficient data-model integration for complex models requires surrogate modeling to reduce model evaluation time. However, building a…

Machine Learning · Statistics 2019-01-17 Dan Lu , Daniel Ricciuto

Recently, the use of neural networks to accelerate the solving of partial differential equations (PDEs) has gained significant traction in both academia and industry. However, employing neural networks as standalone surrogate models raises…

This paper proposes a non-intrusive, data-driven reduced-order modeling framework for stochastic optimal control problems governed by partial differential equations. The control problem is formulated with a quadratic cost functional and…

Optimization and Control · Mathematics 2026-05-20 Lingling Ma , Jingyi Zhang , Qiuqi Li

Simulation models are widely used in practice to facilitate decision-making in a complex, dynamic and stochastic environment. But they are computationally expensive to execute and optimize, due to lack of analytical tractability. Simulation…

Optimization and Control · Mathematics 2021-06-14 L. Jeff Hong , Xiaowei Zhang