Dual neural network architecture for determining epistemic and aleatoric uncertainties

A machine learning method for geological formation modeling comprising:

• in a training phase, training a first neural network to predict a mean value and epistemic uncertainty of an unknown geophysical property of a geological formation given a vector of measurement data of the geological formation as input, and training a second neural network to predict total uncertainty of the unknown geophysical property of the geological formation given the vector of measurement data of the geological formation as input, wherein the training phase further comprises training the second neural network by minimizing a cost function that involves differences between a predicted mean value of the unknown geophysical property of the geological formation from the first neural network and a ground-truth value of the unknown geophysical property of the geological formation;
• in an inference phase, supplying at least one vector of measurement data of the geological formation to the trained first neural network to predict a mean value and epistemic uncertainty of the unknown geophysical property of the geological formation, using the trained second neural network to predict total uncertainty of the unknown geophysical property of the geological formation, and determining aleatoric uncertainty of the unknown geophysical property of the geological formation based on the epistemic uncertainty and the total uncertainty of the unknown geophysical property of the geological formation.