  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.
