PINN surrogate of Li-ion battery models for parameter inference. Part II: Regularization and application of the pseudo-2D model

TL;DR

A physics-informed neural network (PINN) is developed as a surrogate for the pseudo-2D (P2D) battery model calibration and the ability to use these PINNs to calibrate scaling parameters for the cathode Li diffusion and the anode exchange current density is highlighted.

Abstract

Bayesian parameter inference is useful to improve Li-ion battery diagnostics and can help formulate battery aging models. However, it is computationally intensive and cannot be easily repeated for multiple cycles, multiple operating conditions, or multiple replicate cells. To reduce the computational cost of Bayesian calibration, numerical solvers for physics-based models can be replaced with faster surrogates. A physics-informed neural network (PINN) is developed as a surrogate for the pseudo-2D (P2D) battery model calibration. For the P2D surrogate, additional training regularization was needed as compared to the PINN single-particle model (SPM) developed in Part I. Both the PINN SPM and P2D surrogate models are exercised for parameter inference and compared to data obtained from a direct numerical solution of the governing equations. A parameter inference study highlights the ability to use these PINNs to calibrate scaling parameters for the cathode Li diffusion and the anode exchange current density. By realizing computational speed-ups of 2250x for the P2D model, as compared to using standard integrating methods, the PINN surrogates enable rapid state-of-health diagnostics. In the low-data availability scenario, the testing error was estimated to 2mV for the SPM surrogate and 10mV for the P2D surrogate which could be mitigated with additional data.

Figures (9)

• Figure 1: PINN architecture schematic used to enforce spatiotemporal and parametric dependencies of the state variables for the SPM (left) and the P2D model (right). White rectangles denote blocks of hidden layers that could be of any type.
• Figure 1: Average terminal voltage error $\varepsilon_{\rm TV}$ (bar height) over the parameter range considered for the exchange current density in the anode $i_{\rm 0,an}$ and the Li diffusivity in the cathode $D_{\rm s,ca}$. The red bar shows the accuracy result for a parameter set not included in the data set. The black bars show the accuracy for the parameter sets included in the data set. The error bar denotes the 95% percentile variability observed for all the realizations.
• Figure 2: (a) Average PINN error over the training realizations (bar height) that illustrates the effect of secondary conservation regularization and strict enforcement of initial potential conditions. The error bar denotes the 95% percentile variability observed for all the realizations. (b) Prediction of Faradaic current in the anode (left), electrolyte Li-ion concentration (middle) and current (right), without secondary regularization (top) and with secondary regularization (bottom). Variables are shown after 0 s (black) and 400 s (gray). The profiles obtained from the PDE are shown as dashed-dotted lines with the same color coding. The electrode/separator boundaries are shown for the electrolyte Li-ion concentration and current (vertical black dashed line).
• Figure 2: Posterior probability $p_{\rm post}$ obtained from integration of 400 realizations of the SPM PDE (bottom left). Marginal posterior PDF with respect to $d_{\rm i_{0,an}}$ (top left) and $d_{\rm D_{s,ca}}$ (bottom left).
• Figure 3: Average PINN error (bar height) for hierarchical training with the SPM as the lower hierarchy level (left), hierarchical training with the SPM as the lower hierarchy level and secondary conservation regularization (middle), and the base model with similar expressiveness as the hierarchical models (right). The error bars denote the 95% percentile variability observed for all the realizations.