Generalizable Fourier Neural Operator for estimation of lithium-ion battery temperature distribution

Accurate and fast estimation, monitoring, and control of battery temperature is critical for modern battery management systems. This paper benchmarks two neural operators for estimating the temperature distribution of cylindrical batteries: the Fourier Neural Operator (FNO) and the Parameter-Embedded FNO (PE-FNO). Parameter embedding enables temperature distribution estimation by leveraging the parameter space of the battery’s density and specific heat capacity, which are included as input parameters. The Channel-Attention Parameter Embedding (CAPE) module embeds Partial Differential Equation (PDE) parameters into the FNO, enabling generalization across the parameter space of defined parameters even after training. From a BMS deployment perspective, this allows a model to be trained once and subsequently adapted to different cell variants by supplying parameter values, without retraining. In a first step, the models are trained on simulated data generated from a one-dimensional electro-thermal coupled model under multiple drive cycles and cooling conditions. To assess transferability under changed thermal parameter settings, transfer learning is performed with varying thermal conductivity and convection coefficients. Furthermore, transfer learning is applied to the experimental data, achieving root-mean-square errors (RMSEs) of 0.09 °C and 0.12 °C at core temperature for FNO and PE-FNO, respectively. Parameter embedding increases error but enables generalization through the PDE parameter density and the specific heat capacity. In terms of RMSE, the two methods yield results at least as good as those of the baseline models. Nevertheless, FNO demonstrates superior performance. The computational time evaluation shows that FNO and PE-FNO run approximately 6 and 5 times faster than a conventional PDE solver, respectively. Overall, the results show that neural operators enable fast, accurate temperature distribution and that, with a slight decrease in accuracy, parameter embedding enables generalization of machine learning models.