Introduction: The concept of integrating physics-based and data-driven approaches has become popular for modeling energy storage systems. However, the existing literature mainly focuses on the data-driven surrogates generated to replace physics-based models. These models often trade accuracy for speed but lack the generalizability, adaptability, and interpretability inherent in physics-based models, which are often indispensable in modeling real-world systems.

Methods: A novel architecture of physics-based learning, termed model-integrated neural networks (MINN) is introduced. It is capable of learning the physics-based dynamics of systems consisting of partial differential-algebraic equations with a control input. This architecture offers a systematic way to obtain optimally simplified models that are physically insightful, numerically accurate, and computationally tractable simultaneously.

Results: We apply the proposed neural network architecture to model the electrochemical dynamics of lithium-ion batteries and show that MINN is extremely data-efficient to train while being sufficiently generalizable to previously unseen input data, owing to its underlying physical invariants. The MINN battery model has an accuracy comparable to the first principle-based model in predicting both the system outputs and any locally distributed electrochemical behaviors but achieves two orders of magnitude reduction in the solution time.

Conclusion: The substantial and practical benefits offered by MINN make it an exceptional choice for developing next-generation battery management systems.