Enterprise AI Analysis
Physically Interpretable and AI-Powered Applied-Field Thrust Modelling for Magnetoplasmadynamic Space Thrusters Using Symbolic Regression: Towards More Explainable Predictions
This paper introduces a physically interpretable, artificial intelligence (AI)-powered thrust model for Applied-Field Magnetoplasmadynamic Thrusters (AF-MPDTs), developed using symbolic regression (SR). It addresses the gap between data-driven prediction and physics-based understanding, offering more explainable predictions. The model achieves 95.98% accuracy and a 28.91% MAPE reduction against benchmark models.
Executive Impact
Our AI-powered symbolic regression models deliver unprecedented accuracy and interpretability for AF-MPDT thrust prediction, translating directly into enhanced design cycles and operational efficiency for space missions.
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Accuracy (Goodness of Fit)
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MAPE Reduction (vs. Benchmark)
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RMSE
Deep Analysis & Enterprise Applications
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Symbolic Regression Framework
Composite-Term Integration
Explainable AI & Validation
The core of our approach is Symbolic Regression (SR), an AI method inspired by genetic programming. Unlike traditional 'black box' AI, SR directly searches for analytical expressions, generating human-readable equations.
This allows for the discovery of hidden nonlinear couplings while ensuring the resulting formulas are bounded by known physical behaviors. We constrain the search space with physics-aware composite-term operators to maintain interpretability.
To bridge the gap between raw data and physical understanding, we introduced four physically motivated composite-terms: Alpha (magnetic force density), Beta (geometric scaling), Gamma (axial design ratio), and Phi (magnetic field contour). These terms transform complex raw inputs into physically meaningful drivers of acceleration, making the SR-derived equations inherently more interpretable.
This approach supports a ranked assessment of which mechanisms dominate thrust variability, consistent with established AF-MPDT physics.
Our methodology emphasizes Explainable AI (XAI) by generating transparent, closed-form correlations that can be directly inspected and audited. We employ a rigorous post-discovery protocol, including Monte Carlo (MC) envelope testing and local sensitivity analysis, to ensure numerical robustness and physical consistency.
Shapley Additive Explanations (SHAP) provide insight into the influence of each composite term, confirming that the models are anchored around expected electrodynamic drivers.
96.76%
Peak Accuracy Achieved by SR7 (Highest Complexity Model)
SR Workflow for Thrust Modelling
Data Collection & Preprocessing
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Composite-Term Creation (Alpha, Beta, Gamma, Phi)
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Symbolic Regression & Bayesian Optimization
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Equation Discovery (Hall of Fame)
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Performance & Complexity Evaluation
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Post-Discovery Robustness & Physics-Consistency Screening
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SR-Derived Model SR5: Optimal Balance
Among the developed SR equations, SR5 stands out as the optimal choice. It achieves a strong performance with 95.98% R², an RMSE of 0.0199, and an MAE of 0.0143. Crucially, SR5 maintains a complexity level (C=24) comparable to the empirical reference model (Coogan's C=25) while significantly outperforming it in accuracy metrics.
This balance of high predictive accuracy, interpretability, and structural simplicity makes SR5 an ideal candidate for early design engineering modeling in low-thrust AF-MPDT regimes, enabling clearer insights into thrust mechanisms.
42%
Reduction in Mean Absolute Error (MAE) for SR5
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Your AI Implementation Roadmap
A structured approach to integrate explainable AI for advanced propulsion system modeling.
Phase 1: Data Curation & Physics Integration
Establish a robust dataset, preprocess for consistency, and define physics-aware composite terms (Alpha, Beta, Gamma, Phi) as fundamental inputs for Symbolic Regression.
Phase 2: AI-Powered Equation Discovery
Utilize Symbolic Regression with Bayesian Optimization (TPE) to evolve candidate thrust equations, constrained by physical principles and optimized for accuracy and interpretability.
Phase 3: Validation & Interpretability Audit
Perform Monte Carlo envelope testing, local sensitivity analysis, and SHAP attribution to ensure numerical robustness, physical consistency, and clear understanding of each composite-term's influence on predictions.
Phase 4: Deployment & Design Integration
Deploy the validated, interpretable closed-form models as computationally efficient tools for AF-MPDT design studies, enabling rapid parametric sweeps and informed engineering decisions.
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