Incorporating Uncertainties in A Model-Based Data-Driven Framework Using Transfer Learning

Abstract

Summary Modelling and optimization in subsurface applications generally deals with uncertainty. To account for this uncertainty, decision-making workflows use an ensemble of model realizations. This approach leads to a large amount of required full-physics simulations, which can take days to complete. To make this process more computationally efficient, we seek ways of replacing an ensemble of full-physics simulation models with an ensemble of fast data-driven models. Training a single data-driven model of a particular realization of the full-physics model requires a significant amount of full-physics simulations. As a consequence, the straightforward approach of training a data-driven model for each realization independently, to form an ensemble of models, would require an infeasible amount of full-physics simulations. The total computational cost would significantly exceed the effort necessary to perform any state-of-the-art decision-making workflow directly on an ensemble of full-physics models. In this work, we developed a framework using concepts of transfer learning from the machine learning (ML) community to create an ensemble of data-driven (ML) models in a computationally efficient way. Transfer learning enables the generation of ML models using a limited amount of training samples (i.e., full-physics simulations) per realization through the utilization of information obtained as a result of the training of a base ML model built on one full-physics model realization. Hence, it dramatically accelerates the training process of the next ML models, enabling the feasible generation of an ensemble of ML models based on an ensemble of full physics models. Our results show that the same prediction accuracy as training with 500 samples (i.e., 500 full-physics simulations minimum number required to achieve an acceptable prediction accuracy in our experiments) per realization can be achieved using as few as 20 training samples per model realization, thereby reducing the computational effort by a factor 25. Our results also confirm the robustness of the approach to different base ML models. We conclude that transfer learning techniques are an effective approach to incorporate uncertainty within a model based data-driven framework, which can be used to make computationally demanding workflows more practical.