AI 中文总结
本研究开发傅里叶神经算子（FNO）作为替代模型，可加速辐射传输方程的求解，在误差相当下比蒙特卡洛模拟快26倍，且能泛化到不同空间离散化，为辐射传输建模提供高效准确的方案。
AI 中文摘要
辐射传输方程（RTE）控制参与性介质中的热辐射，对燃烧、大气、高温及辐射热管理应用的建模至关重要。然而，由于辐射传输固有的高维特性，RTE的数值解会产生显著的计算成本。本研究开发了一种傅里叶神经算子（FNO），作为快速、离散化无关的替代模型，用于预测参与性介质中的吸收热通量场。使用蒙特卡洛模拟生成了基准二维问题的数据集，该问题模拟热表面向具有空间变化特性的参与性介质的发射过程。对FNO进行训练以学习解算子，将输入的特性场和几何结构映射到所得的热通量场。在误差相当的情况下，训练后的FNO与蒙特卡洛模拟相比可提供高达26倍的计算加速。此外，由于FNO学习的是解算子而非图像到图像的映射，训练后的FNO能准确泛化到各种空间离散化，包括训练数据集中未出现的离散化。对热通量预测中空间频率的频谱分析表明，FNO能够抑制训练数据集中存在的高频噪声，同时保留具有物理意义的中低频频谱。这些结果表明，傅里叶神经算子替代模型可对参与性介质中的辐射传输提供准确、计算高效且离散化无关的预测。通过学习潜在的解算子，该方法朝着开发能够跨广泛几何结构、离散化和边界条件泛化的辐射传输替代模型迈出了一步。
英文摘要
The radiative transfer equation (RTE) governs thermal radiation in participating media, which is critical to modeling combustion, atmospheric, high-temperature, and radiative thermal management applications. However, due to the inherently high-dimensional nature of radiative transfer, numerical solutions to the RTE induce significant computational cost. This work develops a Fourier neural operator (FNO) as a fast, discretization-invariant, surrogate model for predicting the absorbed heat flux field in participating media. A dataset is generated on a benchmark 2-dimensional problem modeling thermal surface emission into a participating medium with spatially varying properties using Monte Carlo simulations. The FNO is trained to learn the solution operator, mapping the input property fields and geometry to the resulting heat flux field. The trained FNO provides up to 26-times computational acceleration compared to Monte Carlo simulation at equivalent error. Furthermore, as the FNO learns the solution operator and not an image-to-image mapping, the trained FNO accurately generalizes to various spatial discretizations, including those not seen in the training dataset. A spectral analysis of the spatial frequencies present in the heat flux prediction demonstrates the FNO's ability to suppress the high-frequency noise present in the training dataset, while preserving the physically meaningful low-mid frequency spectrum. These results demonstrate the Fourier neural operator surrogate model can provide accurate, computationally efficient, and discretization-invariant predictions for radiative transfer in a participating medium. By learning the underlying solution operator, this approach moves toward the development of surrogate models for radiative transfer capable of generalizing across a broad range of geometries, discretizations, and boundary conditions.
Comments16 pages, 7 figures
