Radiative transfer as a Bayesian linear regression problem
Radiative transfer as a Bayesian linear regression problem
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辐射传输作为贝叶斯线性回归问题
DOI：
10.1093/mnras/stac3461
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发表时间：
2023
影响因子：
4.8
通讯作者：
De Ceuster F
中科院分区：
文献类型：
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作者：
De Ceuster F
电磁辐射在各种物理和化学过程中起着至关重要的作用。因此，几乎所有天体物理模拟都需要某种形式的辐射传输模型。尽管辐射传输算法及其实现有许多创新，但现实的辐射传输模型的计算成本仍然非常高，因此人们经常不得不求助于近似描述。这些模型的复杂性使得评估任何近似的有效性和量化模型结果的不确定性变得困难。这妨碍了科学的严谨性，特别是在将模型与观察结果进行比较时，或者将其结果用作其他模型的输入时。我们提出了一种概率数值方法，通过将辐射传输视为贝叶斯线性回归问题来解决这些问题。这使我们能够利用相关概率分布的方差对模型输入和输出的不确定性进行建模。此外，这种方法自然允许我们创建具有可量化精度的降阶辐射传输模型。这些是精确辐射传输模型的近似解，与经常使用的近似模型的精确解相反。作为第一个演示，我们推导了特征方法的概率版本，这是解决辐射传输问题的常用技术。
Electromagnetic radiation plays a crucial role in various physical and chemical processes. Hence, almost all astrophysical simulations require some form of radiative transfer model. Despite many innovations in radiative transfer algorithms and their implementation, realistic radiative transfer models remain very computationally expensive, such that one often has to resort to approximate descriptions. The complexity of these models makes it difficult to assess the validity of any approximation and to quantify uncertainties on the model results. This impedes scientific rigour, in particular, when comparing models to observations, or when using their results as input for other models. We present a probabilistic numerical approach to address these issues by treating radiative transfer as a Bayesian linear regression problem. This allows us to model uncertainties on the input and output of the model with the variances of the associated probability distributions. Furthermore, this approach naturally allows us to create reduced-order radiative transfer models with a quantifiable accuracy. These are approximate solutions to exact radiative transfer models, in contrast to the exact solutions to approximate models that are often used. As a first demonstration, we derive a probabilistic version of the method of characteristics, a commonly-used technique to solve radiative transfer problems.