Related papers: Projection-based model-order reduction via graph a…
Reduced Order Models (ROMs) have gained a great attention by the scientific community in the last years thanks to their capabilities of significantly reducing the computational cost of the numerical simulations, which is a crucial objective…
Sparse-view Computed Tomography (CT) is an emerging protocol designed to reduce X-ray dose radiation in medical imaging. Traditional Filtered Back Projection algorithm reconstructions suffer from severe artifacts due to sparse data. In…
Prediction of a molecule's 3D conformer ensemble from the molecular graph holds a key role in areas of cheminformatics and drug discovery. Existing generative models have several drawbacks including lack of modeling important molecular…
This paper presents a novel end-to-end Learned Point Cloud Geometry Compression (a.k.a., Learned-PCGC) framework, to efficiently compress the point cloud geometry (PCG) using deep neural networks (DNN) based variational autoencoders (VAE).…
This paper investigates a model reduction problem for linear directed network systems, in which the interconnections among the vertices are described by general weakly connected digraphs. First, the definitions of pseudo controllability and…
High-fidelity simulation of nonequilibrium plasmas -- crucial to applications in electric propulsion, hypersonic re-entry, and astrophysical flows -- requires state-specific collisional-radiative (CR) kinetic models, but these come at a…
Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized {nonlinear} elliptic partial differential equations (PDEs). CB-pMOR is designed to deal with large-scale problems for which full-order…
Graph autoencoders have gained attention in nonlinear reduced-order modeling of parameterized partial differential equations defined on unstructured grids. Despite they provide a geometrically consistent way of treating complex domains,…
We present a unified algorithmic framework for the numerical solution, constrained optimization, and physics-informed learning of PDEs with a variational structure. Our framework is based on a Galerkin discretization of the underlying…
The simulation of microcirculatory blood flow in realistic vascular architectures poses significant challenges due to the multiscale nature of the problem and the topological complexity of capillary networks. In this work, we propose a…
We propose a new nonlinear factorization model for graphs that are with topological structures, and optionally, node attributes. This model is based on a pseudometric called Gromov-Wasserstein (GW) discrepancy, which compares graphs in a…
Computed tomography (CT) metal artifact reduction (MAR) aims to reduce the severe streaking artifacts induced by metallic implants and other high-density objects. Effective MAR generally requires both accurate artifact localization and…
We propose a family of high-order local discontinuous Galerkin (LDG) methods, built on a parametric representation and coupled with a semi-implicit backward Euler time discretization, for isotropic and anisotropic curve-shortening flows.…
We present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a…
Turbulent flow control has numerous applications and building reduced-order models (ROMs) of the flow and the associated feedback control laws is extremely challenging. Despite the complexity of building data-driven ROMs for turbulence, the…
Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…
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…
We propose a combination of a variational autoencoder and a transformer based model which fully utilises graph convolutional and graph pooling layers to operate directly on graphs. The transformer model implements a novel node encoding…