Machine learning (ML) has often been applied to space weather (SW) problems in recent years. SW originates from solar perturbations and is comprised of the resulting complex variations they cause within the systems between the Sun and Earth. These systems are tightly coupled and not well understood. This creates a need for skillful models with knowledge about the confidence of their predictions. One example of such a dynamical system is the thermosphere, the neutral region of Earth's upper atmosphere. Our inability to forecast it has severe repercussions in the context of satellite drag and collision avoidance operations for objects in low Earth orbit. Even with (assumed) perfect driver forecasts, our incomplete knowledge of the system results in often inaccurate neutral mass density predictions. Continuing efforts are being made to improve model accuracy, but density models rarely provide estimates of uncertainty. In this work, we propose two techniques to develop nonlinear ML models to predict thermospheric density while providing calibrated uncertainty estimates: Monte Carlo (MC) dropout and direct prediction of the probability distribution, both using the negative logarithm of predictive density (NLPD) loss function. We show the performance for models trained on local and global datasets. This shows that NLPD provides similar results for both techniques but the direct probability method has a much lower computational cost. For the global model regressed on the SET HASDM density database, we achieve errors of 11% on independent test data with well-calibrated uncertainty estimates. Using an in-situ CHAMP density dataset, both techniques provide test error on the order of 13%. The CHAMP models (on independent data) are within 2% of perfect calibration for all prediction intervals tested. This model can also be used to obtain global predictions with uncertainties at a given epoch.
翻译:近年来,机器学习(ML)经常被应用于空间气象(SW)问题。SW源于太阳扰动,包括由此在太阳和地球之间系统中产生的复杂变异。这些系统是紧密结合的,没有很好地理解。这就需要技能丰富的模型,了解其预测的信心。这种动态系统的一个实例是热层,地球高层大气的中性区域。我们无法预测它在低地球轨道物体的卫星拖动和避免碰撞操作中产生严重影响。即使在(假设的)完美驱动数据预报,我们对系统不完全的知识导致在太阳和地球之间系统内部产生的复杂变异。这些系统是紧密结合的。这些系统正在不断努力提高模型的准确性,但密度模型很少提供不确定性的估计。在这项工作中,我们提出开发非线性 ML模型来预测热层密度,同时提供校准的不确定性估计:Monte Carlo(MC) 向13度的准确度模型提供退出和直接预测概率分布的预测,同时使用预测密度的负对数值(NPD)的驱动力预测,我们不完全地对2系统进行这样的系统进行不准确的预测。我们用模型来进行全球测算数据计算,在本地和计算数据计算数据中,在本地数据中也提供一种直接的精确的计算方法上进行这样的数据,在使用一种精确的计算方法上进行。