Machine-learning-based prediction of regularization parameters for seismic inverse problems

Abstract

Regularization parameter selection (RPS) is one of the most important tasks in solving inverse problems. The most common approaches seek the optimal regularization parameter (ORP) from a sequence of candidate values. However, these methods are often time-consuming because they need to conduct the estimation process on all candidate values, and they are always restricted to solve certain problem types. In this paper, we propose a novel machine learning-based prediction framework (MLBP) for the RPS problem. The MLBP first generates a large number of synthetic data by varying the inputs with different noise conditions. Then, MLBP extracts some pre-defined features to represent the input data and computes the ORP of each synthetic example by using true models. The pairs of ORP and extracted features construct a training set, which is used to train a regression model to describe the relationship between the ORP and input data. Therefore, for newly practical inverse problems, MLBP can predict their ORPs directly with the pre-trained regression model, avoiding wasting computational resources on improper regularization parameters. The numerical results also show that MLBP requires significantly less computing time and provides more accurate solutions for different tasks than traditional methods. Especially, even though the MLBP trains the regression model on synthetic data, it can also achieve satisfying performance when directly applied to field data.