Fast and Stable Nonlinear Emulation of TIEGCM Using an Autoregressive SINDy Framework

Abstract: The ever-growing number of satellites and resident space objects in low Earth orbit keeps increasing the risk of collision between these objects. To mitigate this risk, the development of new space situational awareness tools and a new generation of probabilistic emulators of the thermosphere is increasingly felt by the community of operators and scientists. We previously built a Reduced Order Probabilistic Emulator based on 3 steps: dimensionality reduction, dynamic modeling, and uncertainty quantification. Here we further develop the dynamic modeling side within ROPE using a class of stable and autoregressive nonlinear models inspired by SINDy, a framework for the identification of the nonlinear dynamics. We use this framework, which we call SINDy-AR, to emulate the thermospheric density simulated by TIEGCM. This is also the first time a SINDy-AR framework is applied to such a high dimensional system as the thermospheric emulation because of its complexity. The dynamical emulators are selected on stability and accuracy criteria, so that they can be relied on in operations and space situational awareness applications. Building surrogate models with SINDy-AR can show dynamical differences between the learned emulations. The state-dependent structure of the TIEGCM emulation shows compatibility with the presence of terdiurnal, 27-day linked to solar rotation, semiannual, and annual tidal waves. The execution speedup of the whole SINDy-AR pipeline with respect to TIEGCM 2.0 is about 90,000 times, which makes the new framework capable of being deployed on board a satellite given the low computational constraints it would be subjected to.