Related papers: PDO-eS2CNNs: Partial Differential Operator Based E…

Applying convolutional neural networks to spherical images requires particular considerations. We look to the millennia of work on cartographic map projections to provide the tools to define an optimal representation of spherical images for…

Accurate modeling of spatiotemporal dynamics is crucial to understanding complex phenomena across science and engineering. However, this task faces a fundamental challenge when the governing equations are unknown and observational data are…

Convolutional neural networks (CNNs) have rapidly risen in popularity for many machine learning applications, particularly in the field of image recognition. Much of the benefit generated from these networks comes from their ability to…

Stochastic partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. Neural Operators, generations of neural networks with capability of learning maps…

Surface meshes are widely used shape representations and capture finer geometry data than point clouds or volumetric grids, but are challenging to apply CNNs directly due to their non-Euclidean structure. We use parallel frames on surface…

Convolutional Neural Networks (CNNs) have been recently employed to solve problems from both the computer vision and medical image analysis fields. Despite their popularity, most approaches are only able to process 2D images while most…

Spherical image processing has been widely applied in many important fields, such as omnidirectional vision for autonomous cars, global climate modelling, and medical imaging. It is non-trivial to extend an algorithm developed for flat…

Energy-Dissipative Evolutionary Deep Operator Neural Network is an operator learning neural network. It is designed to seed numerical solutions for a class of partial differential equations instead of a single partial differential equation,…

The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Euclidean spaces. The purpose of this work is to generalize…

In the last ten years, Convolutional Neural Networks (CNNs) have formed the basis of deep-learning architectures for most computer vision tasks. However, they are not necessarily optimal. For example, mathematical morphology is known to be…

When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently,…

Neural operators approximate PDE solution maps, but they need not respect the symmetries of the governing equation. In out-of-distribution (OOD) regimes, a standard neural operator must often learn coordinate alignment and physical…

Equivariant Graph Neural Networks (GNNs) have significantly advanced the modeling of 3D molecular structure by leveraging group representations. However, their message passing, heavily relying on Clebsch-Gordan tensor product convolutions,…

With the growth of data from new radio telescope facilities, machine-learning approaches to the morphological classification of radio galaxies are increasingly being utilised. However, while widely employed deep-learning models using…

Establishing correspondences between 3D shapes is a fundamental task in 3D Computer Vision, typically addressed by matching local descriptors. Recently, a few attempts at applying the deep learning paradigm to the task have shown promising…

The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon…

Pre-processing and Data Augmentation play an important role in Deep Convolutional Neural Networks (DCNN). Whereby several methods aim for standardization and augmentation of the dataset, we here propose a novel method aimed to feed DCNN…

Semantic segmentation for aerial platforms has been one of the fundamental scene understanding task for the earth observation. Most of the semantic segmentation research focused on scenes captured in nadir view, in which objects have…

Depthwise separable convolutions and frequency-domain convolutions are two recent ideas for building efficient convolutional neural networks. They are seemingly incompatible: the vast majority of operations in depthwise separable CNNs are…

Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…