PyNumDiff: A Python package for numerical differentiation of noisy time-series data

Abstract

The numerical computation of derivatives is ubiquitous in every scientific discipline and engineering application because derivatives express fundamental relationships among many quantities of interest. As a result, a large number of diverse algorithms have been developed to differentiate numerical data. These efforts are challenging because, in reality, practitioners often have sparse and noisy measurements and data, which undermine the ability to estimate accurate derivatives. Among the diversity of mathematical approaches that have been formulated, many are ad hoc in nature and require significant bespoke tuning of multiple parameters to produce reasonable results. Thus, at a practical level, it is often unclear which method should be used, how to choose parameters, and how to compare results from different methods. Regardless of application domain, scientists of various levels of mathematical expertise would benefit from a unified toolbox for differentiation techniques and parameter tuning. To address these needs, we built the open-source package PyNumDiff, with two primary goals in mind: (1) to develop a unified source for a diversity of differentiation methods using a common API, and (2) to provide an objective approach for choosing optimal parameters with a single universal hyperparameter (gamma) that functions similarly for all differentiation methods (Van Breugel et al., 2020). By filling these needs, PyNumdiff facilitates easy computations of derivatives on diverse time-series data sets.