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

In this work, we propose a novel neural network focusing on semantic labeling of ALS point clouds, which investigates the importance of long-range spatial and channel-wise relations and is termed as global relation-aware attentional network…

The Obstacle Avoiding Rectilinear Steiner Minimum Tree (OARSMT) problem, which seeks the shortest interconnection of a given number of terminals in a rectilinear plane while avoiding obstacles, is a critical task in integrated circuit…

Deep learning has emerged as a compelling framework for scientific and engineering computing, motivating growing interest in neural network-based solvers for partial differential equations (PDEs). Within this landscape, network…

Finding parameters in a deep neural network (NN) that fit training data is a nonconvex optimization problem, but a basic first-order optimization method (gradient descent) finds a global optimizer with perfect fit (zero-loss) in many…

Partial differential equations (PDEs) underlie our understanding and prediction of natural phenomena across numerous fields, including physics, engineering, and finance. However, solving parametric PDEs is a complex task that necessitates…

This paper explores the application of geometric algebra to Galilean spacetime and its physical implications. We introduce the Galilean Spacetime Algebra (GSTA), a five-dimensional conformal geometric algebra (CGA) generated by a specific…

Neural surrogates for stiff differential-algebraic equations (DAEs) face two barriers: soft-constraint methods leave algebraic residuals that stiffness amplifies into errors, and hard-constraint methods require trajectory data from stiff…

In this work, we propose data-integrated neural networks (DataInNet) for solving partial differential equations (PDEs), offering a novel approach to leveraging data (e.g., source terms, initial conditions, and boundary conditions). The core…

Stellar atmospheric parameters and elemental abundances are traditionally determined using template matching techniques based on high-resolution spectra. However, these methods are sensitive to noise and unsuitable for ultra-low-resolution…

We develop a unified model, known as MgNet, that simultaneously recovers some convolutional neural networks (CNN) for image classification and multigrid (MG) methods for solving discretized partial differential equations (PDEs). This model…

We present the first public release of our generic neural network training algorithm, called SkyNet. This efficient and robust machine learning tool is able to train large and deep feed-forward neural networks, including autoencoders, for…

One of the main challenges since the advancement of convolutional neural networks is how to connect the extracted feature map to the final classification layer. VGG models used two sets of fully connected layers for the classification part…

We introduce a hybrid "Modified Genetic Algorithm-Multilevel Stochastic Gradient Descent" (MGA-MSGD) training algorithm that considerably improves accuracy and efficiency of solving 3D mechanical problems described, in strong-form, by PDEs…

Recent advances in solving ordinary differential equations (ODEs) with neural networks have been remarkable. Neural networks excel at serving as trial functions and approximating solutions within functional spaces, aided by gradient…

This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams…

This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…

In this work we propose a deep adaptive sampling (DAS) method for solving partial differential equations (PDEs), where deep neural networks are utilized to approximate the solutions of PDEs and deep generative models are employed to…

Traditional lost-in-space algorithms, such as those implemented in astrometry.net, solve for spacecraft orientation by matching observed star fields to celestial catalogs using geometric asterisms alone. In this work, we propose a novel…

Computational electromagnetics (CEM) is employed to numerically solve Maxwell's equations, and it has very important and practical applications across a broad range of disciplines, including biomedical engineering, nanophotonics, wireless…

Recently, leveraging on the development of end-to-end convolutional neural networks (CNNs), deep stereo matching networks have achieved remarkable performance far exceeding traditional approaches. However, state-of-the-art stereo frameworks…