Physics-Informed Neural Networks for geoid modeling: preliminary results in Colorado

Although machine learning has become increasingly important in geodesy related fields such as geophysics, seismology and remote sensing, its applications in geodesy, especially in physical geodesy, are still in its early stages. The main reason for this can be attributed to the black box nature of pure data-driven machine learning, which lacks physical interpretability and credibility, making it difficult for machine learning approaches to be used in physical geodesy that takes reliability and accuracy as its core criteria. Physics-Informed Neural Networks (PINNs) is a class of deep learning algorithms aims to seamlessly integrate data and physical prior knowledge including ordinary or partial differential equations, it can yield more physically interpretable machine learning models that provide robust and accurate predictions. We present the PINN approach for gravimetric geoid modeling from Earth gravity model, terrestrial and airborne gravity datasets. A convolutional neural network (CNN) deep learning architecture is used, gravity measurements and physical laws are integrated by embedding the Laplace’s equation of disturbing potential and the fundamental equation of gravity anomaly into the loss function of the neural network using automatic differentiation. The PINN based geoid computation approach is tested in the area of the Colorado 1-cm geoid experiment. Simulated gravity observations and GNSS leveling derived geoid heights based on EIGEN-6C4 are used to validate the theoretical correctness and validity of the proposed PINN approach, and its performance on precise geoid modeling in this challenging area is evaluated using the actual terrestrial and airborne gravity observations, GNSS leveling measured geoid heights and high resolution DEM provided by NGS/NOAA.