Robust physics discovery via supervised and unsupervised pattern recognition using the Euler characteristic

TL;DR

This paper introduces the use of Euler characteristics as topological features in machine learning to robustly identify underlying physics in noisy dynamical system data, enhancing feature representativeness and discovery accuracy.

Contribution

It proposes a novel application of Euler characteristics for physics discovery, improving robustness and confidence in noisy data scenarios through supervised and unsupervised learning.

Findings

Euler characteristics effectively distinguish different dynamical systems.

Using EC improves the robustness of physics discovery in noisy data.

Machine learning with EC enhances confidence in sparse regression methods.

Abstract

Machine learning approaches have been widely used for discovering the underlying physics of dynamical systems from measured data. Existing approaches, however, still lack robustness, especially when the measured data contain a large level of noise. The lack of robustness is mainly attributed to the insufficient representativeness of used features. As a result, the intrinsic mechanism governing the observed system cannot be accurately identified. In this study, we use an efficient topological descriptor for complex data, i.e., the Euler characteristics (ECs), as features to characterize the spatiotemporal data collected from dynamical systems and discover the underlying physics. Unsupervised manifold learning and supervised classification results show that EC can be used to efficiently distinguish systems with different while similar governing models. We also demonstrate that the machine learning approaches using EC can improve the confidence level of sparse regression methods of physics discovery.