TY - JOUR
T1 - Robust physics discovery via supervised and unsupervised pattern recognition using the Euler Characteristic
AU - Zhang, Zhiming
AU - Xu, Nan
AU - Liu, Yongming
N1 - Funding Information:
The research reported in this paper was supported by funds from NASA University Leadership Initiative Program (Contract No. NNX17AJ86A , Project Officer: Dr. Anupa Bajwa, Principal Investigator: Dr. Yongming Liu). The support is gratefully acknowledged.
Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/7/1
Y1 - 2022/7/1
N2 - 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.
AB - 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.
KW - Euler Characteristic
KW - Partial differential equation
KW - Pattern recognition
KW - Physics discovery
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U2 - 10.1016/j.cma.2022.115110
DO - 10.1016/j.cma.2022.115110
M3 - Article
AN - SCOPUS:85130587112
SN - 0045-7825
VL - 397
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 115110
ER -