Evolution of learning curve and white box machine learning models for estimating in-situ stresses based on velocity-stress relationship

• Learning curve analysis of machine learning models to identify minimum dataset size. • Model-agnostic interpretation of Machine learning models for scientific validation. • Exploration of velocity-stress constitutive relationship by machine learning models. • Integrated workflow to estimate the in-situ stresses in subsurface rock formations. Reliable estimation of in-situ stresses has recently been demonstrated using an integrated deep learning/machine learning (DL/ML)-based workflow requiring training and validation using laboratory-based true triaxial ultrasonic velocity (TUV) experimental data representing ultrasonic velocities at various stress combinations. However, it remains to clarify how many TUV experiments must be performed in order to effectively and efficiently train the model. This paper presents analysis of the learning curve of the model for different dataset sizes, thereby defining the smallest effective training dataset to develop reliable prediction models. The ML/DL models were developed using TUV data obtained using five different subsurface core samples from the Utah FORGE well 16B(78)–32. Velocities were measured for 93 stress combinations per sample. Initially, prediction performances of ML/DL models were compared using 20, 40, 60, 80 and 100 percent of the total dataset. Learning curve analysis demonstrated the improvement in prediction performance up to 80% of the dataset, indicating that a model with similar predictive capacity could have been developed with 20% fewer data points collected in the laboratory. Introducing a learning curve analysis early in a project can therefore lead to significant cost savings when applying a DL/ML approach to in-situ stress estimate based on velocity-stress relationships.