Physical Equation Discovery Using Physics-Consistent Neural Network (PCNN) under Incomplete Observability

Haoran Li, Yang Weng

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publicationKDD 2021 - Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining
PublisherAssociation for Computing Machinery
Pages925-933
Number of pages9
ISBN (Electronic)9781450383325
DOIs
StatePublished - Aug 14 2021
Event27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2021 - Virtual, Online, Singapore
Duration: Aug 14 2021Aug 18 2021

Publication series

NameProceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

Conference

Conference27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2021
Country/TerritorySingapore
CityVirtual, Online
Period8/14/218/18/21

Keywords

  • convex optimization
  • deep neural network
  • incomplete observability
  • physical equation discovery
  • physical system

ASJC Scopus subject areas

  • Software
  • Information Systems

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