Physics-based statistical learning perspectives on droplet formation characteristics in microfluidic cross-junctions

Abstract

Size-controllable micro-droplets obtained in microfluidic cross-junctions are significant in microfluidics. Modeling and predictions in microfluidic-based droplet formation characteristics to date using various traditional theoretical or empirical correlations are far from satisfactory. Driven by unprecedented data volumes from microfluidic experiments and simulations, statistical learning can offer a powerful technique to extract data that can be interpreted into underlying fluid physics and modeling. This Letter historically combines the current experimental data and experimental/numerical data from previous publications as a microfluidics-based droplet formation characteristics database. Two supervised statistical learning algorithms, deep neural network and factorization-machine-based neural network (Deep-FM), were established to model and predict the formed droplet size in microfluidic cross-junctions. As a newly developed statistical learning code in 2017, the Deep-FM manifests a better prediction performance, where the average relative error was only 4.09% and nearly 98% of the data points had individual relative errors of 10% or less. Such high accuracy can be attributed to the outstanding interactions between high-order and low-order features of the Deep-FM framework. Another innovation in this Letter lies in the training dataset shrinkage and optimization without sacrificing the prediction accuracy. Such a method pioneers statistical learning algorithms in small-sample modeling problems, which is different from big data modeling and analyses. The improved statistical learning proposed in this Letter provides universal high-accuracy modeling for microfluidic-based droplet characteristics prediction, which can be an influential data-processing framework that can boost and probably transform current lines of microfluidic physics research and industrial applications.