Combining Physics-Based and Machine Learning Methods to Accelerate Innovation in Sustainable Transportation and Beyond - A Control Perspective

Aug 6, 2026

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Lithium-ion batteries underpin the sustainable energy transition, yet effective design and utilization require solving modeling, estimation, and prediction tasks that capture strong dependencies on aging, temperature, C-rate, and state of charge. The tutorial reviews three battery modeling methodologies—first-principles, machine learning, and hybrid modeling—analyzing their distinct strengths, weaknesses, and key challenges. Three case studies illustrate how each approach supports electrochemical modeling, health estimation, and physics-informed learning for broader system innovation goals.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages14

Reading Time35 min

AccessFree to download

Introduction and Motivation

Physics-Based Modeling

Battery Modeling Methodologies

Case Studies and Applications

Combining physics-based and machine learning methods to accelerate innovation in sustainable transportation and beyond: a control perspective Gabriele Pozzato 1 and Simona Onori 1 ;􀀃 ; IEEE Senior Member arXiv :2305 .04840v1 [ ee ss . SY] 4 May 2023 Abstract—Lithium-ion batteries are playing a key role in the sustainable energy transition. To fully exploit the potential of this technology, a variety of modeling, estimation, and prediction problems need to be addressed to enhance its design and optimize its utilization. Batteries are complex electrochemical systems whose behavior drastically changes as a function of aging, temperature, C-rate, and state of charge, posing unique modeling and control research questions. In this tutorial paper, we provide insights into three battery modeling methodologies, namely ﬁrst principle, machine learning, and hybrid modeling. Each approach has its own strengths and weaknesses, and by means of three case studies we describe main characteristics and challenges of each of the three methods. I. INTRODUCTION AND MOTIVATION According to a recent McKinsey&Company [1] report, the lithium-ion battery chain, from mining through recycling, is projected to have an annual growth of over 30% from 2022 to 2030 and reach a market size of 4 .7TWh. To support the transition to electriﬁed transportation systems and decarbonization, high speciﬁc power and energy storage devices are needed. Compared to other electrochemical solutions available on the market, lithium-ion batteries (LIBs) – with power and energy density of 300-1500W/kg and 100- 250Wh/kg [2], respectively – play a dominant role. A LIB is composed of positive and negative electrodes, a separator, an electrolyte, and current collectors. In a cell, lithium ions are shufﬂed between the electrodes through the separator, a permeable membrane placed between the electrodes, while electrons ﬂow through an external circuit. Electrochemical models are well-established approaches to describe lithium transport in the liquid phase, and intercalation in the negative and positive electrodes (the solid phase) . Electrochemical models based on the conservation of mass and charge partial differential equations (PDEs) are in the form of single-particle (SPM) [3], [4], enhanced single particle (ESPM) [5], and Doyle-Fuller-Newman (DFN) [6] models. These models are effective tools to describe the underlying electrochemical phenomena under different operating conditions and can be extended to account foraging modes. The key limitation of electrochemical models is overparametrization and parameters identiﬁability [7], which could hinder their use in particular when cell's properties are changing over time. 1 Energy Science & Engineering, Stanford University, Stanford, CA. 􀀃 corresponding author sonori@stanford .edu In the last years, machine learning models have gained attention as promising tools for battery state of health (SOH) estimation and residual useful life (RUL) prediction [8] . Provided that a comprehensive dataset is available, this modeling approach is appealing because does not require a deep understanding of electrochemical kinetics and transport phenomena and is characterized by a relatively short development time. The model complexity is not ﬁxed and can be chosen through optimization routines such as grid search. Moreover, these models do not require the solution of PDEs and, if trained properly, can achieve high accuracy with low computational cost. Machine learning models are black box models, i.e., they use historical data to learn the input-output behavior of the system and do not provide any insight into the underlying physics. A key limitation of machine learning approaches is their limited or nonexistent extrapolation capability [9] . The most common solution to this problem is to increase the cardinality of the training dataset in order to cover the whole operating region of the battery (e.g., in terms of current, volta

FAQs

What key factors make lithium-ion battery modeling challenging?

Battery behavior changes significantly with aging, temperature, C-rate, and state of charge, which complicates accurate modeling and control across operating conditions.

What three battery modeling methodologies are discussed in the tutorial?

The tutorial covers first-principles modeling, machine learning modeling, and hybrid modeling, comparing their respective strengths and limitations.

Why are physics-based models limited in practice?

They can suffer from overparameterization and parameter identifiability issues, which may reduce usability when cell properties evolve over time.

Aug 6, 2026

Upload by Jiven