Related papers: Geometric Neural Operators (GNPs) for Data-Driven …

Bias formation in deep neural networks (DNNs) remains a critical yet poorly understood challenge, influencing both fairness and reliability in artificial intelligence systems. Inspired by the human visual system, which decouples object…

Deep networks excel in learning patterns from large amounts of data. On the other hand, many geometric vision tasks are specified as optimization problems. To seamlessly combine deep learning and geometric vision, it is vital to perform…

We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN…

For partial differential equations on domains of arbitrary shapes, existing works of neural operators attempt to learn a mapping from geometries to solutions. It often requires a large dataset of geometry-solution pairs in order to obtain a…

Neural operators have become increasingly popular in solving \textit{partial differential equations} (PDEs) due to their superior capability to capture intricate mappings between function spaces over complex domains. However, the…

Machine-learning-based surrogate models offer significant computational efficiency and faster simulations compared to traditional numerical methods, especially for problems requiring repeated evaluations of partial differential equations.…

Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide…

Learning from graph-structured data is an important task in machine learning and artificial intelligence, for which Graph Neural Networks (GNNs) have shown great promise. Motivated by recent advances in geometric representation learning, we…

Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…

Geometric graph neural networks (GNNs) have emerged as powerful tools for modeling molecular geometry. However, they encounter limitations in effectively capturing long-range interactions in large molecular systems. To address this…

Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…

In this paper, we introduce a novel way to use geometric deep learning for knot data by constructing a functor that takes knots to graphs and using graph neural networks. We will attempt to predict several knot invariants with this…

In this paper, we evaluate the accuracy of deep learning approaches on geospatial vector geometry classification tasks. The purpose of this evaluation is to investigate the ability of deep learning models to learn from geometry coordinates…

Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive…

One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks. Graph neural…

Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…

Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-dependent nonlinear partial differential equations (PDEs). In…

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…

We introduce the framework of continuous--depth graph neural networks (GNNs). Graph neural ordinary differential equations (GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of…

We study data-driven representations for three-dimensional triangle meshes, which are one of the prevalent objects used to represent 3D geometry. Recent works have developed models that exploit the intrinsic geometry of manifolds and…