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<p>This work demonstrates the first successful application of SINDYc, a framework for dynamics identification with control, to model thermospheric density. It also marks the first use of SINDYc on such a high-dimensional system, significantly exceeding the complexity of prior applications in the literature, thus highlighting its operational and scientific value. Here we develop and study the components of a probabilistic emulator of the thermosphere using the output of TIE-GCM, a physics-based model used to describe the thermosphere-ionosphere system. The analysis covers altitudes ranging from 100 to 450 km. The thermospheric density state is represented by a tensor <InlineEquation ID="IEq1"><EquationSource Format="TEX">\(\rho (t) \in \mathbb {R}^{24 \times 20 \times 16} \sim \mathbb {R}^{7680}\)</EquationSource></InlineEquation>. From this, we obtain the latent space representation using PCA and do SINDYc-based nonlinear modeling. Building upon previous Dynamic Mode Decomposition with control (DMDc) approaches with nonlinear inputs, we show that the relative MAPE improvement of SINDYc models over DMDc reaches a peak of <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(\sim 70\%\)</EquationSource></InlineEquation> during the recovery phase of geomagnetic storms. Moreover, the SINDYc model accurately tracks the dynamical evolution of the density state, matching or exceeding the fidelity of the NRL-MSIS model along the CHAMP satellite trajectory during the storm. The framework’s seamless transition between discrete and continuous formulations further underscores its versatility, making this advancement significant for both scientific exploration and operational applications.</p>

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Nonlinear reduced order probabilistic emulation for high-dimensional thermospheric density using SINDYc

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  • 发表日期：

    2026年8月5日

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  • Daniele Sicoli,
  • Piyush M. Mehta

摘要

This work demonstrates the first successful application of SINDYc, a framework for dynamics identification with control, to model thermospheric density. It also marks the first use of SINDYc on such a high-dimensional system, significantly exceeding the complexity of prior applications in the literature, thus highlighting its operational and scientific value. Here we develop and study the components of a probabilistic emulator of the thermosphere using the output of TIE-GCM, a physics-based model used to describe the thermosphere-ionosphere system. The analysis covers altitudes ranging from 100 to 450 km. The thermospheric density state is represented by a tensor \(\rho (t) \in \mathbb {R}^{24 \times 20 \times 16} \sim \mathbb {R}^{7680}\). From this, we obtain the latent space representation using PCA and do SINDYc-based nonlinear modeling. Building upon previous Dynamic Mode Decomposition with control (DMDc) approaches with nonlinear inputs, we show that the relative MAPE improvement of SINDYc models over DMDc reaches a peak of \(\sim 70\%\) during the recovery phase of geomagnetic storms. Moreover, the SINDYc model accurately tracks the dynamical evolution of the density state, matching or exceeding the fidelity of the NRL-MSIS model along the CHAMP satellite trajectory during the storm. The framework’s seamless transition between discrete and continuous formulations further underscores its versatility, making this advancement significant for both scientific exploration and operational applications.