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

arXiv: https://arxiv.org/abs/2106.11451 · HTML: https://mlsanity.com/paper/2106.11451/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 47 references that are in the map.
- First posted on arXiv 21 Jun 2021.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport](https://mlsanity.com/paper/1912.02968/) (2019)
- [Learning Unknown Physics of non-Newtonian Fluids](https://mlsanity.com/paper/2009.01658/) (2020)
- [A comparative study of physics-informed neural network models for learning unknown dynamics and constitutive relations](https://mlsanity.com/paper/1904.04058/) (2019)

## Built on by (most cited first, 9 of 9)

- [Thermodynamically Consistent Machine-Learned Internal State Variable Approach for Data-Driven Modeling of Path-Dependent Materials](https://mlsanity.com/paper/2205.00578/) (2022)
- [Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations](https://mlsanity.com/paper/2505.08740/) (2025)
- [A Multi-Resolution Physics-Informed Recurrent Neural Network: Formulation and Application to Musculoskeletal Systems](https://mlsanity.com/paper/2305.16593/) (2023)
- [PINN surrogate of Li-ion battery models for parameter inference. Part I: Implementation and multi-fidelity hierarchies for the single-particle model](https://mlsanity.com/paper/2312.17329/) (2023)
- [Inferring electrochemical performance and parameters of Li-ion batteries based on deep operator networks](https://mlsanity.com/paper/2205.03508/) (2022)
- [Physics-informed machine learning of redox flow battery based on a two-dimensional unit cell model](https://mlsanity.com/paper/2306.01010/) (2023)
- [PINN surrogate of Li-ion battery models for parameter inference. Part II: Regularization and application of the pseudo-2D model](https://mlsanity.com/paper/2312.17336/) (2023)
- [Enhanced physics-constrained deep neural networks for modeling vanadium redox flow battery](https://mlsanity.com/paper/2203.01985/) (2022)
- [Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements](https://mlsanity.com/paper/2509.00203/) (2025)

## Abstract (arXiv)

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.