近似贝叶斯神经多普勒成像
Approximate Bayesian Neural Doppler Imaging
摘要：
利用多普勒成像技术对旋转活动星表面温度的非均匀分布进行了常规成像。表面的不均匀性在高分辨率光谱观测中产生特征，这些特征根据它们在可见半球上的位置而改变波长。反演问题已经系统地解决了最大后验正则化方法假设平滑或最大熵。在这项工作中，我们的目标是解决完整的贝叶斯推断问题，通过提供访问后验分布的表面温度在恒星。我们使用摊销神经后验估计产生一个模型，近似高维后验分布的光谱观测选定的光谱范围内采样在任意旋转相位。后验分布近似与条件规范化流，这是灵活的，易于处理和容易采样的近似任意分布。当以光谱观测为条件时，它们提供了一种从后验分布获得样本的非常有效的方法。观测条件是通过使用Transformer编码器获得的，它可以处理任意波长的采样和旋转相位。我们的模型每秒可以产生数千个后验样本。我们对非常高信噪比观测的模型的验证表明，它正确地近似了后验，尽管对加宽有一些高估。我们将该模型应用于中等速度的转子II钉，产生第一个贝叶斯地图的温度不均匀性。我们的结论是，条件归一化流是一个非常有前途的工具，进行近似贝叶斯推断在更复杂的问题，在恒星物理学，如约束的磁性。
英文摘要：
The non-uniform surface temperature distribution of rotating active stars is routinely mapped with the Doppler Imaging technique. Inhomogeneities in the surface produce features in high-resolution spectroscopic observations that shift in wavelength depending on their position on the visible hemisphere. The inversion problem has been systematically solved using maximum a-posteriori regularized methods assuming smoothness or maximum entropy. Our aim in this work is to solve the full Bayesian inference problem, by providing access to the posterior distribution of the surface temperature in the star. We use amortized neural posterior estimation to produce a model that approximates the high-dimensional posterior distribution for spectroscopic observations of selected spectral ranges sampled at arbitrary rotation phases. The posterior distribution is approximated with conditional normalizing flows, which are flexible, tractable and easy to sample approximations to arbitrary distributions. When conditioned on the spectroscopic observations, they provide a very efficient way of obtaining samples from the posterior distribution. The conditioning on observations is obtained through the use of Transformer encoders, which can deal with arbitrary wavelength sampling and rotation phases. Our model can produce thousands of posterior samples per second. Our validation of the model for very high signal-to-noise observations shows that it correctly approximates the posterior, although with some overestimation of the broadening. We apply the model to the moderately fast rotator II Peg, producing the first Bayesian map of its temperature inhomogenities. We conclude that conditional normalizing flows are a very promising tool to carry out approximate Bayesian inference in more complex problems in stellar physics, like constraining the magnetic properties.
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