TY - JOUR
T1 - Data-driven automated discovery of variational laws hidden in physical systems
AU - Huang, Zhilong
AU - Tian, Yanping
AU - Li, Chunjiang
AU - Lin, Guang
AU - Wu, Lingling
AU - Wang, Yong
AU - Jiang, Hanqing
N1 - Funding Information:
YW acknowledges the National Natural Science Foundation of China under Grant Nos. 11872328 and 11472240. HJ acknowledges the Guang Biao Professorship of Zhejiang University. ZL acknowledges the National Natural Science Foundation of China under Grant Nos. 11532011 and 11621062. GL would like to acknowledge the support from the National Science Foundation (DMS-1555072, DMS-1736364, and DMS-1821233). YW and HJ would like to thank Prof. JQ Lu and Prof. XL Jin from Zhejiang University for helpful discussions.
Funding Information:
YW acknowledges the National Natural Science Foundation of China under Grant Nos. 11872328 and 11472240 . HJ acknowledges the Guang Biao Professorship of Zhejiang University. ZL acknowledges the National Natural Science Foundation of China under Grant Nos. 11532011 and 11621062 . GL would like to acknowledge the support from the National Science Foundation (DMS- 1555072 , DMS- 1736364 , and DMS- 1821233 ). YW and HJ would like to thank Prof. JQ Lu and Prof. XL Jin from Zhejiang University for helpful discussions.
Publisher Copyright:
© 2020
PY - 2020/4
Y1 - 2020/4
N2 - The automated discovery of physical laws from discrete noisy data is significant for evaluating the response, stability, and reliability of dynamic systems. In contract to the existing work on the discovery of differential laws, this paper presents a data-driven method to discover the variational laws of physical systems. The effectiveness and robustness to measurement noise are demonstrated with five physical cases. Two features of variational laws, the compact form and holistic viewpoint, lead to two intrinsic advantages in the data-driven discovery of variational laws, namely, reduced data requirement and robustness to noise. The presented data-driven method can be applied to discover variational laws in real time for physical fields or more complicated social sciences, with or without prior knowledge.
AB - The automated discovery of physical laws from discrete noisy data is significant for evaluating the response, stability, and reliability of dynamic systems. In contract to the existing work on the discovery of differential laws, this paper presents a data-driven method to discover the variational laws of physical systems. The effectiveness and robustness to measurement noise are demonstrated with five physical cases. Two features of variational laws, the compact form and holistic viewpoint, lead to two intrinsic advantages in the data-driven discovery of variational laws, namely, reduced data requirement and robustness to noise. The presented data-driven method can be applied to discover variational laws in real time for physical fields or more complicated social sciences, with or without prior knowledge.
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U2 - 10.1016/j.jmps.2020.103871
DO - 10.1016/j.jmps.2020.103871
M3 - Article
AN - SCOPUS:85078090291
SN - 0022-5096
VL - 137
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
M1 - 103871
ER -