Potentialities and Limitations of Machine Learning to Solve Mixing Problems: A Case Study

Cut-and-shuffle mixing is an instructive candidate system with which to assess the potential of machine learning (ML) as an approach to solve difficult mixing problems. We focus on a specific subset of cut-and-shuffle systems, the one-dimensional interval exchange transform. This class of mixing operations is well studied, and a simple mixing methodology, which we refer to as the longest segment (LS) method, works well under a broad range of situations. We use supervised learning to train a neural network (NN) to emulate the LS mixing algorithm for mixing a one-dimensional domain of two species. We find that a generic deep NN can emulate the LS method with good accuracy but cannot generalize to conditions significantly outside its training repertoire. The challenges in defining the mixing problem and generalizing a ML mixing approach are indicative of those expected for more complex systems where optimal or near optimal mixing methods remain unknown.