Reduced order models with unknown closure relations are ubiquitous in transport problems. In this work, we present a machine-learning approach to finding closure relations utilising differentiable programming. We use the Su Olson radiation transport test problem as an example training data set. We present novel closures for second angular moment (variable Eddington factor), third angular moment and flux-limited diffusion models. We evaluate the improvement of the machine-learnt closures over those from the literature. These improvements are then tested by considering a modification to the Su Olson problem. Comparisons to literature closures show the machine learning models out-perform them in both the trained and unseen problems.

中文翻译：

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使用可微分编程学习闭合关系：辐射传输的一个例子

具有未知闭包关系的降阶模型在运输问题中普遍存在。在这项工作中，我们提出了一种利用可微分编程寻找闭包关系的机器学习方法。我们使用 Su Olson 辐射传输测试问题作为训练数据集的示例。我们提出了第二角矩（可变爱丁顿因子）、第三角矩和通量限制扩散模型的新颖闭包。我们评估了机器学习闭包相对于文献中的闭包的改进。然后通过考虑对 Su Olson 问题的修改来测试这些改进。与文献闭包的比较表明，机器学习模型在训练过的问题和未见过的问题上都优于它们。