Related papers: MeshODENet: A Graph-Informed Neural Ordinary Diffe…
Anatomical segmentation is a fundamental task in medical image computing, generally tackled with fully convolutional neural networks which produce dense segmentation masks. These models are often trained with loss functions such as…
Mesh generation plays a crucial role in scientific computing. Traditional mesh generation methods, such as TFI and PDE-based methods, often struggle to achieve a balance between efficiency and mesh quality. To address this challenge,…
As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…
We describe a framework that can integrate prior physical information, e.g., the presence of kinematic constraints, to support data-driven simulation in multi-body dynamics. Unlike other approaches, e.g., Fully-connected Neural Network…
We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…
Mechanics-related problems often present unique challenges in achieving accurate geometric and physical representations, particularly for non-uniform structures. Graph neural networks (GNNs) have emerged as a promising tool to tackle these…
Graph Neural Networks (GNNs) have emerged as powerful tools for learning representations from structured data. Despite their growing popularity and success across various applications, GNNs encounter several challenges that limit their…
Since the seminal work of [9] and their Physics-Informed neural networks (PINNs), many efforts have been conducted towards solving partial differential equations (PDEs) with Deep Learning models. However, some challenges remain, for…
Utilizing machine learning to address partial differential equations (PDEs) presents significant challenges due to the diversity of spatial domains and their corresponding state configurations, which complicates the task of encompassing all…
Recently, graph-based models designed for downstream tasks have significantly advanced research on graph neural networks (GNNs). GNN baselines based on neural message-passing mechanisms such as GCN and GAT perform worse as the network…
Graph neural networks (GNNs) are among the most powerful tools in deep learning. They routinely solve complex problems on unstructured networks, such as node classification, graph classification, or link prediction, with high accuracy.…
Generative models generate vast numbers of hypothetical materials, necessitating fast, accurate models for property prediction. Graph Neural Networks (GNNs) excel in this domain but face challenges like high training costs, domain…
Currently the state of the art network models are based or depend on Discrete Event Simulation (DES). While DES is highly accurate, it is also computationally costly and cumbersome to parallelize, making it unpractical to simulate high…
Learned graph neural networks (GNNs) have recently been established as fast and accurate alternatives for principled solvers in simulating the dynamics of physical systems. In many application domains across science and engineering,…
Graph neural networks (GNNs) naturally align with sparse operators and unstructured discretizations, making them a promising paradigm for physics-informed machine learning in computational mechanics. Motivated by discrete physics losses and…
A graph neural network (GNN) approach is introduced in this work which enables mesh-based three-dimensional super-resolution of fluid flows. In this framework, the GNN is designed to operate not on the full mesh-based field at once, but on…
Surrogate models for the rapid inference of nonlinear boundary value problems in mechanics are helpful in a broad range of engineering applications. However, effective surrogate modeling of applications involving the contact of deformable…
Accurately simulating physics is crucial across scientific domains, with applications spanning from robotics to materials science. While traditional mesh-based simulations are precise, they are often computationally expensive and require…
This paper proposes the Mesh Neural Network (MNN), a novel architecture which allows neurons to be connected in any topology, to efficiently route information. In MNNs, information is propagated between neurons throughout a state transition…
Graph Neural Networks (GNNs) with equivariant properties have emerged as powerful tools for modeling complex dynamics of multi-object physical systems. However, their generalization ability is limited by the inadequate consideration of…