[Paper Review] Reduced Order Probabilistic Emulation for Physics-Based Thermosphere Models

Richard J. Licata, Piyush M. Mehta|arXiv (Cornell University)|Nov 8, 2022

Ionosphere and magnetosphere dynamics4 citations

TL;DR

This paper proposes a reduced order probabilistic emulator (TIE-GCM ROPE) that uses principal component analysis (PCA) and ensemble long short-term memory (LSTM) networks to accelerate and quantify uncertainty in physics-based thermosphere density predictions from the TIE-GCM model. It achieves sub-5 km bias in satellite orbit propagation during the 2003 Halloween storm—outperforming deterministic linear models by a factor of 2 and providing calibrated uncertainty distributions via Monte Carlo sampling.

ABSTRACT

The geospace environment is volatile and highly driven. Space weather has effects on Earth's magnetosphere that cause a dynamic and enigmatic response in the thermosphere, particularly on the evolution of neutral mass density. Many models exist that use space weather drivers to produce a density response, but these models are typically computationally expensive or inaccurate for certain space weather conditions. In response, this work aims to employ a probabilistic machine learning (ML) method to create an efficient surrogate for the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIE-GCM), a physics-based thermosphere model. Our method leverages principal component analysis to reduce the dimensionality of TIE-GCM and recurrent neural networks to model the dynamic behavior of the thermosphere much quicker than the numerical model. The newly developed reduced order probabilistic emulator (ROPE) uses Long-Short Term Memory neural networks to perform time-series forecasting in the reduced state and provide distributions for future density. We show that across the available data, TIE-GCM ROPE has similar error to previous linear approaches while improving storm-time modeling. We also conduct a satellite propagation study for the significant November 2003 storm which shows that TIE-GCM ROPE can capture the position resulting from TIE-GCM density with < 5 km bias. Simultaneously, linear approaches provide point estimates that can result in biases of 7 - 18 km.

Motivation & Objective

• To develop a computationally efficient surrogate for the physics-based TIE-GCM thermosphere model that enables real-time or operational use.
• To improve storm-time modeling accuracy by capturing nonlinear dynamics not resolved by linear reduced order models.
• To provide probabilistic forecasts of thermospheric density with calibrated uncertainty quantification (UQ) for operational applications.
• To enable long-term dynamic predictions (up to a year) with minimal error while preserving physical consistency.
• To demonstrate the operational advantage of probabilistic modeling over deterministic surrogates in satellite state propagation under extreme space weather.

Proposed method

• Dimensionality reduction via principal component analysis (PCA) is applied to TIE-GCM output data to project high-dimensional density fields into a lower-dimensional latent space.
• Ensemble long short-term memory (LSTM) networks are trained on the reduced-state time series to model the dynamic evolution of thermospheric density.
• A hierarchical ensemble approach combines predictions from two distinct LSTM architectures using performance-based, fixed weights to improve robustness and calibration.
• Uncertainty quantification is achieved through Monte Carlo sampling of the ensemble, with a scaling method applied to improve calibration of predictive distributions.
• The model is trained on seven years of TIE-GCM data from solar cycle 23 and an additional year of simulated drivers (Sim1) to enhance storm representation.
• Model performance is evaluated via long-term dynamic predictions and a satellite propagation study during the November 2003 geomagnetic storm.

Experimental results

Research questions

• RQ1 Can a nonlinear, probabilistic reduced order model outperform linear dynamic mode decomposition (DMD) techniques in capturing TIE-GCM’s thermospheric density dynamics during geomagnetic storms?
• RQ2 To what extent does ensemble LSTM modeling improve long-term dynamic prediction accuracy compared to linear surrogates?
• RQ3 Can a hierarchical ensemble of LSTMs with calibrated uncertainty quantification better represent the true density distribution than deterministic models?
• RQ4 How does the inclusion of nonlinear inputs affect the accuracy and uncertainty of satellite orbit propagation during extreme space weather events?
• RQ5 Can the proposed emulator maintain low bias and high reliability in long-term (multi-day to yearly) forecasts without state updates?

Key findings

• TIE-GCM ROPE achieves a final along-track position bias of less than 5 km relative to TIE-GCM during the November 2003 storm, significantly outperforming deterministic DMDc models with 7–18 km bias.
• The probabilistic nature of TIE-GCM ROPE captures the true TIE-GCM position within its 20 km predictive distribution spread, while deterministic models provide only point estimates.
• TIE-GCM ROPE maintains approximately 10% mean error over 8,700 time steps (over a year), demonstrating robust long-term dynamic prediction capability.
• The model shows superior performance in capturing storm-time dynamics, particularly during the 2003 Halloween storm, where DMDc models fail to represent the full magnitude of density changes.
• The hierarchical ensemble approach is essential, as it mitigates overconfidence from individual architectures and improves uncertainty calibration across diverse storm conditions.
• The use of nonlinear inputs in the LSTM framework reduces bias by roughly half compared to linear-input DMDc models, highlighting the advantage of nonlinear modeling for extreme events.