Related papers: STAResNet: a Network in Spacetime Algebra to solve…

LiDAR semantic segmentation essential for advanced autonomous driving is required to be accurate, fast, and easy-deployed on mobile platforms. Previous point-based or sparse voxel-based methods are far away from real-time applications since…

Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and…

End-to-end deep learning methods have advanced stereo vision in recent years and obtained excellent results when the training and test data are similar. However, large datasets of diverse real-world scenes with dense ground truth are…

Extracting geometric edges from unstructured point clouds remains a significant challenge, particularly in thin-walled structures that are commonly found in everyday objects. Traditional geometric methods and recent learning-based…

We introduce CGA-PoseNet, which uses the 1D-Up approach to Conformal Geometric Algebra (CGA) to represent rotations and translations with a single mathematical object, the motor, for camera pose regression. We do so starting from PoseNet,…

The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have…

Despite their dominance in vision and language, deep neural networks often underperform relative to tree-based models on tabular data. To bridge this gap, we incorporate five key inductive biases into deep learning: robustness to irrelevant…

In recent years residual neural networks (ResNets) as introduced by [He, K., Zhang, X., Ren, S., and Sun, J., Proceedings of the IEEE conference on computer vision and pattern recognition (2016), 770-778] have become very popular in a large…

End-to-end deep networks represent the state of the art for stereo matching. While excelling on images framing environments similar to the training set, major drops in accuracy occur in unseen domains (e.g., when moving from synthetic to…

Solving partial differential equations (PDEs) has been indispensable in scientific and engineering applications. Recently, deep learning methods have been widely used to solve high-dimensional problems, one of which is the physics-informed…

We train deep learning models on thousands of galaxy catalogues from the state-of-the-art hydrodynamic simulations of the CAMELS project to perform regression and inference. We employ Graph Neural Networks (GNNs), architectures designed to…

Methods for solving PDEs using neural networks have recently become a very important topic. We provide an a priori error analysis for such methods which is based on the $\mathcal{K}_1(\mathbb{D})$-norm of the solution. We show that the…

DeepONet has recently been proposed as a representative framework for learning nonlinear mappings between function spaces. However, when it comes to approximating solution operators of partial differential equations (PDEs) with…

Classification of spectra (1) and anomaly detection (2) are fundamental steps to guarantee the highest accuracy in redshift measurements (3) in modern all-sky spectroscopic surveys. We introduce a new Galaxy Spectra Neural Network…

Deep learning approaches for partial differential equations (PDEs) have received much attention in recent years due to their mesh-freeness and computational efficiency. However, most of the works so far have concentrated on time-dependent…

GreenLearning networks (GL) directly learn Green's function in physical space, making them an interpretable model for capturing unknown solution operators of partial differential equations (PDEs). For many PDEs, the corresponding Green's…

Galaxy edges or truncations are low-surface-brightness (LSB) features located in the galaxy outskirts that delimit the distance up to where the gas density enables efficient star formation. As such, they could be interpreted as a…

Models recently used in the literature proving residual networks (ResNets) are better than linear predictors are actually different from standard ResNets that have been widely used in computer vision. In addition to the assumptions such as…

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…

This article is based on a talk given by the author at MSRI in the workshop "Connections for Women" in January 2013, while being a part of the program "Noncommutative Algebraic Geometry and Representation Theory" at MSRI. One purpose of the…