Related papers: Projection-based model-order reduction via graph a…

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov…

We introduce Graph Memory (GM), a structured non-parametric framework that represents an embedding space through a compact graph of reliability-annotated prototype regions. GM encodes local geometry and regional ambiguity through prototype…

Predictive high-fidelity finite element simulations of human cardiac mechanics co\-mmon\-ly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics.…

We design a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. Although existing nonlinear manifold learning methods seem to be compelling tools to…

We propose a new model-order reduction framework to poorly reducible problems arising from parametric partial differential equations with geometric variability. In such problems, the solution manifold exhibits a slowly decaying Kolmogorov…

Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…

An image denoiser can be used for a wide range of restoration problems via the Plug-and-Play (PnP) architecture. In this paper, we propose a general framework to build an interpretable graph-based deep denoiser (GDD) by unrolling a solution…

Low-rank approximation models of data matrices have become important machine learning and data mining tools in many fields including computer vision, text mining, bioinformatics and many others. They allow for embedding high-dimensional…

Representation learning for high-dimensional, complex physical systems aims to identify a low-dimensional intrinsic latent space, which is crucial for reduced-order modeling and modal analysis. To overcome the well-known Kolmogorov barrier,…

Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying…

This paper presents a structure-preserving model reduction framework for linear systems, in which the $\mathcal{H}_2$ optimization is incorporated with the Petrov-Galerkin projection to preserve structural features of interest, including…

Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…

High-performance computing enables simulation of high-dimensional physical systems, but downstream analyses such as inverse problems and control remain computationally expensive, motivating model order reduction (MOR) to construct efficient…

This study explores the combination of automated machine learning (AutoML) with model-based deep unfolding (DU) for optimizing wireless beamforming and waveforms. We convert the iterative proximal gradient descent (PGD) algorithm into a…

This article studies the recovery of graphons when they are convolution kernels on compact (symmetric) metric spaces. This case is of particular interest since it covers the situation where the probability of an edge depends only on some…

Graph Neural Networks (GNNs) are the dominant architecture for molecular machine learning, particularly for molecular property prediction and machine learning interatomic potentials (MLIPs). GNNs perform message passing on predefined graphs…

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…

This research paper investigates the Adjoint Petrov-Galerkin (APG) method for reduced order models (ROM) and fluid dynamics governed by the incompressible Navier-Stokes equations. The Adjoint Petrov-Galerkin ROM, derived using the…

Data-driven surrogate modeling has surged in capability in recent years with the emergence of graph neural networks (GNNs), which can operate directly on mesh-based representations of data. The goal of this work is to introduce an…

Reduced-order modeling techniques, including balanced truncation and $\mathcal{H}_2$-optimal model reduction, exploit the structure of linear dynamical systems to produce models that accurately capture the dynamics. For nonlinear systems…