Related papers: PDO-s3DCNNs: Partial Differential Operator Based S…

Building large models with parameter sharing accounts for most of the success of deep convolutional neural networks (CNNs). In this paper, we propose doubly convolutional neural networks (DCNNs), which significantly improve the performance…

When manipulating three-dimensional data, it is possible to ensure that rotational and translational symmetries are respected by applying so-called SE(3)-equivariant models. Protein structure prediction is a prominent example of a task…

Deep neural networks (DNNs) have achieved extraordinary performance in solving different tasks in various fields. However, the conventional DNN model is steadily approaching the ground-truth value through loss backpropagation. In some…

Scientific machine learning has enabled the extraction of physical insights and data-driven modeling of high-dimensional spatiotemporal data, yet achieving physically interpretable latent representations and computationally efficient…

Pre-trained deep image representations are useful for post-training tasks such as classification through transfer learning, image retrieval, and object detection. Data augmentations are a crucial aspect of pre-training robust…

Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many computer vision tasks especially when dealing with multiscale inputs. We study, in this paper, a…

Machine learning and data processing techniques relying on covariance information are widespread as they identify meaningful patterns in unsupervised and unlabeled settings. As a prominent example, Principal Component Analysis (PCA)…

Fast and accurate surrogates for physics-driven partial differential equations (PDEs) are essential in fields such as aerodynamics, porous media design, and flow control. However, many transformer-based models and existing neural operators…

Within the world of machine learning there exists a wide range of different methods with respective advantages and applications. This paper seeks to present and discuss one such method, namely Convolutional Neural Networks (CNNs). CNNs are…

We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms. A comparative analysis between…

In dynamical systems reconstruction (DSR) we aim to recover the dynamical system (DS) underlying observed time series. Specifically, we aim to learn a generative surrogate model which approximates the underlying, data-generating DS, and…

Group Equivariant CNNs (G-CNNs) have shown promising efficacy in various tasks, owing to their ability to capture hierarchical features in an equivariant manner. However, their equivariance is fixed to the symmetry of the whole group,…

Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…

Analyzing volumetric data with rotational invariance or equivariance is an active topic in current research. Existing deep-learning approaches utilize either group convolutional networks limited to discrete rotations or steerable…

Normalizing flows (NFs) provide a powerful tool to construct an expressive distribution by a sequence of trackable transformations of a base distribution and form a probabilistic model of underlying data. Rotation, as an important quantity…

A desireable property of accelerometric gait-based identification systems is robustness to new device orientations presented by users during testing but unseen during the training phase. However, traditional Convolutional neural networks…

Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…

Spherical equivariant graph neural networks (EGNNs) provide a principled framework for learning on three-dimensional molecular and biomolecular systems, where predictions must respect the rotational symmetries inherent in physics. These…

Deep convolutional neural networks (CNNs) are usually over-parameterized, which cannot be easily deployed on edge devices such as mobile phones and smart cameras. Existing works used to decrease the number or size of requested convolution…

Deep generative models are increasingly used for molecular discovery, with most recent approaches relying on equivariant graph neural networks (GNNs) under the assumption that explicit equivariance is essential for generating high-quality…