An Interpretable Physics-Constrained Deep Operator Network for Battery Internal Temperature Estimation With Limited Data

Accurate internal temperature estimation is crucial for developing effective safety management strategies in battery energy storage systems (BESSs) and electric vehicles (EVs). Traditional model-based methods often suffer from complexities in model parameters, while data-driven approaches heavily rely on large amounts of training data and lack theoretical interpretability. To address these challenges, this article proposes an interpretable physics-constrained deep operator network (PC-DeepONet) for internal temperature estimation of batteries. By integrating data loss from DeepONet with physical loss from a lumped-thermal model, the network offers strong theoretical interpretability, aligning better with the underlying thermal dynamics and significantly reducing data dependence. Additionally, battery thermal model parameters are innovatively embedded into the network as trainable components and optimized via backpropagation (BP), enhancing the network’s adherence to physical constraints. To address the imbalance between the losses, a log dynamic weight averaging (LDWA) method is employed to reduce the scale disparity and dynamically balance the weights. The experimental results demonstrate that, despite using limited training data at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$25~^{\circ } $ </tex-math></inline-formula>C, the proposed method exhibits enhanced stability and higher accuracy under various operating conditions and different temperatures. Compared to traditional methods, the estimated root-mean-square error (RMSE) can be reduced by 59.5% at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0~^{\circ } $ </tex-math></inline-formula>C and 35.9% at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$40~^{\circ } $ </tex-math></inline-formula>C, respectively.