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

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 (DNNs) to approximate the model parameters as functions of the operating conditions. This method allows the integration of the 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 DNN training.