MINN: Learning the dynamics of differential-algebraic equations and application to battery modeling

TL;DR

This paper introduces MINN, a neural network architecture that learns the physics-based dynamics of systems described by PDAEs, demonstrated on lithium-ion battery modeling, achieving high accuracy with reduced computational cost.

Contribution

The paper presents a novel MINN architecture that integrates physics-based dynamics into neural networks for efficient, accurate modeling of complex systems like batteries.

Findings

MINN accurately predicts battery behavior with physics-based insights.

MINN reduces solution time by two orders of magnitude.

The model is data-efficient and generalizes well to unseen inputs.

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.