We introduce a novel neural architecture termed thermoNET, designed to
represent thermospheric density in satellite orbital propagation using a
reduced amount of differentiable computations. Due to the appearance of a
neural network on the right-hand side of the equations of motion, the resulting
satellite dynamics is governed by a NeuralODE, a neural Ordinary Differential
Equation, characterized by its fully differentiable nature, allowing the
derivation of variational equations (hence of the state transition matrix) and
facilitating its use in connection to advanced numerical techniques such as
Taylor-based numerical propagation and differential algebraic techniques.
Efficient training of the network parameters occurs through two distinct
approaches. In the first approach, the network undergoes training independently
of spacecraft dynamics, engaging in a pure regression task against ground truth
models, including JB-08 and NRLMSISE-00. In the second paradigm, network
parameters are learned based on observed dynamics, adapting through ODE
sensitivities. In both cases, the outcome is a flexible, compact model of the
thermosphere density greatly enhancing numerical propagation efficiency while
maintaining accuracy in the orbital predictions.

通过引入名为 thermoNET 的新型神经网络架构，我们能够以较少的可微分计算来表示卫星轨道传播中的热层密度。该网络结构通过 NeuralODE（神经常微分方程）控制卫星动力学，实现完全可微分的变分方程的推导，并能够与先进的数值技术（如基于泰勒级数的数值传播和微分代数技术）进行连接，从而实现网络参数的高效训练。通过纯回归任务和基于观察到的动态的 ODE 敏感性的自适应学习，我们得到了一个灵活而紧凑的热层密度模型，极大地提高了数值传播的效率，并在轨道预测中保持了准确性。

用于 VLEO 模拟的神经 ODE：介绍 thermoNET 对热层建模

NeuralODEs for VLEO simulations: Introducing thermoNET for Thermosphere  Modeling

Accurate estimation of thermospheric density is critical for precise modeling
of satellite drag forces in low Earth orbit (LEO). Improving this estimation is
crucial to tasks such as state estimation, collision avoidance, and re-entry
calculations. The largest source of uncertainty in determining thermospheric
density is modeling the effects of space weather driven by solar and
geomagnetic activity. Current operational models rely on ground-based proxy
indices which imperfectly correlate with the complexity of solar outputs and
geomagnetic responses. In this work, we directly incorporate NASA's Solar
Dynamics Observatory (SDO) extreme ultraviolet (EUV) spectral images into a
neural thermospheric density model to determine whether the predictive
performance of the model is increased by using space-based EUV imagery data
instead of, or in addition to, the ground-based proxy indices. We demonstrate
that EUV imagery can enable predictions with much higher temporal resolution
and replace ground-based proxies while significantly increasing performance
relative to current operational models. Our method paves the way for
assimilating EUV image data into operational thermospheric density forecasting
models for use in LEO satellite navigation processes.

将太空中的极紫外光图像数据直接融入神经网络热层密度模型，可以代替地面代理指标、提高预测性能，为低地球轨道卫星导航流程中的操作性热层密度预测模型引入极紫外光数据的使用方法。