Rapid Inverse Parameter Inference Using Physics-Informed Neural Networks

As Li-ion batteries become more essential in today's economy, tools need to be developed to accurately and rapidly diagnose a battery's internal state-of-health. Using a Li-ion battery's (high-rate) voltage response, it is proposed to determine a battery's internal state through Bayesian calibration. However, Bayesian calibration is notoriously slow and requires thousands of model runs. To accelerate parameter inference using Bayesian calibration, a surrogate model is developed to replace the underlying physics-based Li-ion model. Developing a surrogate model for rapid Bayesian calibration analysis is discussed for both the single particle model (SPM) and the pseudo two-dimensional (P2D) model. Surrogate models are constructed using physics-informed neural networks (PINNs) that encode the influence of internal properties on observed voltage responses. In practice, a neural network can be trained by: 1) using simulation results of the physics-based model (i.e., a data-loss approach); 2) using the residuals of the governing equations themselves (i.e., a physics-loss approach); or 3) using a combination of simulation results and governing equation residuals. In the present work, PINNs are developed using a variety of training losses and neural network architectures. In this analysis, it is shown that a PINN surrogate model can be reliably trained with only physics-informed loss. However, using a coupled data-informed and physics-loss approach produced the most accurate PINNs. Figure~\ref{fig:spm_2d} illustrates the absolute relative errors of trained PINN networks using several different training losses and neural network architectures. After determining a consistent training strategy for both the SPM and P2D PINN surrogate models, the PINNs are extended to determine additional internal state-of-health parameters. As more and more parameters were introduced, the PINN training suffered from ``the curse of dimensionality", which was mitigated by using a hierarchical training approach (where a PINN trained with fewer variable model parameters was used to train a PINN with more variable model parameters). Next, the high-dimensionality PINN surrogates are then integrated into Bayesian calibration schemes to identify internal Li-ion battery properties from experimentally measured voltages. Interpreting the high-dimensional parameter posteriors is discussed with respect to model error, parameter prior choices, and experimental errors. Figure 1