Physics-constrained deep neural network method for estimating parameters in a redox flow battery

Qi Zhi He, Panos Stinis, Alexandre M. Tartakovsky

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


In this paper, we present a physics-constrained deep neural network (PCDNN) method for parameter estimation in the zero-dimensional (0D) model of the vanadium redox flow battery (VRFB). In this approach, we use deep neural networks to approximate the model parameters as functions of the operating conditions. This method allows the integration of VRFB computational models as the physical constraints in the parameter learning process, leading to enhanced accuracy of parameter estimation and cell voltage prediction. Using an experimental dataset, we demonstrate that the PCDNN method can estimate model parameters for a range of operating conditions and improve the 0D model prediction of voltage compared to the 0D model prediction with constant operation-condition-independent parameters estimated with traditional inverse methods. We also demonstrate that the PCDNN approach has an improved generalization ability for estimating parameter values for operating conditions not used in the training process.

Original languageEnglish (US)
Article number231147
JournalJournal of Power Sources
StatePublished - Apr 30 2022
Externally publishedYes

Bibliographical note

Funding Information:
The authors thank Litao Yan, Yunxiang Chen, and Jie Bao for helpful discussions. The work was supported by the Energy Storage Materials Initiative (ESMI) , which is a Laboratory Directed Research and Development project at Pacific Northwest National Laboratory. Pacific Northwest National Laboratory is operated by Battelle for the U.S. Department of Energy under Contract DE-AC05-76RL01830.

Publisher Copyright:
© 2022 Elsevier B.V.


  • Electrochemical reaction
  • Machine learning
  • Parameter estimation
  • Physics-constrained deep neural networks
  • Redox flow battery


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