分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： Multi-channel imaging data is a prevalent data format in scientific fields such as astronomy and biology. The structured information and the high dimensionality of these 3-D tensor data makes the analysis an intriguing but challenging topic for statisticians and practitioners. The low-rank scalar-on-tensor regression model, in particular, has received widespread attention and has been re-formulated as a tensor Gaussian Process (Tensor-GP) model with multi-linear kernel in Yu et al. (2018). In this paper, we extend the Tensor-GP model by integrating a dimensionality reduction technique, called tensor contraction, with a Tensor-GP for a scalar-on-tensor regression task with multi-channel imaging data. This is motivated by the solar flare forecasting problem with high dimensional multi-channel imaging data. We first estimate a latent, reduced-size tensor for each data tensor and then apply a multi-linear Tensor-GP on the latent tensor data for prediction. We introduce an anisotropic total-variation regularization when conducting the tensor contraction to obtain a sparse and smooth latent tensor. We then propose an alternating proximal gradient descent algorithm for estimation. We validate our approach via extensive simulation studies and applying it to the solar flare forecasting problem.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： Multi-channel imaging data is a prevalent data format in scientific fields such as astronomy and biology. The structured information and the high dimensionality of these 3-D tensor data makes the analysis an intriguing but challenging topic for statisticians and practitioners. The low-rank scalar-on-tensor regression model, in particular, has received widespread attention and has been re-formulated as a tensor Gaussian Process (Tensor-GP) model with multi-linear kernel in Yu et al. (2018). In this paper, we extend the Tensor-GP model by integrating a dimensionality reduction technique, called tensor contraction, with a Tensor-GP for a scalar-on-tensor regression task with multi-channel imaging data. This is motivated by the solar flare forecasting problem with high dimensional multi-channel imaging data. We first estimate a latent, reduced-size tensor for each data tensor and then apply a multi-linear Tensor-GP on the latent tensor data for prediction. We introduce an anisotropic total-variation regularization when conducting the tensor contraction to obtain a sparse and smooth latent tensor. We then propose an alternating proximal gradient descent algorithm for estimation. We validate our approach via extensive simulation studies and applying it to the solar flare forecasting problem.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
Zhenguang Huang
Gabor Toth
Nishtha Sachdeva
Lulu Zhao
Bartholomeus van der Holst
Igor Sokolov
Ward Manchester
Tamas Gombosi
摘要： We describe our first attempt to systematically simulate the solar wind during different phases of the last solar cycle with the Alfv\'en Wave Solar atmosphere Model (AWSoM) developed at the University of Michigan. Key to this study is the determination of the optimal values of one of the most important input parameter of the model, the Poynting flux, which prescribes the energy flux passing through the chromospheric boundary of the model in form of Alfv\'en wave turbulence. It is found that the optimal value of the Poynting flux parameter is correlated with: 1) the open magnetic flux with the linear correlation coefficient of 0.913; 2) the area of the open magnetic field regions with the linear correlation coefficient of 0.946. These highly linear correlations could shed light on understanding how Alfv\'en wave turbulence accelerates the solar wind during different phases of the solar cycle and estimating the Poynting flux parameter for real-time solar wind predictions with AWSoM.
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