A data-driven method for automated data superposition with applications in soft matter science

Abstract The superposition of data sets with internal parametric self-similarity is a longstanding and widespread technique for the analysis many types experimental across physical sciences. Typically, this performed manually, or recently through application one few automated algorithms. However, these methods are often heuristic in nature, prone to user bias via manual shifting parameterization, lack native framework handling uncertainty both resulting model superposed data. In work, we develop data-driven, nonparametric method superposing arbitrary coordinate transformations, which employs Gaussian process regression learn statistical models that describe data, then uses maximum posteriori estimation optimally superpose sets. This robust noise automatically produces estimates learned transformations. Moreover, it distinguished from black-box machine learning its interpretability—specifically, may itself be interrogated gain insight into system under study. We demonstrate salient features our four representative characterizing mechanics soft materials. every case, replicates results obtained using other approaches, but reduced addition estimates. enables standardized, treatment self-similar fields, producing interpretable data-driven inform applications such as materials classification, design, discovery.