A novel machine learning approach for reduced-order model development with imbalanced data

Abstract:

Developing reduced-order models (ROMs) is a powerful approach to reducing the complexity of predictive physics-based numerical simulations for a wide range of applications, including fluid mechanics such as geologic CO₂ sequestration. Traditional approaches generate a single ROM for each simulated response (e.g., CO₂ and brine leakage rates through a single cemented wellbore). However, for an imbalanced data set with a large number of labels or simulated responses equal to a particular value (e.g., zero in our case), we demonstrate that the single ROM approach may not perform well when the ground truth for the labels fall into the imbalanced data range. Specifically, we developed a single ROM using a traditional approach for the prediction of maximum debonding between cemented wellbores and the surrounding rock formation. In this case, the single ROM incorrectly predicted non-zero values for values that should have been zero.

In order to address this issue, we proposed a novel machine learning approach for ROM development when imbalanced data exist in the training samples. In this approach, we first set all non-zero labels (i.e., simulated responses) equal to “1”, and train a “classifier” to categorically identify the “0” and ”1” cases using Support Vector Classification (SVC). For all non-zero labeled data in the original dataset, we then train a “regressor” using Multivariate Adaptive Regression Splines (MARS). The prediction process then involves: (1) determination of zero or non-zero using the “classifier” and (2) prediction using the “regressor” if classified as non-zero, returning a zero otherwise. We found that our approach is a robust and general framework for ROM development with an imbalanced data set, reducing the average predictive “error” from 17.58% to only 1.46% for the four examples in our study.