# The Physics-Informed Neural Network Gravity Model: Generation III

arXiv: https://arxiv.org/abs/2312.10257 · HTML: https://mlsanity.com/paper/2312.10257/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 48 references that are in the map.
- First posted on arXiv 15 Dec 2023.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Machine learning for metal additive manufacturing: Predicting temperature and melt pool fluid dynamics using physics-informed neural networks](https://mlsanity.com/paper/2008.13547/) (2020)
- [Real-Time Optimal Control for Irregular Asteroid Landings Using Deep Neural Networks](https://mlsanity.com/paper/1901.02210/) (2019)

## Built on by (most cited first, 1 of 1)

- [MasconCube: Fast and Accurate Gravity Modeling with an Explicit Representation](https://mlsanity.com/paper/2509.08607/) (2025)

## Abstract (arXiv)

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.