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The superposition of data sets with internal parametric self-similarity is alongstanding and widespread technique for the analysis of many types ofexperimental data across the physical sciences. Typically, this superpositionis performed manually, or recently by one of a few automated algorithms.However, these methods are often heuristic in nature, are prone to user biasvia manual data shifting or parameterization, and lack a native framework forhandling uncertainty in both the data and the resulting model of the superposeddata. In this work, we develop a data-driven, non-parametric method forsuperposing experimental data with arbitrary coordinate transformations, whichemploys Gaussian process regression to learn statistical models that describethe data, and then uses maximum a posteriori estimation to optimally superposethe data sets. This statistical framework is robust to experimental noise, andautomatically produces uncertainty estimates for the learned coordinatetransformations. Moreover, it is distinguished from black-box machine learningin its interpretability -- specifically, it produces a model that may itself beinterrogated to gain insight into the system under study. We demonstrate thesesalient features of our method through its application to four representativedata sets characterizing the mechanics of soft materials. In every case, ourmethod replicates results obtained using other approaches, but with reducedbias and the addition of uncertainty estimates. This method enables astandardized, statistical treatment of self-similar data across many fields,producing interpretable data-driven models that may inform applications such asmaterials classification, design, and discovery.

A Data-Driven Method for Automated Data Superposition with Applications in Soft Matter Science