TY - GEN
T1 - Physical Equation Discovery Using Physics-Consistent Neural Network (PCNN) under Incomplete Observability
AU - Li, Haoran
AU - Weng, Yang
N1 - Publisher Copyright:
© 2021 ACM.
PY - 2021/8/14
Y1 - 2021/8/14
N2 - Deep neural networks (DNNs) have been extensively applied to various fields, including physical-system monitoring and control. However, the requirement of a high confidence level in physical systems made system operators hard to trust black-box type DNNs. For example, while DNN can perform well at both training data and testing data, but when the physical system changes its operation points at a completely different range, never appeared in the history records, DNN can fail. To open the black box as much as possible, we propose a Physics-Consistent Neural Network (PCNN) for physical systems with the following properties: (1) PCNN can be shrunk to physical equations for sub-areas with full observability, (2) PCNN reduces unobservable areas into some virtual nodes, leading to a reduced network. Thus, for such a network, PCNN can also represent its underlying physical equation via a specifically designed deep-shallow hierarchy, and (3) PCNN is theoretically proved that the shallow NN in the PCNN is convex with respect to physical variables, leading to a set of convex optimizations to seek for the physics-consistent initial guess for the PCNN. We also develop a physical rule-based approach for initial guesses, significantly shortening the searching time for large systems. Comprehensive experiments on diversified systems are implemented to illustrate the outstanding performance of our PCNN.
AB - Deep neural networks (DNNs) have been extensively applied to various fields, including physical-system monitoring and control. However, the requirement of a high confidence level in physical systems made system operators hard to trust black-box type DNNs. For example, while DNN can perform well at both training data and testing data, but when the physical system changes its operation points at a completely different range, never appeared in the history records, DNN can fail. To open the black box as much as possible, we propose a Physics-Consistent Neural Network (PCNN) for physical systems with the following properties: (1) PCNN can be shrunk to physical equations for sub-areas with full observability, (2) PCNN reduces unobservable areas into some virtual nodes, leading to a reduced network. Thus, for such a network, PCNN can also represent its underlying physical equation via a specifically designed deep-shallow hierarchy, and (3) PCNN is theoretically proved that the shallow NN in the PCNN is convex with respect to physical variables, leading to a set of convex optimizations to seek for the physics-consistent initial guess for the PCNN. We also develop a physical rule-based approach for initial guesses, significantly shortening the searching time for large systems. Comprehensive experiments on diversified systems are implemented to illustrate the outstanding performance of our PCNN.
KW - convex optimization
KW - deep neural network
KW - incomplete observability
KW - physical equation discovery
KW - physical system
UR - http://www.scopus.com/inward/record.url?scp=85114957888&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85114957888&partnerID=8YFLogxK
U2 - 10.1145/3447548.3467448
DO - 10.1145/3447548.3467448
M3 - Conference contribution
AN - SCOPUS:85114957888
T3 - Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
SP - 925
EP - 933
BT - KDD 2021 - Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining
PB - Association for Computing Machinery
T2 - 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2021
Y2 - 14 August 2021 through 18 August 2021
ER -