⚡ electrical engineering

Study of Machine Learning Techniques for Performance Prediction in Low-Power Hall Effect Thruster Operating on Monoatomic and Molecular Propellants

This study develops a robust, propellant-agnostic machine learning framework that combines data augmentation and physics-informed feature injection to accurately predict the performance of low-power Hall effect thrusters operating on diverse monoatomic and molecular propellants, achieving over 98% accuracy in thrust prediction using XGBoost.

Original authors: Shantanusinh Parmar, Joseph A. Moskovitz, Dan Lev, Mitchell L. R. Walker

Published 2026-08-13

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CC BY 4.0

Original authors: Shantanusinh Parmar, Joseph A. Moskovitz, Dan Lev, Mitchell L. R. Walker

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to bake the perfect cake, but instead of flour and sugar, your ingredients are invisible clouds of charged gas, and your oven is a tiny, super-hot engine floating in the vacuum of space. This is the world of electric propulsion, specifically a device called a Hall Effect Thruster. Think of it as a high-tech ion cannon that pushes satellites forward. For decades, engineers have mostly used Xenon, a heavy noble gas, as their "flour." They have a set of old, reliable recipe cards (scaling laws) that tell them exactly how much power to use and how much thrust to expect when baking with Xenon. But here's the problem: Xenon is getting expensive and hard to find, like a rare spice that costs a fortune. Scientists are now desperate to bake cakes with cheaper, more common ingredients like carbon dioxide (CO2) or nitrogen (N2)—the gases we breathe or that make up our atmosphere. The trouble is, these new "flours" behave completely differently in the oven; they don't follow the old recipe cards at all. If you try to use the old rules, your engine might sputter, fail, or just not work. We need a new way to predict how these engines will behave with these weird new gases, but testing them in real life is incredibly slow, expensive, and difficult because the machines are finicky and the data is scarce.

This is where a team of researchers from Cornell University and Georgia Tech steps in with a digital solution. Instead of baking thousands of physical cakes to figure out the recipe, they decided to teach a computer to guess the outcome using Machine Learning. They treated the engine like a complex video game where you tweak the settings (like voltage and gas flow) and the computer learns the pattern of what happens next. However, they faced a major hurdle: they didn't have enough data points. It's like trying to learn to play a new video game when you only have a few screenshots instead of a full walkthrough. To fix this, they built a clever "data factory." First, they used a statistical trick called "truncated Gaussian resampling" to fill in the missing gaps in their data without making up fake numbers that would break the physics. Then, they used a technique called "Monte Carlo augmentation" to create thousands of synthetic copies of their real data, essentially simulating the tiny errors that happen in real-world measurements to make the dataset bigger and more robust.

But simply making more data wasn't enough. The researchers realized that if they just fed raw numbers into the computer, it would be like asking a student to solve a physics problem without ever teaching them the formulas. So, they injected "theoretical knowledge" directly into the computer's brain. They added features like "theoretical thrust" and "Hall parameter proxies"—which are basically math shortcuts that describe how the engine should work according to the laws of physics. They then tested ten different types of machine learning algorithms, ranging from simple linear equations to complex "boosting" trees that make decisions step-by-step.

The results were impressive. The study found that the computer models, particularly one called XGBoost, became incredibly accurate at predicting how the engine would perform. When the models were given both the real data and the injected physics knowledge, they could predict the engine's thrust with an accuracy (R²) exceeding 98%. This means the computer's guesses were almost indistinguishable from reality. The study explicitly showed that without these physics-based "hints," the models struggled, especially with the tricky molecular gases like CO2 and Nitrogen. The computer learned that for these new gases, the engine needs stronger magnetic fields and different flow rates to stay stable, a nuance the old recipe cards missed entirely.

However, the authors are careful not to claim this is a magic bullet that solves everything. They note that while the models are great at predicting performance within the range of data they've seen (interpolation), they still struggle a bit when asked to guess what happens in completely new, untested scenarios (extrapolation), especially for the molecular gases where data is still very thin. The study suggests that while these tools are powerful for speeding up the design process and reducing the need for expensive, slow physical tests, they still rely on the quality of the data fed into them. The researchers conclude that this approach provides a highly adaptable tool for the future, allowing engineers to quickly figure out the best settings for next-generation thrusters using alternative fuels, but they warn that more data is still needed to make these predictions perfect for every possible gas and engine configuration.

Technical Summary: Study of Machine Learning Techniques for Performance Prediction in Low-Power Hall Effect Thruster Operating on Monoatomic and Molecular Propellants

Problem Statement
The transition toward low-power Hall Effect Thrusters (HETs) and the increasing demand for alternative molecular propellants (e.g., CO₂, N₂) present significant challenges for traditional performance modeling. Conventional design relies on empirical and semi-empirical scaling laws derived primarily for xenon-fueled, high-power stationary plasma thrusters. These laws often lack the fidelity required to predict performance in low-power regimes (<500 W) or when utilizing non-traditional molecular propellants, which exhibit complex dissociation pathways and different ionization costs. Furthermore, the scarcity of experimental data due to the slow throughput of vacuum facility testing and the high cost of cryopanel regeneration for molecular gases creates a "data-sparse" environment that hinders rapid optimization. First-principles closure models exist but are often computationally prohibitive for rapid design iteration.

Methodology
To address these limitations, the authors developed a robust, propellant-agnostic machine learning (ML) framework using empirical data from the CAMILA and CAM200 low-power thrusters. The study utilized a comprehensive five-phase data processing pipeline:

Data Pre-processing and Imputation: The raw dataset (682 unique points) contained gaps, particularly in beam current ( $I_b$ ) measurements. Instead of discarding these points or using boundary clipping, the authors employed a truncated Gaussian resampling technique to impute missing $I_b$ values. This method preserved the natural variance and distribution shape of the data while ensuring physical realism (no negative currents).
Data Augmentation: To mitigate data sparsity, a Monte Carlo augmentation strategy was applied exclusively to the training set. Leveraging known instrument uncertainties (assumed Gaussian, 2 $\sigma$ ), 50 synthetic clones were generated for each empirical data point, effectively expanding the training dataset from ~636 rows to ~31,800 rows.
Theoretical Input Injection: To bridge the gap between empirical data and physical laws, the authors injected 14 derived features into the input space. These included:
- Physics-Informed Features: Non-linear transforms based on electrostatic and kinematic relationships (e.g., theoretical exhaust velocity, theoretical thrust, theoretical discharge current, ionization power).
- Arithmetic Proxies: Operational ratios capturing magnetic field topology and energy barriers (e.g., Hall parameter proxies, E $\times$ B drift proxies, total energy barriers).
Model Benchmarking: Ten distinct regression algorithms were evaluated, spanning Ordinary Least Squares (OLS), Kernel methods (KNN, SVR), Tree-based models (Decision Tree, Random Forest), and Boosting techniques (XGBoost, LightGBM, CatBoost).
Training and Evaluation: Models were trained on the augmented dataset with a stratified propellant-wise split (Xe, Kr, Ar, CO₂, N₂). Performance was evaluated using $R^2$ , Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE) on a held-out verification set. Hyperparameters were tuned using adaptive GridSearchCV and RandomizedSearchCV.

Key Contributions

Propellant-Agnostic Framework: The study demonstrates a methodology capable of predicting thrust, beam current, and discharge current across both monoatomic (Xe, Kr, Ar) and molecular (CO₂, N₂) propellants within a single model architecture.
Novel Data Pipeline: The integration of truncated Gaussian imputation and Monte Carlo augmentation specifically designed for sparse vacuum facility data, coupled with physics-informed feature injection, establishes a new standard for training ML models in data-constrained regimes.
Ablation Studies: The paper provides rigorous ablation studies quantifying the impact of data augmentation and theoretical input injection. Results confirm that injecting theoretical similarity parameters (e.g., Hall parameter proxies) systematically enhances model accuracy, particularly for tree-based and boosting models.

Results

Predictive Accuracy: Tree-based and boosting models, specifically XGBoost, demonstrated superior performance. XGBoost achieved an $R^2$ of 98.12% for thrust prediction, 90.18% for beam current, and 98.98% for discharge current on the augmented dataset. Support Vector Regression (SVR) also performed exceptionally well, achieving $R^2$ values of 98.15% (thrust) and 99.24% (discharge current).
Impact of Augmentation and Injection: Ablation studies revealed that data augmentation improved $R^2$ accuracy across all models, with linear models showing the most significant gains. The addition of theoretical and arithmetic features further boosted performance, confirming that anchoring ML models to physical scaling laws improves convergence and fidelity.
Propellant-Specific Performance: While models achieved high accuracy for xenon (most predictions <10% error), performance variance increased for molecular propellants (CO₂, N₂), with errors frequently exceeding 20%. This disparity is attributed to the extreme sparsity of molecular data points and the complexity of partial ionization and dissociation in molecular gases, which challenges the ideal full-ionization assumptions of the derived theoretical features.
Feature Importance: Analysis indicated that propellant atomic mass, theoretical thrust, theoretical discharge power, and volumetric flow rate were the dominant predictors. However, the study notes that specific feature attributions can be influenced by algorithmic architecture and local data correlations (e.g., XGBoost using atomic mass as a primary split node to separate propellant regimes).

Significance and Claims
The paper claims that this data-driven methodology provides a highly adaptable tool for predicting stable operating points in low-power HETs, significantly reducing reliance on expensive and time-consuming experimental campaigns. By successfully integrating physics-informed inputs with data augmentation, the framework overcomes the limitations of static scaling laws when transitioning to alternative propellants.

The authors modestly conclude that while the current framework excels at interpolation within the engineered feature space, it faces challenges with out-of-bounds extrapolation due to the inherent limitations of tree-based models. They posit that future work should explore deep neural networks for smoother extrapolation across highly parameterized regimes, provided larger datasets (on the order of $10^4$ to $10^5$ points) become available. Ultimately, this study establishes a foundation for accelerating the optimization of next-generation thruster configurations for both traditional and emerging propellant types.

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