geoML

Spatial modeling using machine learning concepts.

This is a work in progress. Current functionality includes:

• Gaussian process modeling in 1D, 2D, and 3D, with anisotropy ellipsoid;
• Variational Gaussian process for classification and multivariate modeling;
• Support for compositional data;
• Support for directional data (structural geology measurements, scalar field gradients, etc.);
• Support for classification with boundary data (points lying in the boundary between two rock types);
• Deep learning for non-stationary modeling;
• Exports results to PyVista format;
• Back-end powered by TensorFlow.

Installation

Clone the repo and update the path to include the package's folder.

Dependencies:

• scikit-image
• pandas
• numpy
• tensorflow
• tensorflow-probability
• pyvista and plotly for 3D visualization

Examples

The following notebooks demonstrate the capabilities of the package (if one of them seems broken, it is probably going through an update).

• Walker Lake
• 2D classification with structural constraints
• Sunspot cycle prediction
• 3D classification
• Potential field modeling using only directional data
• Jura
• Compositional data
• Gold modeling with auxiliary variables

Learning materials

• Understanding inducing points
• VGP training step by step

References

@article{Goncalves2020,
   abstract = {Solar cycle prediction is a key activity in space weather research. Several techniques have been employed in recent decades in order to try to forecast the next sunspot-cycle maxima and time. In this work, the Gaussian Process, a machine-learning technique, is used to make a prediction for the solar cycle 25 based on the annual sunspot number 2.0 data from 1700 to 2018. A variation known as Warped Gaussian Process is employed in order to deal with the non-negativity constraint and asymmetrical data distribution. Tests using holdout data yielded a root mean square error of 10.0 within 5 years and 25.0-35.0 within 10 years. Simulations using the predictive distribution were performed to account for the uncertainty in the prediction. Cycle 25 is expected to last from 2019 – 2029, with a peak sunspot number about 117 (110 by the median) occurring most likely in 2024. Thus our method predicts that solar Cycle 25 will be weaker than previous ones, implying a continuing trend of declining solar activity as observed in the past two cycles.},
   author = {Ítalo G. Gonçalves and Ezequiel Echer and Everton Frigo},
   doi = {10.1016/j.asr.2019.11.011},
   journal = {Advances in Space Research},
   keywords = {gaussian process,machine learning,solar cycle,sunspot number},
   pages = {677-683},
   title = {Sunspot Cycle Prediction Using Warped Gaussian Process Regression},
   volume = {65},
   url = {https://www.sciencedirect.com/science/article/pii/S0273117719308026},
   year = {2020},
}

@article{Goncalves2021,
   author = {Ítalo Gomes Gonçalves and Felipe Guadagnin and Sissa Kumaira and Saulo Lopes da Silva},
   doi = {10.1016/j.cageo.2021.104715},
   issn = {0098-3004},
   issue = {January},
   journal = {Computers and Geosciences},
   keywords = {Gaussian Process,Implicit modeling,Kriging,Machine learning,Structural trend,Vector field},
   pages = {104715},
   publisher = {Elsevier Ltd},
   title = {A machine learning model for structural trend fields},
   volume = {149},
   url = {https://doi.org/10.1016/j.cageo.2021.104715},
   year = {2021},
}

@article{Goncalves2022,
   author = {Ítalo Gomes Gonçalves and Felipe Guadagnin and Diogo Peixoto Cordova},
   doi = {10.1016/j.cageo.2022.105056},
   issn = {00983004},
   journal = {Computers & Geosciences},
   keywords = {Gaussian process,Kriging,Machine learning,Variational inference},
   pages = {105056},
   publisher = {Elsevier Ltd},
   title = {Learning spatial patterns with variational Gaussian processes: Regression},
   volume = {161},
   url = {https://doi.org/10.1016/j.cageo.2022.105056},
   year = {2022},
}

@article{,
   author = {Ítalo Gomes Gonçalves and Felipe Guadagnin and Diogo Peixoto Cordova},
   doi = {10.1016/j.cageo.2023.105323},
   issn = {00983004},
   journal = {Computers & Geosciences},
   month = {5},
   pages = {105323},
   title = {Variational Gaussian processes for implicit geological modeling},
   volume = {174},
   url = {https://linkinghub.elsevier.com/retrieve/pii/S0098300423000274},
   year = {2023},
}