MINN: Learning the Dynamics of Differential-Algebraic Equations and Application to Battery Modeling

2023-04-27

IEEE Transactions on Pattern Analysis and Machine Intelligence

AI Summary

Addressing the challenge of high-accuracy, high-efficiency, and interpretable modeling for energy systems (e.g., lithium-ion batteries) under data scarcity, this paper proposes the Model-Integrated Neural Network (MINN)—the first method to directly embed differential-algebraic equation (DAE)-based physical structural priors into a neural network architecture. MINN explicitly encodes DAE constraints and employs a hybrid data–physics joint training paradigm to enable end-to-end learning of system-level physical dynamics. Compared to conventional first-principles models, MINN achieves comparable global output accuracy and local electrochemical behavior prediction using only a minimal amount of training data, while accelerating computation by two orders of magnitude. This work uniquely unifies physical interpretability, numerical fidelity, and computational scalability, establishing a new paradigm for control-oriented modeling of sustainable energy systems.

Abstract

The concept of integrating physics-based and data-driven approaches has become popular for modeling sustainable energy 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 dynamic systems for optimization and control purposes. We propose a novel machine learning architecture, termed model-integrated neural networks (MINN), that can learn the physics-based dynamics of general autonomous or non-autonomous systems consisting of partial differential-algebraic equations (PDAEs). The obtained architecture systematically solves an unsettled research problem in control-oriented modeling, i.e., how to obtain optimally simplified models that are physically insightful, numerically accurate, and computationally tractable simultaneously. 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.

Problem

• Complex System Modeling
• Energy Systems
• Data Scarcity

Innovation

• MINN
• Physics-Informed Machine Learning
• Lithium-Ion Battery Simulation