Related papers: From Structured to Unstructured:A Comparative Anal…
Deep learning has been employed to identify flow characteristics from Computational Fluid Dynamics (CFD) databases to assist the researcher to better understand the flow field, to optimize the geometry design and to select the correct CFD…
We combine concepts from multilevel solvers for partial differential equations (PDEs) with neural network based deep learning and propose a new methodology for the efficient numerical solution of high-dimensional parametric PDEs. An…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the AMG method, a Multi-Graph…
Graphs, consisting of vertices and edges, are vital for representing complex relationships in fields like social networks, finance, and blockchain. Visualizing these graphs helps analysts identify structural patterns, with readability…
Deep learning surrogate models are being increasingly used in accelerating scientific simulations as a replacement for costly conventional numerical techniques. However, their use remains a significant challenge when dealing with real-world…
Deep neural networks have enabled researchers to create powerful generalized frameworks, such as transformers, that can be used to solve well-studied problems in various application domains, such as text and image. However, such generalized…
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…
The problem of distinguishing natural images from photo-realistic computer-generated ones either addresses natural images versus computer graphics or natural images versus GAN images, at a time. But in a real-world image forensic scenario,…
A neural network architecture is presented that exploits the multilevel properties of high-dimensional parameter-dependent partial differential equations, enabling an efficient approximation of parameter-to-solution maps, rivaling…
To address the challenge of segmenting noisy images with blurred or fragmented boundaries, this paper presents a robust version of Variational Model Based Tailored UNet (VM_TUNet), a hybrid framework that integrates variational methods with…
Mesh generation is a crucial step in numerical simulations, significantly impacting simulation accuracy and efficiency. However, generating meshes remains time-consuming and requires expensive computational resources. In this paper, we…
We present a new meshing algorithm called guided and augmented meshing, GAMesh, which uses a mesh prior to generate a surface for the output points of a point network. By projecting the output points onto this prior and simplifying the…
This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams…
As the intermediate-level representations bridging the two levels, structured representations of visual scenes, such as visual relationships between pairwise objects, have been shown to not only benefit compositional models in learning to…
Traditional image segmentation methods, such as variational models based on partial differential equations (PDEs), offer strong mathematical interpretability and precise boundary modeling, but often suffer from sensitivity to parameter…
One characteristic that sets humans apart from modern learning-based computer vision algorithms is the ability to acquire knowledge about the world and use that knowledge to reason about the visual world. Humans can learn about the…
Geometrical Volume-of-Fluid (VoF) methods mainly support structured meshes, and only a small number of contributions in the scientific literature report results with unstructured meshes and three spatial dimensions. Unstructured meshes are…
Segmenting unseen object instances in cluttered environments is an important capability that robots need when functioning in unstructured environments. While previous methods have exhibited promising results, they still tend to provide…
To enable heterogeneous computing systems with autonomous programming and optimization capabilities, we propose a unified, end-to-end, programmable graph representation learning (PGL) framework that is capable of mining the complexity of…