用于M1辐射传输的双曲神经封闭模型
A Hyperbolic Neural Closure for M1 Radiation Transfer
- Purdue University（普渡大学）
- University of Notre Dame（圣母大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对辐射传输模拟中M1方法简化系统不封闭问题，提出双曲神经封闭模型。通过两个神经网络对雅可比矩阵参数化确保实特征值，经数值积分重建封闭模型。该模型提高了封闭及解的精度，在相关模拟中保持稳定。
AI中文摘要：
在辐射传输模拟中，M1方法通过用低阶矩系统取代完整角传输方程实现了显著的计算节省。由于简化系统不封闭，需要一个封闭模型用低阶矩表示未知高阶矩。虽然基于机器学习的封闭模型能提高精度，但无约束的模型可能产生非实特征速度并导致数值求解器崩溃。为保证与机器学习封闭模型相关的雅可比矩阵有实特征值，我们提出了用于M1辐射传输系统的双曲神经封闭模型。我们通过两个神经网络对雅可比矩阵进行参数化，而非直接预测封闭项。这些组件组合产生一个类似于对称矩阵的雅可比矩阵，确保实特征值。然后通过沿规定积分路径对学习到的雅可比矩阵场进行数值积分来重建封闭模型。数值实验表明，所提出的封闭模型不仅比经典解析封闭模型具有更高的封闭精度，还提高了解的精度，并且在辐射传输问题的间断伽辽金模拟中保持稳定。
英文摘要：
In radiation transfer simulations, an M1 method achieves substantial computational savings by replacing the full angular transport equation with a low-order moment system. Because this reduced system is not closed, a closure model is required to represent the unknown higher-order moments using lower-order moments. While machine learning (ML)-based closures can improve accuracy beyond classical analytic closures, unconstrained learned closures may produce non-real characteristic speeds and consequently cause numerical solver breakdown. To guarantee real eigenvalues of the Jacobian associated with ML closures, we propose a hyperbolic neural closure for the M1 radiative transfer system. Rather than directly predicting closure terms, we parameterize the Jacobian through two neural networks: (i) a symmetric matrix network and (ii) a strictly convex entropy network whose Hessian defines a positive definite symmetrizer. These components are combined to yield a Jacobian that is similar to a symmetric matrix, thereby ensuring real eigenvalues. The closure is then reconstructed by numerical integration of the learned Jacobian field along a prescribed integration path. Numerical experiments show that the proposed closure not only achieves higher closure accuracy than classical analytic closures, but also improves solution accuracy and remains stable in discontinuous Galerkin simulations for radiative transfer problems.
