arXiv subjects

Jean Ragusa

Publications and source records attributed to Jean Ragusa.

4 recordsLinked to original sources

arXiv2025

Offline Maximizing Minimally Invasive Proper Orthogonal Decomposition for Reduced Order Modeling of $S_n$ Radiation Transport

Deterministic solutions to the Sn transport equation can be computationally expensive to calculate. Reduced Order Models (ROMs) provide an efficient means of approximating the Full Order Model (FOM) solution. We propose a novel approach for constructing ROMs of the Sn radiation transport equation, Offline Maximizing Minimally Invasive (OMMI) Proper Orthogonal Decomposition (POD). POD uses snapshot data to build a reduced basis, which is then used to project the FOM. Minimally Invasive POD leverages the sweep infrastructure within deterministic Sn transport solvers to construct the reduced linear system, even though the FOM linear system is never directly assembled. OMMI-POD extends Minimally Invasive POD by performing transport sweeps offline, thereby maximizing the potential speedup. It achieves this by generating a library of reduced systems from a training set, which is then interpolated in the online stage to provide a rapid approximate solution to the Sn transport equation. The model's performance is evaluated on a multigroup 2-D test problem, demonstrating low error and a 1600-fold speedup over the full order model.

math.NA↗

arXiv2020

Deep learning for 2D passive source detection in presence of complex cargo

Methods for source detection in high noise environments are important for single-photon emission computed tomography (SPECT) medical imaging and especially crucial for homeland security applications, which is our main interest. In the latter case, one deals with passively detecting the presence of low emission nuclear sources with significant background noise (with Signal To Noise Ratio ($SNR$) $1\%$ or less). In passive emission problems, direction sensitive detectors are needed, to match the dimensionalities of the image and the data. Collimation, used for that purpose in standard Anger $γ$-cameras, is not an option. Instead, Compton $γ$-cameras (and their analogs for other types of radiation) can be utilized. Backprojection methods suggested before by two of the authors and their collaborators enable detection in the presence of a random uniform background. In most practical applications, however, cargo packing in shipping containers and trucks creates regions of strong absorption and scattering, while leaving some streaming gaps open. In such cases backprojection methods prove ineffective and lose their detection ability. Nonetheless, visual perception of the backprojection pictures suggested that some indications of presence of a source might still be in the data. To learn such features (if they do exist), a deep neural network approach is implemented in 2D, which indeed exhibits higher sensitivity and specificity than the backprojection techniques in a low scattering case and works well when presence of complex cargo makes backprojection fail completely.

physics.ins-det↗

arXiv2019

Acceleration of Radiation Transport Solves Using Artificial Neural Networks

Discontinuous Finite Element Methods (DFEM) have been widely used for solving $S_n$ radiation transport problems in participative and non-participative media. In the DFEM $S_n$ methodology, the transport equation is discretized into a set of algebraic equations that have to be solved for each spatial cell and angular direction, strictly preserving the following of radiation in the system. At the core of a DFEM solver a small matrix-vector system (of 8 independent equations for tri-linear DFEM in 3D hexehdral cells) has to be assembled and solved for each cell, angle, energy group, and time step. These systems are generally solved by direct Gaussian Elimination. The computational cost of the Gaussian Elimination, repeated for each phase-space cell, amounts to a large fraction to the total compute time. Here, we have designed a Machine Learning algorithm based in a shallow Artificial Neural Networks (ANNs) to replace that Gaussian Elimination step, enabling a sizeable speed up in the solution process. The key idea is to train an ANN with a large set of solutions of random one-cell transport problems and then to use the trained ANN to replace Gaussian Elimination large scale transport solvers. It has been observed that ANNs decrease the solution times by at least a factor of 4, while introducing mean absolute errors between 1-3 \% in large scale transport solutions.

physics.comp-ph↗

arXiv2019

Positive asymptotic preserving approximation of the radiation transport equation

We introduce a (linear) positive and asymptotic preserving method or solving the one-group radiation transport equation. The approximation in space is discretization agnostic: the space approximation can be done with continuous or discontinuous finite elements (or finite volumes, or finite differences). The method is first-order accurate in space. This type of accuracy is coherent with Godunov's theorem since the method is linear. The two key theoretical results of the paper are Theorem~4.4 and Theorem~4.8. The method is illustrated with continuous finite elements. It is observed to converge with the rate $\calO(h)$ in the $L^2$-norm on manufactured solutions, and it is $\calO(h^2)$ in the diffusion regime. Unlike other standard techniques, the proposed method does not suffer from overshoots at the interfaces of optically thin and optically thick regions.

math.NA↗