Chained Quantile Morphing with Normalizing Flows

Accounting for inaccuracies in Monte Carlo simulations is a crucial step in any high energy physics analysis. It becomes especially important when training machine learning models, which can amplify simulation inaccuracies and introduce large discrepancies and systematic uncertainties when the model is applied to data. In this paper, we introduce a method to transform simulated events to better match data using normalizing flows, a class of deep learning-based density estimation models. Our proposal uses a technique called chained quantile morphing, which corrects a set of observables by iteratively shifting each entry according to a conditonal cumulative density function. We demonstrate the technique on a realistic particle physics dataset, and compare it to a neural network-based reweighting method. We also introduce a new contrastive learning technique to correct high dimensional particle-level inputs, which naively cannot be efficiently corrected with morphing strategies.