Data-driven automated discovery of variational laws hidden in physical systems

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. (C) 2020 Elsevier Ltd. All rights reserved.