Related papers: Acceleration of Radiation Transport Solves Using A…
Defect detection is a basic and essential task in automatic parts production, especially for automotive engine precision parts. In this paper, we propose a new idea to construct a deep convolutional network combining related knowledge of…
Averaging techniques such as Ruppert--Polyak averaging and exponential movering averaging (EMA) are powerful approaches to accelerate optimization procedures of stochastic gradient descent (SGD) optimization methods such as the popular ADAM…
Geometry optimization is an important part of both computational materials and surface science because it is the path to finding ground state atomic structures and reaction pathways. These properties are used in the estimation of…
The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computational time. To this end, algorithmically, the standard adaptive finite…
Neutron cross section matrices for fission and scattering data are required for each material, temperature, and enrichment level to calculate the neutron transport equation accurately. This information can be a limiting factor when using…
Neural operators aim to learn mappings between infinite-dimensional function spaces, but their performance often degrades on complex or irregular geometries due to the lack of geometry-aware representations. We propose the Finite Element…
We address distributed learning problems, both nonconvex and convex, over undirected networks. In particular, we design a novel algorithm based on the distributed Alternating Direction Method of Multipliers (ADMM) to address the challenges…
The semi-airborne transient electromagnetic method (SATEM) is capable of conducting rapid surveys over large-scale and hard-to-reach areas. However, the acquired signals are often contaminated by complex noise, which can compromise the…
High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial…
A novel method to compute time eigenvalues of neutron transport problems is presented based on solutions to the time dependent transport equation. Using these solutions we use the dynamic mode decomposition (DMD) to form an approximate…
Physics-informed neural networks (PINNs) were recently proposed in [1] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution while a PDE-induced NN is coupled to the solution NN,…
This paper presents an efficient parallel method for the deterministic solution of the 3D stationary Boltzmann transport equation applied to diffusive problems such as nuclear core criticality computations. Based on standard…
Beams of radioactive heavy ions allow researchers to study rare and unstable atomic nuclei, shedding light into the internal structure of exotic nuclei and on how chemical elements are formed in stars. However, the extraction and transport…
In this paper, two flux-only least-squares finite element methods (LSFEM) for the linear hyperbolic transport problem are developed. The transport equation often has discontinuous solutions and discontinuous inflow boundary conditions, but…
In safety-critical systems (e.g., autonomous vehicles and robots), Deep Neural Networks (DNNs) are becoming a key component for computer vision tasks, particularly semantic segmentation. Further, since the DNN behavior cannot be assessed…
Prediction of particle radiative heat transfer flux is an important task in the large discrete granular systems, such as pebble bed in power plants and industrial fluidized beds. For particle motion and packing, discrete element method…
We consider a mesh-based approach for training a neural network to produce field predictions of solutions to parametric partial differential equations (PDEs). This approach contrasts current approaches for "neural PDE solvers" that employ…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single…
Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…