Enhanced physics-constrained deep neural networks for modeling vanadium redox flow battery

Qi Zhi He, Yucheng Fu, Panos Stinis, Alexandre Tartakovsky

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Numerical simulation has become indispensable in advancing cost-effective process optimization and control of flow batteries. We propose an enhanced version of the physics-constrained deep neural network (PCDNN) approach (He et al., 2022) to provide high-accuracy voltage predictions in the vanadium redox flow batteries (VRFBs). The purpose of the PCDNN approach is to enforce the physics-based zero-dimensional (0D) VRFB model in a neural network to assure model generalization for various battery operation conditions. However, limited by the simplifications of the 0D model, the PCDNN cannot capture sharp voltage changes in the extreme SOC regions. To improve the accuracy of voltage prediction at extreme ranges, we introduce a second (enhanced) DNN to mitigate the prediction errors carried from the 0D model itself and call the resulting approach enhanced PCDNN (ePCDNN). By comparing with experimental data, we demonstrate that the ePCDNN approach can accurately capture the voltage response throughout the charge–discharge cycle, including the tail region of the voltage discharge curve. The loss function for training the ePCDNN is designed to be flexible by adjusting the weights of the physics-constrained DNN and the enhanced DNN. This allows the ePCDNN framework to be transferable to battery systems with variable physical model fidelity.

Original languageEnglish (US)
Article number231807
JournalJournal of Power Sources
StatePublished - Sep 15 2022

Bibliographical note

Funding Information:
This research was supported by the Energy Storage Materials Initiative (ESMI) at Pacific Northwest National Laboratory (PNNL). PNNL is a multi-program national laboratory operated for the U.S. Department of Energy (DOE) by Battelle Memorial Institute under Contract No. DE-AC05-76RL01830. Q.H. would also like to acknowledge the University of Minnesota CEGE Startup Funds for support.

Publisher Copyright:
© 2022 Elsevier B.V.


  • Electrochemical model
  • Energy storage
  • Machine learning
  • Physics-constrained neural networks
  • Redox flow battery


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