相关论文: Solving time-dependent parametric PDEs by multicla…

We propose a reduced basis method to solve time-dependent partial differential equations based on the Laplace transform. Unlike traditional approaches, we start by applying said transform to the evolution problem, yielding a…

We extend our previous work [F. Henr'iquez and J. S. Hesthaven, arXiv:2403.02847 (2024)] to the linear, second-order wave equation in bounded domains. This technique uses two widely known mathematical tools to construct a fast and efficient…

In this paper, we propose a model order reduction based adaptive parareal method for time-dependent partial differential equations. By using the data obtained by the fine propagator in each iteration of the plain parareal method together…

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…

Model Predictive Control (MPC) is a well-established approach to solve infinite horizon optimal control problems. Since optimization over an infinite time horizon is generally infeasible, MPC determines a suboptimal feedback control by…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

This paper is interested in developing reduced order models (ROMs) for repeated simulation of fractional elliptic partial differential equations (PDEs) for multiple values of the parameters (e.g., diffusion coefficients or fractional…

This thesis presents recent advances in model order reduction methods with the primary aim to construct online-efficient reduced surrogate models for parameterized multiscale phenomena and accelerate large-scale PDE-constrained parameter…

The vast majority of reduced-order models (ROMs) first obtain a low dimensional representation of the problem from high-dimensional model (HDM) training data which is afterwards used to obtain a system of reduced complexity. Unfortunately,…

The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical…

Problems with dominant advection, discontinuities, travelling features, or shape variations are widespread in computational mechanics. However, classical linear model reduction and interpolation methods typically fail to reproduce even…

In the present work, we introduce a data-driven approach to enhance the accuracy of non-intrusive Reduced Order Models (ROMs). In particular, we focus on ROMs built using Proper Orthogonal Decomposition (POD) in an under-resolved and…

We provide an introduction to POD-MOR with focus on (nonlinear) parametric PDEs and (nonlinear) time-dependent PDEs, and PDE constrained optimization with POD surrogate models as application. We cover the relation of POD and SVD, POD from…

A non-intrusive reduced order model based on convolutional autoencoders (NIROM-CAEs) is proposed as a data-driven tool to build an efficient nonlinear reduced-order model for stochastic spatio-temporal large-scale physical problems. The…

The use of reduced-order models (ROMs) in physics-based modeling and simulation almost always involves the use of linear reduced basis (RB) methods such as the proper orthogonal decomposition (POD). For some nonlinear problems, linear RB…

In this paper, we investigate the modeling of sub-scale components of proper orthogonal decomposition reduced order models (POD-ROMs) of convection-dominated flows. We propose ROM closure models that depend on the ROM residual. We…

We present a new surrogate modeling technique for efficient approximation of input-output maps governed by parametrized PDEs. The model is hierarchical as it is built on a full order model (FOM), reduced order model (ROM) and…

The domain decomposition (DD) nonlinear-manifold reduced-order model (NM-ROM) represents a computationally efficient method for integrating underlying physics principles into a neural network-based, data-driven approach. Compared to linear…

High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given…

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…