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

This paper proposes a general framework for structure-preserving model reduction of a secondorder network system based on graph clustering. In this approach, vertex dynamics are captured by the transfer functions from inputs to individual…

Hamiltonian particle-based simulations of plasma dynamics are inherently computationally intensive, primarily due to the large number of particles required to obtain accurate solutions. This challenge becomes even more acute in many-query…

Algorithm unfolding creates an interpretable and parsimonious neural network architecture by implementing each iteration of a model-based algorithm as a neural layer. However, unfolding a proximal splitting algorithm with a positive…

Graph Neural Networks (GNNs) have received increasing attention in many fields. However, due to the lack of prior graphs, their use for semantic labeling has been limited. Here, we propose a novel architecture called the Self-Constructing…

Machine learning (ML) and deep learning (DL) techniques have gained significant attention as reduced order models (ROMs) to computationally expensive structural analysis methods, such as finite element analysis (FEA). Graph neural network…

We present a novel graph Transformer generative adversarial network (GTGAN) to learn effective graph node relations in an end-to-end fashion for challenging graph-constrained architectural layout generation tasks. The proposed…

Recently, transformers have shown promising performance in learning graph representations. However, there are still some challenges when applying transformers to real-world scenarios due to the fact that deep transformers are hard to train…

The Linear Parameter-Varying (LPV) framework is a powerful tool for controlling nonlinear and complex systems, but the conversion of nonlinear models into LPV forms often results in high-dimensional and overly conservative LPV models. To be…

We present an accelerated greedy strategy for training of projection-based reduced-order models for parametric steady and unsteady partial differential equations. Our approach exploits hierarchical approximate proper orthogonal…

This paper presents a novel p-adaptive, high-order mesh-free framework for the accurate and efficient simulation of fluid flows in complex geometries. High-order differential operators are constructed locally for arbitrary node…

Reduced Order Modelling (ROM) has been widely used to create lower order, computationally inexpensive representations of higher-order dynamical systems. Using these representations, ROMs can efficiently model flow fields while using…

Unsteady fluid systems are nonlinear high-dimensional dynamical systems that may exhibit multiple complex phenomena both in time and space. Reduced Order Modeling (ROM) of fluid flows has been an active research topic in the recent decade…

Recent works on machine learning for combinatorial optimization have shown that learning based approaches can outperform heuristic methods in terms of speed and performance. In this paper, we consider the problem of finding an optimal…

In this paper, we propose an efficient proper orthogonal decomposition based reduced-order model(POD-ROM) for nonstationary Stokes equations, which combines the classical projection method with POD technique. This new scheme mainly owns two…

We investigate model order reduction (MOR) strategies for simulating unsteady hemodynamics within cerebrovascular systems, contrasting a physics-based intrusive approach with a data-driven non-intrusive framework. High-fidelity 3D…

With the advancement of neural networks, there has been a notable increase, both in terms of quantity and variety, in research publications concerning the application of autoencoders to reduced-order models. We propose a polytopic…

The proper orthogonal decomposition (POD) -- a popular projection-based model order reduction (MOR) method -- may require significant model dimensionalities to successfully capture a nonlinear solution manifold resulting from a…

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

We develop an optimization-based algorithm for parametric model order reduction (PMOR) of linear time-invariant dynamical systems. Our method aims at minimizing the $\mathcal{H}_\infty \otimes \mathcal{L}_\infty$ approximation error in the…

Graph Neural Networks usually rely on the assumption that the graph topology is available to the network as well as optimal for the downstream task. Latent graph inference allows models to dynamically learn the intrinsic graph structure of…