  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.
