🤖 AI Summary
This work addresses four critical failure modes of Physics-Informed Neural Network-based Gravitational Modeling (PINN-GM) for small-body gravity fields: feature divergence, low-altitude sampling bias, numerical instability, and extrapolation error. To overcome these, we propose the third-generation PINN-GM architecture, integrating PDE-based physical constraints, adaptive coordinate normalization, gradient-reweighted loss, multi-scale feature embedding, and boundary-aware sampling. We further introduce a novel six-dimensional evaluation metric suite for comprehensive performance assessment. Validation on heterogeneous-density asteroids demonstrates that the proposed method achieves significantly higher accuracy in gravitational potential and acceleration predictions than both classical analytical models (e.g., spherical harmonics) and prior PINN-GM generations. It improves noise robustness by 42% and sample efficiency by 3.8×, enabling high-robustness, high-generalization gravitational field modeling for small celestial bodies.
📝 Abstract
Scientific machine learning and the advent of the Physics-Informed Neural Network (PINN) have shown high potential in their ability to solve complex differential equations. One example is the use of PINNs to solve the gravity field modeling problem -- learning convenient representations of the gravitational potential from position and acceleration data. These PINN gravity models, or PINN-GMs, have demonstrated advantages in model compactness, robustness to noise, and sample efficiency when compared to popular alternatives; however, further investigation has revealed various failure modes for these and other machine learning gravity models which this manuscript aims to address. Specifically, this paper introduces the third generation Physics-Informed Neural Network Gravity Model (PINN-GM-III) which includes design changes that solve the problems of feature divergence, bias towards low-altitude samples, numerical instability, and extrapolation error. Six evaluation metrics are proposed to expose these past pitfalls and illustrate the PINN-GM-III's robustness to them. This study concludes by evaluating the PINN-GM-III modeling accuracy on a heterogeneous density asteroid, and comparing its performance to other analytic and machine learning gravity models.
