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The Physics-Informed Neural Network Gravity Model: Generation III

John Martin, Hanspeter Schaub

TL;DR

This work introduces PINN-GM-III, a robust third-generation physics-informed neural network gravity model designed to overcome feature divergence, altitude-bias, numerical instability, and extrapolation errors in gravity field modeling. It achieves this through a sequence of architectural innovations: 5D spherical input features, a loss function augmented with relative error to balance high- and low-altitude accuracy, learned numerics via a proxy potential, smooth boundary-condition transitions, and fusion with low-fidelity analytic models. A comprehensive benchmarking suite with six metrics demonstrates that PINN-GM-III attains superior robustness and accuracy on heterogeneous-density asteroids (e.g., Eros, Bennu) compared to analytic models and prior ML methods, while maintaining competitive inference speed. The results establish PINN-GM-III as a strong, data-efficient approach for irregular-body gravity fields and outline a path for integrating analytic priors and physics constraints in future planetary science applications.

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.

The Physics-Informed Neural Network Gravity Model: Generation III

TL;DR

This work introduces PINN-GM-III, a robust third-generation physics-informed neural network gravity model designed to overcome feature divergence, altitude-bias, numerical instability, and extrapolation errors in gravity field modeling. It achieves this through a sequence of architectural innovations: 5D spherical input features, a loss function augmented with relative error to balance high- and low-altitude accuracy, learned numerics via a proxy potential, smooth boundary-condition transitions, and fusion with low-fidelity analytic models. A comprehensive benchmarking suite with six metrics demonstrates that PINN-GM-III attains superior robustness and accuracy on heterogeneous-density asteroids (e.g., Eros, Bennu) compared to analytic models and prior ML methods, while maintaining competitive inference speed. The results establish PINN-GM-III as a strong, data-efficient approach for irregular-body gravity fields and outline a path for integrating analytic priors and physics constraints in future planetary science applications.

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.
Paper Structure (38 sections, 34 equations, 10 figures, 12 tables, 1 algorithm)

This paper contains 38 sections, 34 equations, 10 figures, 12 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Analytic Models
  4. Machine Learning Models
  5. Current Challenges
  6. PINN-GM-III
  7. Feature Engineering
  8. Modified Loss Function to Account for High-Altitude Samples
  9. Improve Numerics by Learning a Proxy to the Potential
  10. Enforcing Boundary Conditions via Transition Function to Avoid Extrapolation Error
  11. Leveraging Preexisting Gravity Information into PINN-GM Solution
  12. Visualizing Modifications' Effects on Model Performance
  13. Benchmarking Suite
  14. Metrics
  15. Experiment
  16. ...and 23 more sections

Figures (10)

  • Figure 1: PINN-GMs offer high-accuracy, low-cost gravity solutions to be deployed across a variety of applications.
  • Figure 2: PINN-GM Generation III with new modifications highlighted in green
  • Figure 3: Visualization of the various weighting factors applied to the neural network potential, boundary condition potential, and the low-fidelity potential.
  • Figure 4: Acceleration percent error as a function of altitude after sequentially applying each of the proposed PINN III modifications.
  • Figure 5: Heterogeneous density distributions found within asteroids can cause standard models and assumptions to break down.
  • ...and 5 more figures