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

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 propose a robust physics discovery method via pattern recognition. In this method, the Euler Characteristic (EC), an efficient topological descriptor for complex data, is used as the feature vector for characterizing the spatiotemporal data collected from dynamical systems. 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 results of sparse regression methods of physics discovery without hard-thresholding or hyperparameter tuning.