Integrating Physics-Based Modeling with Machine Learning for Lithium-Ion Batteries

Aug 3, 2026

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Mathematical modeling of lithium-ion batteries remains a central challenge for advanced battery management due to the need for both accuracy and computational feasibility. This paper presents two new hybrid frameworks that deeply integrate physics-based models with machine learning by feeding state information from physical models into learning architectures. Hybrid models combine electrochemical and equivalent circuit models with feedforward neural networks, yielding parsimonious structures and strong voltage prediction accuracy across a wide C-rate range. The approach extends to aging-aware, state-of-health conscious hybrid modeling, with experiments showing high voltage predictive accuracy over the battery’s cycle life.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages15

Reading Time38 min

AccessFree to download

Abstract

Physics-based and electrochemical modeling background

Single particle model (SPM) and its limits

Degradation-aware extensions and model order reduction

Equivalent circuit model (ECM) background

Common ECMs and recent accuracy improvements

Aging-aware modeling

Machine learning battery modeling

Benefits and limitations of black-box ML

Proposed hybrid physics-ML frameworks

Integrating Physics-Based Modeling with Machine Learning for Lithium-Ion Batteries Hao Tua , Scott Mourab , Yebin Wangc , Huazhen Fanga,􀀃 a Department of Mechanical Engineering, University of Kansas, Lawrence, KS 66045, USA b Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720, USAc Mitsubishi Electric Research Laboratories, Cambridge, MA 02139, USA 7 Nov 2022 Abstract Mathematical modeling of lithium-ion batteries (LiBs) is a primary challenge in advanced battery management. This paper proposes two new frameworks to integrate physics-based models with machine learning to achieve high-precision modeling for LiBs. The frameworks are characterized by informing the machine learning model of the state information of the physical model, enabling a deep integration between physics and machine learning. Based on the frameworks, a series of hybrid models are constructed, through combining an electrochemical model and an equivalent circuit model, respectively, with a feedforward neural network. The hybrid models are relatively parsimonious in structure and can provide considerable voltage predictive accuracy under a broad range of C-rates, as shown by extensive simulations and experiments. The study further expands to conduct aging-aware hybrid modeling, leading to the design of a hybrid model conscious of the state-of-health to make prediction. The experiments show that the model has high voltage predictive accuracy throughout a LiB's cycle life. Keywords: Hybrid modeling, Physics, Machine learning, Lithium-ion batteries 􀀃 Corresponding author Email address: [fang@ku.edu](fang@ku.edu) (Huazhen Fang) model, which is broadly considered reliable and precise enough for almost all LiB management scenarios [3, 4] . Its accuracy yet comes with enormous computational complexity. This hence has motivated an incessant search for streamlined electrochemical models to balance between accuracy and computational costs. The single particle model (SPM) is one of the most parsimonious, which represents each electrode as a spherical particle and delineates lithium-ion intercalation and di􀀋usionin the particles [5] . With its simpliﬁed structure, it is computationally fast but accurate only for low to medium C-rates (below 1 C-rate) . Based on the SPM, there is a wide range of improved versions for higher accuracy under di􀀋erent conditions. They usually supplement the SPM with characterizations of thermal behavior [6, 7], electrolyte dynamics [8–11], degradation physics [12], and stress buildup [11] . Another important line of research lies in applying model order reduction methods to the DFN, SPM or other electrochemical models, with the aim of accelerating numerical computation [13–19] . Di􀀋erently, ECMs leverage electrical circuits, usually based on resistors, capacitors, and voltage sources, to capture LiBs'current/voltage dynamics in a physically interpretable way. Compared to electrochemical models, ECMs have greatly more parsimonious structures and simpler governing equations, thus advantageous for computation and conducive to real-time control, prediction, and simulation. Some widely used ECMs include the Rint model, the Thevenin model, and the Dual Polarization model [20–22] . Recent literature has expanded the development of ECMs toward better prediction accuracy. Some studies seek to account for the e􀀋ects of hysteresis and temperature on a LiB's electrical dynamics [23–27] . Others design new ECMs to approximate certain electrochemical models [28–32] . Preprint submitted to Applied Energy November 8, 2022 While ECMs have found increasing popularity, their structural simplicity restricts their accuracy, making them useful only for low to medium C-rates. For all the aforementioned models, their e􀀋ectiveness and ﬁdelity will decrease as a LiB ages, since many parameters of a model can change drastically with the LiB's state-of-health (SoH). This hence has stimulated research

FAQs

What problem does the paper target in lithium-ion battery modeling?

Achieving high-precision battery models while avoiding excessive computational complexity, and addressing performance degradation as batteries age.

How do the proposed frameworks integrate physics-based models with machine learning?

They inform the machine learning model of state information from the physical model, enabling deep integration between physics and learning.

How is aging-aware prediction achieved in the hybrid modeling approach?

The paper expands hybrid modeling to be state-of-health (SoH) conscious, constructing aging-aware hybrid models and validating voltage prediction accuracy across cycle life.

Aug 3, 2026

Upload by Jiven