Thermal Earth Model for the Conterminous United States Using an
  Interpolative Physics-Informed Graph Neural Network (InterPIGNN)
Mohammad J. Aljubran Roland N. Horne
This study presents a data-driven spatial interpolation algorithm based on
physics-informed graph neural networks used to develop national
temperature-at-depth maps for the conterminous United States. The model was
trained to approximately satisfy the three-dimensional heat conduction law by
simultaneously predicting subsurface temperature, surface heat flow, and rock
thermal conductivity. In addition to bottomhole temperature measurements, we
incorporated other physical quantities as model inputs, such as depth,
geographic coordinates, elevation, sediment thickness, magnetic anomaly,
gravity anomaly, gamma-ray flux of radioactive elements, seismicity, and
electric conductivity. We constructed surface heat flow, and temperature and
thermal conductivity predictions for depths of 0-7 km at an interval of 1 km
with spatial resolution of 18 km$^2$ per grid cell. Our model showed superior
temperature, surface heat flow and thermal conductivity mean absolute errors of
4.8{\deg} C, 5.817 mW/m$^2$ and 0.022 W/(C-m)$, respectively. The predictions
were visualized in two-dimensional spatial maps across the modeled depths. This
thorough modeling of the Earth's thermal processes is crucial to understanding
subsurface phenomena and exploiting natural underground resources.