Physics-Informed Neural Network with Fourier Features for Radiation Transport in Heterogeneous Media

离散化 计算机科学 人工神经网络 玻尔兹曼方程 傅里叶变换 启发式 数学优化 应用数学 算法 计算科学 人工智能 物理 数学分析 数学 量子力学 操作系统
作者
Quincy A. Huhn,Mauricio Tano,Jean C. Ragusa
出处
期刊:Nuclear Science and Engineering [Taylor & Francis]
卷期号:197 (9): 2484-2497 被引量:5
标识
DOI:10.1080/00295639.2023.2184194
摘要

Typical machine learning (ML) methods are difficult to apply to radiation transport due to the large computational cost associated with simulating problems to create training data. Physics-informed Neural Networks (PiNNs) are a ML method that train a neural network with the residual of a governing equation as the loss function. This allows PiNNs to be trained in a low-data regime in the absence of (experimental or synthetic) data. PiNNs also are trained on points sampled within the phase-space volume of the problem, which means they are not required to be evaluated on a mesh, providing a distinct advantage in solving the linear Boltzmann transport equation, which is difficult to discretize. We have applied PiNNs to solve the streaming and interaction terms of the linear Boltzmann transport equation to create an accurate ML model that is wrapped inside a traditional source iteration process. We present an application of Fourier Features to PiNNs that yields good performance on heterogeneous problems. We also introduce a sampling method based on heuristics that improves the performance of PiNN simulations. The results are presented in a suite of one-dimensional radiation transport problems where PiNNs show very good agreement when compared to fine-mesh answers from traditional discretization techniques.

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