This repository contains the code and results for our REX research project. The code builds a Physics Informed Neural Network (PINN) for a Single Particle Model (SPM) for Lithium-Ion batteries. The goal of the model is to solve the partial differential equations proposed by Marquis et al. [4] to improve the current battery models.
The built-in PINN in the NeuralPDE package of Julia [1] is used in this project. The pinn_spm.jl models our PINN to solve the positive and negative electrode concentrations (i.e., c_sp and c_sn) with respect to scaled time t and particle radius r. The Neural Network contains three layers including the input and output, and the hidden layer consists of 15 neurons in this model. 10,000 iterations were performed to solve the equations. Both time and radius are discretized into 11 points in [0,1]. The ode_spm provides the numerical discretization of the same equations using the MethodOfLines package. [2] These results are useful to calculate errors. The analysis.jl includes the pipeline of running the PINN model and MethodOfLines discretization, as well as the errors and plots for each result. The error is calculated as the absolute value of the difference between results of PINN and MethodOfLine. The analytical plots are generated and saved in the plots folder. The gif plots are the animation of concentrations against dt in changes of dr. The c_sn_error and c_sp_error are heat maps of errors. When dr stays the same, the error is larger when dt is larger.
The parameters in the models related to the network structure are changeable to make sure the code is robust, which makes the model is easy to maintain in future improvement and usage of solving similar equation problems. Detailed explanation is provided in the Usage part.
- Make sure that the Julia environment (at least 1.7.1) is installed. If not, the packages can be downloaded here.
- Clone this repo using
git clone https://github.com/luckyberen/PINN_for_battery.git - If you are using VS Code, install the Julia Extension
- You can change the maximum iterations, number of hidden layer neurons, and discretization levels in
pinn_spm.jlandode_spm.jlif you want to explore the model more. Make sure that thedtanddrin the two files are the same. - Start the Julia environment. Enter the repository root, use
cd("src")in Julia terminal to enter the code path. - Run it by
include("analysis.jl"). The analysis results will automatically generated.
The other contributors of this Rex project: Maricela, Chloe, Harry, Emerald, Roy.
[1] The PINN code structures are based on the Julia tutorial: https://neuralpde.sciml.ai/stable/pinn/system/
[2]MethodOfLines discretization: https://github.com/SciML/MethodOfLines.jl
[3]Cen, Z, Kubiak, P. Lithium-ion battery SOC/SOH adaptive estimation via simplified single particle model. Int J Energy Res. 2020; 44: 12444– 12459. https://doi.org/10.1002/er.5374
[4]Marquis, S. G., Sulzer, V., Timms, R., Please, C. P., & Chapman, S. J. (2019). An asymptotic derivation of a single particle model with electrolyte. arXiv [physics.chem-ph]. Opgehaal van http://arxiv.org/abs/1905.12553