Coupled physics-deep learning inversion

Abstract

Application of machine learning (ML) or deep learning (DL) to geophysical data inversion is a growing topic of interest. Opportunities are in the areas of enhanced efficiency, resolution, and uniqueness for the inversion of geophysical ill-posed problems. Direct application of standard data-driven ML approaches to inversion have quickly shown limitations in the practical implementation. Some of the problems reside in the scarcity of appropriate labeled data caused by the lack of prior knowledge on the earth model being explored. Physics-informed network training is reducing the solution to physically bounded models. ML-inversion, however, needs to compete against the battery of highly evolved physics-based (Phy) inversion techniques that represent the most efficient and best result-oriented approaches. We have developed robust and efficient workflows and algorithms for combining ML and physics-based inversions in a unified approach by providing reciprocal interference. The workflow consists of linking the ML and Phy schemes through penalty functions applied to the common model term. A process of network retraining using partial inversion results further complements the procedure. The network progressively learns the Phy requirements and steers its predictions toward the data misfit reduction. The Phy inversion process also evolves by adding pseudo randomness and nonlinearity to the deterministic approach through the pseudo-stochastic model space sampling and nonlinear hyperparameter determination provided by DL. The procedure tends to converge after several iterations to common agreeable models introducing a stochastic flavor. The Phy-DL inversion (PhyDLI) scheme is demonstrated on synthetic and field transient electromagnetic data.