MasconCube: Fast and Accurate Gravity Modeling with an Explicit Representation

2025-09-10

AI Summary

Traditional gravity field modeling for irregular small bodies—e.g., via spherical harmonic expansions—suffers from divergence inside the Brillouin sphere and inaccuracies induced by the uniform-density assumption; meanwhile, existing deep learning approaches incur high computational overhead and slow training. To address these issues, this paper proposes MasconCubes: an explicit point-mass (mascon) distribution optimization method based on a regular 3D voxel grid. For the first time, gravitational inversion is formulated as a self-supervised, physics-constrained optimization problem over a mascon grid, integrating prior topographic information and gradient-based optimization to jointly ensure high accuracy, real-time performance, and physical interpretability. Validation on representative asteroids—including Bennu and Eros—demonstrates that MasconCubes achieves ~40× faster training than GeodesyNets, while delivering superior gravitational field accuracy and more physically plausible density distributions.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Learning with Manifolds
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The geodesy of irregularly shaped small bodies presents fundamental challenges for gravitational field modeling, particularly as deep space exploration missions increasingly target asteroids and comets. Traditional approaches suffer from critical limitations: spherical harmonics diverge within the Brillouin sphere where spacecraft typically operate, polyhedral models assume unrealistic homogeneous density distributions, and existing machine learning methods like GeodesyNets and Physics-Informed Neural Networks (PINN-GM) require extensive computational resources and training time. This work introduces MasconCubes, a novel self-supervised learning approach that formulates gravity inversion as a direct optimization problem over a regular 3D grid of point masses (mascons). Unlike implicit neural representations, MasconCubes explicitly model mass distributions while leveraging known asteroid shape information to constrain the solution space. Comprehensive evaluation on diverse asteroid models including Bennu, Eros, Itokawa, and synthetic planetesimals demonstrates that MasconCubes achieve superior performance across multiple metrics. Most notably, MasconCubes demonstrate computational efficiency advantages with training times approximately 40 times faster than GeodesyNets while maintaining physical interpretability through explicit mass distributions. These results establish MasconCubes as a promising approach for mission-critical gravitational modeling applications requiring high accuracy, computational efficiency, and physical insight into internal mass distributions of irregular celestial bodies.

Problem

• Modeling gravity fields for irregular small celestial bodies
• Overcoming limitations of traditional gravity modeling methods
• Achieving fast and accurate mass distribution estimation

Innovation

• Self-supervised learning with explicit 3D mass grid optimization
• Leverages known asteroid shape to constrain solution space
• Computationally efficient with 40x faster training than alternatives