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DY: Fachverband Dynamik und Statistische Physik

DY 19: Machine Learning in Dynamics and Statistical Physics II (joint session DY/SOE)

DY 19.1: Talk

Tuesday, March 19, 2024, 09:30–09:45, BH-N 243

Pareto-Based Selection of Data-Driven Ordinary Differential Equations — •Gianmarco Ducci, Karsten Reuter, and Christoph Scheurer — Fritz-Haber-Institut der MPG, Berlin

Data-driven approaches enable the approximation of governing laws of physical processes with parsimonious equations. However, they face challenges due to inherent noise in data, which impacts the sparsity of the result. While a great effort over the last decade has been made in this field, data-driven approaches generally rely on the paradigm of imposing a fixed base of library functions. In order to promote sparsity, finding the optimal set of basis functions is a necessary condition but a challenging task to guess in advance.

In this work, we propose an alternative approach which consists of optimizing the very library of functions while imposing sparsity. The robustness of our results is not only evaluated by the quality of the fit of the discovered model, but also by the statistical distribution of the residuals with respect to the original noise in the data. The model selection is then chosen from a subset of optimal models obtained in a Pareto fashion. We illustrate how this method can be used as a tool to derive microkinetic equations from experimental data.

Keywords: data-driven modelling; sparse model discovery