Differentiable Geomodeling: Opportunities and Challenges

Geological models can be constructed with a variety of mathematical methods. Generally, we can describe the modeling process in a formal way as a functional relationship between input parameters (geological observations, orientations, interpolation parameters) and an output in space (lithology, stratigraphy, rock property, etc.). We evaluate here the potential of using not only the output value (prediction) itself, but also its partial derivative with respect to the input parameters to gain insight into the interpolation process, to speed-up model calibration, and to enable high-dimensional uncertainty quantification.

The calculation of this partial derivative through the complex modeling procedure requires additional work – however, this step has been greatly simplified due to progress in automatic differentiation approaches in recent years. Specifically, all modern machine learning frameworks enable a calculation of the derivatives, as this is an essential component of training in deep neural networks. We can benefit from these developments for specific geological modeling functions – and if we take specific care in the numerical implementation.

In this presentation, we discuss the basic principles between differentiable geomodelling methods, show implementation methods, and discuss potential difficulties and open challenges. We exemplify the advantage of the additional work through efficient implementations of sensitivity analyses and gradient-based sampling methods for uncertainty quantification in geological models.