Multi-fidelity physics-informed convolutional neural network for heat map prediction of battery packs

The layout of battery cells in liquid-based battery thermal management systems determines the temperature distribution within a battery pack, which, in turn, affects the safety, reliability, and efficiency of the battery system. Therefore, real-time heat map prediction is of great importance for battery design optimization and control strategy refinement. However, the scarcity of high-fidelity data as well as the imperfections of low-fidelity physics knowledge significantly hinder the accuracy of both data-driven and physic-informed machine learning (PIML) surrogate models. To tackle these challenges, this paper proposes a novel multi-fidelity physics-informed convolutional neural network (MFPI-CNN) that integrates low-fidelity domain-specific knowledge with limited high-fidelity data to provide accurate and trustworthy real-time battery heat map estimations. First, to facilitate the integration of heat transfer knowledge into machine learning models, a complex three-dimensional battery heat transfer problem is simplified to an equivalent two-dimensional representation as low-fidelity physics knowledge. Then, the MFPI-CNN with a physics-informed backbone and a high-fidelity projection head is proposed to generate battery heat maps at various fidelity levels. The backbone's pre-training employs an unsupervised PIML framework, embedding heat transfer partial differential equations and boundary conditions within the loss function and padding modes. The high-fidelity projection head with a simplified structure is then appended to the fixed backbone and trained by limited labeled data. Both the backbone and projection head are equipped with appropriate modules and linear-weighting loss functions to normalize convergence speed. The efficacy of the model simplification is verified by various battery experiments and simulations. Comparative results and ablation studies on heat map predictions demonstrate that the proposed MFPI-CNN outperforms traditional data-driven, physics-informed, and other multi-fidelity surrogate models.