Assessing AI-Enhanced Single-Sweep Approximations for Problems with Forward-Peaked Scattering in Slab Geometry

TL;DR

This paper explores the use of Fourier neural operators to develop AI-enhanced single-sweep solutions for the Boltzmann transport equation with forward-peaked scattering, aiming to overcome slow convergence issues.

Contribution

It introduces a novel AI-based approach using neural operators within a predictor-corrector framework for efficient transport equation solutions.

Findings

Demonstrates potential of neural operators for fast approximations

Achieves improved convergence over traditional methods

Provides a new framework for transport problem solutions

Abstract

While the Boltzmann transport equation can accurately model transport problems with highly forward-peaked scattering, obtaining its solution can become arbitrarily slow due to near-unity spectral radius associated with source iteration. Standard acceleration techniques like diffusion synthetic acceleration and nonlinear diffusion acceleration obtain merely one order of magnitude speedups compared to source iteration due to slowly decaying error moments. Additionally, converging approximations to the Boltzmann equation like Fokker-Planck and Boltzmann Fokker Planck run into similar problems with slow convergence. In this paper we assess the feasibility of using Fourier neural operators to obtain AI-enhanced low order, and single-sweep solutions for the transport equation in slab geometry using a predictor-corrector framework.