Lithium-ion battery digitalization: Combining physics-based models and machine learning

Digitalization of lithium-ion batteries can significantly advance the performance improvement of lithium-ion batteries by enabling smarter controlling strategies during operation and reducing risk and expenses in the design and development phase. Accurate physics-based models play a crucial role in the digitalization of lithium-ion batteries by providing an in-depth understanding of the system. Unfortunately, the high accuracy comes at the cost of increased computational cost preventing the employment of these models in real-time applications and for parametric design. Machine learning models have emerged as powerful tools that are increasingly being used in lithium-ion battery studies. Hybrid models can be developed by integrating physics-based models and machine learning algorithms providing high accuracy as well as computational efficiency. Therefore, this paper presents a comprehensive review of the current trends in integration of physics-based models and machine learning algorithms to accelerate the digitalization of lithium-ion batteries. Firstly, the current direction in explicit modeling methods and machine learning algorithms used in battery research are reviewed. Then a thorough investigation of contemporary hybrid models is presented addressing both battery design and development as well as real-time monitoring and control. The objective of this work is to provide details of hybrid methods including the various applications, type of employed models and machine learning algorithms, the architecture of hybrid models, and the outcome of the proposed models. The challenges and research gaps are discussed aiming to provide inspiration for future works in this field.


Introduction
To achieve sustainable electrification and decarbonization of the energy sector, reliable energy storage devices are essential.The lithiumion battery (LIB) is the cornerstone of portable and stationary energy storage in the modern industrial age [1].It is primarily due to their high specific energy (170-250 Wh/kg), high specific power (200-1000 W/kg), high voltage (3.05-4.2V), low self-discharge rate (less than 10 % per month), long cycle life (up to 3000 cycles), high efficiency (95 %), high rate capability, low toxicity, safety, compatibility with existing infrastructures and low heat release [2][3][4][5].It is pertinent to note that, despite the exponential growth of LIBs in the last decade, large amounts of electrical energy storage are required to meet societal demands such as growing need for long-range hybrid and electric vehicles [6] and also maintaining reliable electricity supply from renewable energy systems [7].In addition, more effective controlling strategies, and better battery designs are needed to allow for higher capacity and power, longer lifetime, lower cost, and increased safety [8,9].
It is conventional to develop novel LIB design ideas by testing several prototypes in the lab, which can be costly, unsustainable, and timeconsuming [10,11].Digitalization of LIB development has made it possible to simulate the behavior of a battery in a virtual environment alongside testing actual batteries in the lab [12].If the simulation method is accurate enough, valuable information about the intricate relationship between the internal battery processes (e.g., ion transport, thermal effects, mechanical stress, and electrochemical reactions) and battery structure and operating condition can be obtained.This, in turn, will accelerate battery research by providing the opportunity for a rapid evaluation of a wide range of design ideas and exploring different operating scenarios.
A creation of digital research and development platform requires accurate models that mimic physical batteries.For many years, electrochemical-thermal models, as one of the most accurate simulation methods available, have been used to study battery behavior using mathematical equations [13].These electrochemical-thermal models are ideal for testing battery design ideas in a digital environment and can be developed further into battery digital twins [14].
In this context, a digital twin (DT) is defined as a virtual dynamic model that replicates the behavior of a physical entity [15].Based on sensor data or historical data, DTs are commonly used to determine a system's control strategy [16][17][18][19][20][21].However, DTs can also be used in the design and development of different systems [22].This is because DTs can analyze system's behavior and determine the effect of different parameters on the performance of the system [23,24].Many advantages can be derived from this technology, including improved performance estimation and behavioral prediction, reduced costs, and lower development risk [24].
It is imperative that the underlining models of a LIB DT are highly detailed in order to calculate local battery parameters with a high degree of accuracy [25,26].To improve the quality of any model findings, it is necessary to incorporate large experimental datasets for parameter extraction and validation.Coupled partial differential equations describing mass and charge conservation and electrochemical reaction kinetics involving multiple electrical and electrochemical parameters such as electrical conductivity and diffusion coefficients must then be solved simultaneously in electrochemical-based models of the DT [27,28], which requires a significant amount of computation, particularly when thousands of iterations are required to obtain the optimal design.Data-driven models and in particular machine learning algorithms offer better computational efficiency compared to physics-based battery models.By analyzing large experimental datasets or synthetic data from simulation results, these algorithms may be able to learn the physics of the LIB and may also act as a surrogate for the electrochemical-based DT.By combining the physical insight provided by the electrochemicalbased DTs with the ML's fast response, the complementary advantages of each approach can be leveraged.This will allow us to develop an efficient DT that can be used to conduct battery experiments, digitally.The ML can be used for different applications, such as real-time parameter estimation, correcting errors of simplified battery models and for finding design related parameters to achieve optimal battery performance for a particular application when combined with optimization algorithms.
Physics-based machine learning can be applied to identify the complex relationship between important battery parameters across a range of battery length scales (from material to pack) and lifecycle stages (from production to end-of-life operation) for reducing the cost of production, enhancing battery performance and improved decision making for battery control [29][30][31][32] (Fig. 1).
In this work, the current state-of-the-art in battery modelling and machine learning to enable the development of a LIB DT is outlined.The work then explores the possibilities for developing a fully functional battery DT that can be used to optimize battery design.This work presents a review of studies towards application of machine learning for advancing the digitalization of battery experimentation.The novelty of this work allows the consolidation of studies in battery digitalization to focus the field on future research into digital experimentation.Moreover, this work consolidates this field to guide focus towards a goal of real-time battery monitoring and control, and digital battery research and development.in digitalization of battery experimentation.The aim is that the opinions and perspectives presented in this work will lead to development of digital tools that can help monitoring and control of batteries, evaluation of innovative ideas, and accelerate the evolution of LIB industry.

Methodology
With consideration of the types of modelling approaches for LIBs, the main physics-based modelling methods used include equivalent circuit models and electrochemical models.Additionally, machine learning approaches are utilized to predict unknown parameters, and to assess battery characteristics that may be computationally heavy for modelling approaches.These machine learning approaches include equivalent circuit models and electrochemical models.All these modelling and machine learning approaches are defined to assess batteries for specific applications and requirements.Considering the focus on performance of LIBs in this work, physics-based models and machine learning methods are discussed.
This work was performed to understand the pros and cons of the different modelling and machine learning approaches when considering battery monitoring and control, and battery design.Therefore, the suitability of these approaches has been evaluated.The following methods were followed for the review of modelling and machine learning approaches.
• Collection of current applications of modelling and machine learning in LIBs towards monitoring, control, and battery design.• Use of graphical-based analysis and comparison for modelling and machine learning applications in LIBs.• Interpretation of the current state-of-the-art.
• Future predictions and trends in the field.
In general, a comprehensive review has been conducted with a thorough investigation of previous studies of modelling and machine learning in LIBs.A state-of-the-art review is provided for understanding modelling and machine learning used in LIBs.Based on the analysis, result interpretation is performed, and key findings are summarized.Finally, the future outlook and conclusions are presented.
This work is limited by the availability of published modelling and machine learning documentation.There are many private institutions where monitoring, control and design of batteries is a key aspect of their research and development portfolios.Developments in this field are therefore propriety information that is not shared in the public domain.Therefore, this work focuses only on available methods and studies that have been published.
Error can also be induced within this work.Modelling of LIBs relies on the use of many parameters that are defined experimentally, and some that are define theoretically.The misuse of parameters within a model of an LIB can cause errors in the results obtained.Furthermore, when incorporating the design of novel LIBs, the parameters determine both experimentally and theoretically may no longer be relevant.This would require experimental validation to ensure minimal errors.

Physics-based modeling of lithium-ion batteries
In LIBs, energy is converted between chemical and electrical energy through electrochemical reactions occurring within the active material of the electrodes [3].To maintain electro-neutrality, electrons flow through an external circuit while Li + ions flow through the electrolyte from one electrode to another.Migration and diffusion are two processes that govern mass transfer due to gradients in potential and concentration, respectively [33].During the operation of a LIB, charge transfer and electrochemical reactions produce heat.Also, some irreversible processes, such as formation of solid-electrolyte interface layer, lithium plating and particle fracture caused by diffusion induced mechanical stress occur [34].Capacity loss, power loss and increased internal resistance are some of the observable effects of these undesired reactions [35].
These dynamic processes of the battery can be estimated in a model using mathematical equations and simplifying assumptions.Models of batteries can be very simple representations of the underlying system or they can be very detailed explanations of the mechanisms involved [36,37].A description of the most famous LIB models with different prediction capability and computational requirements is provided.

Equivalent circuit model
In equivalent circuit models (ECMs), circuit elements such as voltage sources, resistors and capacitors are combined to reflect the voltage variation of the LIB with regards to an applied current [38].These models have simple structure with low computation time [39], are easy to implement and can have different form and components depending on the required application [40].
The simplest type of ECM is called Rint model consisted of an ideal voltage source in series with a resistor.The voltage source represents the OCV and the resistor is equivalent to the internal resistance of the cell which is caused by different battery and also side reactions [41].
Rint model only considers ohmic polarization which reflects the instant changes in voltage [42], therefore it is not suitable for practical applications [43].For a more realistic simulation of voltage behavior, gradual changes due to other polarization effects also need to be considered.These polarization effects can be represented by parallel resistor-capacitor (RC) networks to the original Rint model.Thevenin model comprises of a parallel RC network in series with other Rint model components.This additional RC pair accounts for electrochemical (activation) polarization which is associated with charge transfer [44].The resistor represents the charge interfacial transfer resistance [45] while the capacitor is related to the double layer capacitance [46].Thevenin model considers both ohmic and electrochemical polarization therefore it can better describe the transient behavior of the battery [47].
A second RC network is added to the Thevenin model in the dual polarization model to represent concentration polarization caused by gradients in the electrolyte and solid phases [48].In this RC network, the resistor and capacitor account for concentration resistance and capacitance [49], respectively.Since this model can describe ohmic, electrochemical and concentration polarizations, it can generate accurate results [50].The schematic of these model is shown in Fig. 2.
By addition of more RC networks the accuracy of the model would also be increased, but at the same time the computational efficiency would be lower [51].ECMs could not be used for describing the spatial parameters of the battery such as ion transport behavior, but they are powerful tools for state of charge (SOC) estimation [52].
As the complexity of ECMs escalates with additional RC networks, and computational efficiency diminishes.Despite their performance in estimating SOC, ECMs exhibit limitations in characterising spatial parameters like ion transport behavior within the battery.The advantages of ECMs include providing a simplified yet practical approach to simulate LIB voltage variations.Therefore, there is a trade-off between model complexity and computational efficiency, emphasizing the suitability of ECMs for SOC estimation while highlighting their inability to capture intricate spatial battery dynamics.Although ECMs can be suitable for real-time monitoring of basic battery parameters, they are not able to be employed for digital battery research and development.

Electrochemical models
A LIB model based on electrochemical principles is more suitable for LIB research since it provides more detailed insight into the electrochemical behavior of the battery by describing the cell's galvanostatic charge and discharge processes, as well as transport phenomena.This kind of modeling also, allows tracking of the battery's spatial and temporal state, and provides estimation of parameters that are difficult to measure (e.g., Li + concentration) [53].
A common electrochemical model is the single particle model (SPM) proposed by Zhang et al. [54] as shown in Fig. 3. Taking each electrode as a spherical particle, this SPM model describes how Li ions diffuse within electrode spheres based on Fick's second law for spheres, as well as charge-discharge kinetics based on Butler-Volmer equation [55].This means that Li diffusion within the spheres are considered as the governing process of the system while Li + concentration in the electrolyte is assumed to be constant [56].This model is relatively fast, but does not provide detailed information regarding the processes occurring within the battery, and the battery's net response is only reliable at low current rates [57].The electrolyte dynamics including electrolyte concentration and potential distribution have been taken into account in order to improve the accuracy of the conventional SPM model [58][59][60].
The Pseudo-two-dimension (P2D) model is a more comprehensive electrochemical model proposed by Doyle Fuller and Newman.In this model, electrodes are described as porous environments containing many spherical particles, with electrolyte filling the spaces between particles [61].This model is schematically illustrated in Fig. 4. P2D model, describes concentration and potential variations in both electrode and electrolyte phases.Li ion diffusion in solid phase and charge-discharge kinetics follow the same physical rules as the SPM.The equation for Li ion concentration has been derived from the general law of mass conservation [62].The electrode and electrolyte potential equations are both governed by Ohm's law, although the electrolyte potential equation has an additional term which incorporates the effects of Li ion concentration [63,64].The P2D model provides more detailed insight of the electrochemical behavior of the battery compared to SPM; but it also requires more computation time.
For a more realistic simulation result, it is possible to incorporate thermal and aging models into the original equations of the electrochemical models.Gu et al. [65], developed a multi-physics electrochemical-thermal model by integrating the P2D model with a thermal expression.In the proposed thermal model, heat generation was assumed to be caused by electrode reactions and Joule heating.This has been used for investigation of electrochemical-thermal behavior of LIBs [66][67][68], and simplified thermal models have been proposed to reduce the computation cost [69].
Degradation elements by Ramadass et al. [70] have also been integrated, allowing investigation of SEI formation on capacity fade [70].Comprehensive electrochemical-aging models have also been developed [71,72], as well as electrochemical-thermal-aging models capable of considering the effect of temperature rise and degradation on electrochemical behavior of LIBs [73][74][75].Data-driven models based on onboard measurable data [76], and empirical equations for estimation of battery parameters are also used for capturing modes of degradation in batteries [77,78], and have been integrated with electrochemical models [79].Further additions to the P2D model include Li ion intercalation-induced stress for a Li y Mn 2 O 4 positive electrode [80], electrochemical-thermal-mechanical stress [81,82], and a electrochemical-thermal-aging-mechanical model considering the effect of SEI formation, lithium plating and mechanical stress on solid particles [83].
A three-dimensional model of battery behavior facilitates enhanced insight, especially regarding heat generation and temperature distribution [84].A 3D electrochemical-thermal model was developed for a standard 18650 cell [85]; whereas, Fang [86] used a 3D electrochemical-thermal model to simulate the Nail-penetration test [87] for internal short-circuit investigation.Such models have been used for thermal analysis of different LIB formats, including pouch and prismatic cells [88,89].Additionally, three-dimensional modeling was used to simulate the electrochemical behavior of an LIB cell with a heterogeneous negative electrode consisting of solid particles of different shapes and sizes [90].
Considering the models developed to describe LIBs' processes with  high level of accuracy.It is becoming possible to move the digital models closer to the physical entities due to their maturity and reliability.By transferring all aspects of LIBs to a digital environment and developing a model with in-depth details, it is possible to develop a LIB DT.This involves transferring all aspects of LIBs, including electrochemical, electrical, thermal, aging, and mechanical, to a digital environment [91].
Developing such a multi-physics DT requires careful parameterization and validation based on extensive test data of LIBs.Such DT can also be developed with the aid of powerful computational resources and battery simulation packages, such as PyBaMM [92], COMSOL [93,94], and LIONSIMBA [95].However, such a DT will be computationally expensive due to the high number of complicated equations that need to be solved simultaneously.Despite this, any simplification that reduces the cost of computation, such as ignoring side reactions will lead to deviation from the reality.Therefore, it is important to come up with methods of reducing the computational cost without sacrificing accuracy and detail.
The prospect of developing a DT for LIBs, amalgamating electrochemical, electrical, thermal, aging, and mechanical aspects into a unified digital environment, holds promise.However, achieving this requires precise parameterization and validation against extensive experimental data, which can be challenging to verify and crosscorrelate between multiple studies due to the different methods used to obtain experimental data.
The significance of electrochemical models in elucidating LIB behavior is clear, due to their capacity to capture detailed electrochemical phenomena and their crucial role in understanding LIB performance.However, there are many challenges associated with computational demands, model complexity, and the quest for balancing computational efficiency without compromising accuracy.Despite this, these models represent a pathway toward accurate digital representations of LIBs, albeit with complexities in computational execution and the need for continued advancements to enhance accuracy and efficiency.This allows the use of electrochemical models for digital design and research, but requires substantial computation power and time, preventing them from being utilized in real-time applications and impeding the development of LIB DTs.

Machine learning approaches for lithium-ion battery applications
The use of machine learning in the technology sector has been widespread for quite some time [29,96]; however, ML in batteries has only gained traction in the last decade.For effective ML parameterization and performance prediction for different battery materials, structures, sizes, and formats, the emergence of advances in sensing technologies and experimental tools [97,98] has benefited the field of battery modelling by improved parameterization and reduced computational requirements [20].Moreover, the application of ML in the battery field has gained significant importance due to the effectiveness of ML methods in reducing the requirement for experimental approaches [99].
Different types of artificial neural networks (ANN) including feed forward neural networks (FNN), deep neural networks (DNN) and recurrent neural networks (RNN) such as long short-term memory (LSTM), support vector machine (SVM), gaussian process regression (GPR), decision tree and random forests [96,100,101] are commonly used ML approaches for LIB estimation and performance prediction [102][103][104].Fig. 5 shows the structure of some of these algorithms.
Table 1 provides information on the findings of studies that investigated ML models for LIB applications.FNN has proven to be a suitable choice for studying the relationship between material and cell properties and the resulting battery performance.Meanwhile, RNN, LSTM and GPR methods have been extensively used for online estimation of timedependent battery states such as state of health (SOH) and SOC estimations.GPR is a suitable choice for capacity estimation which can be trained with small dataset, but the complexity of the model has shown to be a challenge.SVM stands out as a simple and accurate model when it is used for regression tasks, providing efficiency comparable to NNs.Both DT and RF have been successfully employed for both classification and regression tasks.
It is, however, very difficult to provide a general comparison on the performance of each ML model across different LIB applications since the predictions of these models are dependent on the training dataset.It is only possible to provide such comparison when different models are trained with the same dataset and for the same task.Many comparative studies have done such investigations across different ML algorithms.Li et al. [118] compared prediction accuracy and computational efficiency of GPR and RF for capacity estimation.The results showed that RF and GPR are both capable of accurately predicting the capacity with a root mean squared error (RMSE) of 0.82 % and 1.16 %, respectively.In addition, RF showed to be at least ten times faster than GPR, indicating the superior capability of RF for online SOH estimation.Zhang et al. [111] developed a LSTM model for RUL prediction of LIBs.The goal was to predict the number of cycles that a battery could undergo before the capacity falls below 80 % of the initial capacity using the data from previous cycles.The prediction capacity and computational time of the LSTM was compared to SVM and a simple RNN model for four different cells.The three models showed better results when larger training data was used.In all cases, the computational time of the SVM model was the lowest (less than 0.01s), while the RNN took the longest to be trained (about 40s).SVM showed superior predictive capabilities compared to simple RNN by predicting the failure cycle closer to the actual values.In contrast, RNN failed in capturing the long-term dependencies of capacity degradation.Overall, LSTM showed better prediction capacity compared to both SVM and RNN with a reasonable training time of around 20s. Sahinoglu et al. [113] developed four GPR variants for battery SOC estimation utilizing voltage, current, and temperature data, along with SOC values from prior cycles.They performed a comparative analysis by evaluating the performance of the GPR models, a NN and a SVM model.All GPR variants showed lower RMSE compared to NN and SVM with NN outperforming SVM.The computational time for GPR models was higher than the other two but still sufficiently low for real-time SOC estimation applications.Liu et al. [119] performed a multi-class classification using a RF model to find the correlation between manufacturing features from coating and mixing stages with battery porosity and mass loading.The accuracy of the developed RF model was compared to a DT and a SVM model.The DT showed the weakest accuracy, while SVM results were very close to RF predictions.
Standardizing the dataset used for ML application in LIBs facilitates meaningful comparisons across various studies.This involves defining specific guidelines for test procedure, measurement methods, and the required input data.In addition, a standard framework of reporting the information such as properties of the tested batteries and utilized equipment and an agreed-upon grading system for dataset quality allows researchers to use consistent train and test datasets.This approach minimizes the diversity in the datasets, making it easier to compare the performance of ML approaches; therefore, any differences in performance could be attributed to the models themselves.
ML algorithms are dependent on experiential data, which is laborintensive, expensive, and time-consuming to acquire.Additionally, these algorithms cannot provide physical insight into the system when trained based on the measurable data obtained from battery experiments (voltage, current, temperature) since the system is regarded as a black box, meaning it treats data solely based on statistical analysis.To be able to utilize the information obtained from these methods to enhance LIBs performance, it is necessary to understand the underlying physical mechanisms.Combining physics-based and data-driven models could be the solution to this problem.
The main idea here is to inform the ML algorithm of the physical relations inside the system so that it can map the inputs directly to the corresponding outputs without having to solve complex non-linear equations in each iteration.This way, accuracy will always be above 90 % while results are achieved much faster [120].As a result, it will not be necessary to simplify the electrochemical model's governing equations.Moreover, large experimental datasets will be eliminated when they are only required during model development, eliminating the need for such datasets.By incorporating ML algorithms, it is possible to develop an extensive, computationally inexpensive LIB DT that can be applied to battery modeling and control, as well as battery design and development.As an overview of the state-of-the-art in physics-based machine learning for LIBs, the following examples are presented.

State-of-the-art in hybrid methods for batteries
Hybrid modeling is referred to a novel modeling approach in which the machine learning algorithms are integrated with physics-based models to harness the advantages of both methods.By combining the ability to learn the complicated patterns and fast computational capabilities of machine learning models with high predictability of physicsbased models, a more flexible and robust framework for LIB research can be developed.
A variety of hybrid methods for modelling batteries must be developed and utilized to achieve a truly intelligent LIB DT.The purpose of this section is to describe selected hybrid methods for monitoring and controlling batteries.An overview of studies using hybrid methods to assess LIB design follows.Combined, these studies give us the foundation for building an intelligent LIB DT that can be used as a digital LIB lab.

Battery monitoring and control 4.1.1. Performance prediction P2D model can accurately predict battery dynamic behavior of the battery during operation but it is computationally expensive for realtime application. There have been efforts to reduce the time of this model to enable the implementation of it for battery management purposes.
Dawson-Elli et al. [121] proposed a combination of a comprehensive pseudeo-two-dimensional model with a variety of ML algorithms including decision trees, random forests and gradient boosted machines to evaluate their execution time and accuracy.Using the P2D model, a dataset containing 24000 parameter combinations with variations across 27 parameters was created.All approaches had reasonable accuracy in predicting the voltage of the next time step using the four previous time steps during constant current discharge; however, the models were unable to predict voltage values for different current rates or battery chemistries rather than that of the training dataset.SOC prediction yielded low accuracy due to the high variances in the dataset, suggesting that the dataset should be restructured and comprehensive ML algorithms should enhance the results [121].
In another work by Li et al. [122] a modified version of LSTM called two-dimensional grid LSTM was used to map measurable battery data to internal spatial-temporal states.To generate training and test datasets, an electrochemical-thermal model was utilized.Using a SOC ranging from 5 to 95 %, and operating temperatures ranging from 0 to 40 • C, fifteen EV drive cycles were used as inputs for the P2D model.By utilizing different voltage, current and ambient temperature values, the physics-informed LSTM was able to predict internal LIB internal states.These states included average and surface Li + concentration and potential in the electrode and electrolyte, which are essential for battery state estimation, safety, and lithium plating.A maximum error of 3.95 % was observed in the prediction of internal states using the proposed model when noisy input data was used.
A schematic illustrating the proposed flowchart of these works is represented in Fig. 6.
It is also possible to increase the accuracy of simple physics-based models such as SPM and ECM by combining them with machine learning algorithms using a hybrid architecture as shown in Fig. 7.
Tu et al. [123] proposed hybrid models by integrating physics-based models and a FNN algorithm.The goal was to enhance the prediction accuracy of a single particle thermal model (SPTM) and an ECM.The FNN was employed to capture voltage deviations between these models and the true voltage value.In the SPTM-FNN hybrid framework, the neural network is trained based on a simulated dataset generated using a full-order P2D model of an LCO-graphite cell.The current profile, initial SOC, and initial temperature were fed to the SPTM, to calculate bulk and surface SOC, and temperature profile as the outputs.The hybrid SPTM-FNN framework produced impressive improvements in prediction accuracy compared to the SPTM.Using experiments conducted on Samsung INR18650-25R LIB cells, the required variables for an ECM model called nonlinear double capacitor (NDC) as well as the training dataset for the FNN algorithm were derived.The initial SOC and current profile are inputs to the NDC model.The outputs include the voltages of the bulk inner regions of the electrode, electrode surface voltages, and transient voltages resulting from ion diffusion.These outputs and the current and temperature profiles were fed to the FNN to calculate the modified voltage.The NDC-based hybrid model has been enhanced to capture the effect of aging on battery voltage response.The proposed framework produces significantly lower voltage errors than the NDC model at all current rates by including state of health as an additional input to the FNN.
For the accurate prediction of battery voltage and temperature, Feng et al. [124] have developed an electro-thermal neural network (ETNN).Based on surface temperature and current, an electrochemical-thermal sub model (ETSM) was applied to estimate terminal voltage and core temperature.The neural network was trained based on experimental dataset to capture the voltage residuals therefore the ETNN was able to deliver high precision under high C-rates (up to 10 • C) and wide temperature ranges (− 10 to 40 • C).The inputs to the neural network were the measured current and estimated voltage, and core temperatures from ETSM.Using an unscented kalman filter, a maximum RMSE of 0.9 % was obtained at 40 • C for estimating SOC and 1.08 • C for estimating state of temperature at − 10 • C.
Combining electrochemical models with ML techniques to enhance accuracy and reduce computational load in predicting LIB performance is a promising route towards LIB DTs.However, there is an ongoing requirement to optimize these hybrid models for accurate and efficient LIB modelling.Despite this, there is substantial potential of combining physics-based models with ML algorithms for improved LIB performance management.

Parameter estimation
Combining P2D with thermal and aging models can provide an understanding of how battery parameters change during operation.While such a comprehensive model may take a considerable amount of time to run the use of machine learning can assist this model to make real-time predictions.
An LSTM algorithm was also developed by Chun et al. [125] for real-time parameter estimation.The algorithm was trained to replicate the dynamics of a Nickel Manganese Cobalt Oxide (NMC) LIB cell using synthesized data of measurable parameters including, voltage, current, temperature, and SOC generated with a P2D model combined with thermal and aging models.This study considers anode electrolyte decomposition, cathode electrode decomposition, and battery volume change phenomena, which affect solid particle surface area and solid  particle conductivities for anode and cathode, normalized available capacity, and SEI layer thickness battery parameters.The training dataset was created by applying variations in the aging-related parameters.The trained LSTM network was validated using experimental data from an NMC battery cell test.The experimental data included voltage, current, and temperature, while SOC was computed using the Coulomb counting method.This data was used as the input of the LSTM network to estimate aging-relevant parameters, where simulated voltage results matched experimentally obtained voltage results with an RMSE of 0.43 %.The proposed parameter estimation workflow of this work is represented in Fig. 8.
In Table 1, this work summarize the existing research on physicsinformed ML for battery control and monitoring, the models involved, the ML methods applied, the method of generating training data, the battery chemistry, and the application of the developed hybrid model.
There is an increasing interest in utilizing ML techniques for parameter estimation and real-time predictions in LIB systems.The effectiveness of ML algorithms, such as LSTMs, in estimating crucial LIB parameters, enhancing the accuracy of predictions, and enabling realtime monitoring and control is promising.This underscores the potential of combining physics-based LIB models with ML algorithms for accurate parameter estimation and efficient LIB management.

Battery design
Hybrid models can be extremely beneficial when it comes to battery design, where complicated models must be run several times before the desired result is achieved.In Fig. 9, a general workflow is shown for combining physics-based models with machine learning algorithms for LIB design applications.Various applications of hybrid models are discussed in this study.

Improved energy and power
A thermal-electrochemical model was combined with neural network algorithms in Wu et al.'s [126] study to determine the optimal design of an NMC-graphite cell to achieve high specific power and specific energy.Electrode thickness, volume fraction, Bruggeman constant, active material radius, and lithium concentration in the electrolyte were selected from those parameters of the positive electrode that can be controlled during manufacturing.For the proposed method, two neural networks were used.The first one served as a classifier that assessed whether an input parameter set was physically feasible.In this neural network, the six design parameters were inputs.As the algorithm's output, a value ranging from 0 to 1 was generated, with 0 representing an abnormal input.A second neural network was used to calculate the specific power and specific energy of a given set of inputs.While C-rate is the most important factor affecting specific power, electrode thickness and porosity are the two most important factors affecting specific energy.To obtain optimal design parameters that satisfy both the requirements for high specific power and energy, a total of 10000 Monte Carlo algorithms were performed on the trained networks.
For a LIB with thick electrodes, Gao et al. [127] obtained an optimized electrolyte channel design, improving battery performance during fast charging and mechanical stability.Their study used electrochemical and mechanical models, deep neural networks, and Markov Chain Monte Carlo.To determine the effect of geometric parameters on cell performance, simulations were conducted using the electrochemical and mechanical model.Various electrolyte channel lengths and widths, and electrode material widths were simulated.Each set of simulations compared specific energy, power, capacity, and mechanical stability with conventional electrodes without channels.Data generated by simulation was used to train DNN.To obtain the optimal channel design, the trained DNN was combined with a Markov Chain Monte Carlo optimization algorithm.By varying the length, width, and tapering degree of the cathode and anode electrolyte channels, specific energy, power, and capacity contours were calculated.A maximum error of 1.94 % was calculated from Ragone plots of possible specific energy and power values.Furthermore, by freely modifying all six channel geometrical parameters and choosing specific energy as the design goal, the optimal channel design improved by 74 %.
A method developed by Deng et al. [128] for obtaining cathode active material distribution resulted in higher specific energy compared to an electrode with a uniform surface.To test the proposed method, they utilized an NMC-Li cell.In the NMC electrode, the average solid volume fraction was 50 %, and the rest was filled with electrolyte.Using a pseudo-three-dimensional model, cell energy was calculated by considering variations perpendicular to electrode thickness.DNN was used to learn the physics of the system and generalized simulated annealing was integrated with the DNN to find the optimal pattern.They fed the DNN with 100 values of volume fraction and their corresponding specific energy values based on the pseudo-three-dimensional model.The energy is calculated with the trained DNN instead of solving the equations of the electrochemical method, and a base value for volume fraction is calculated using generalized simulated annealing.A new set of volume fractions was then generated by adding noise to the base value.An updated training dataset was created with volume fraction values closer to the optimal region; therefore, training the DNN with this dataset would be more accurate.The optimal solid material distribution showed a periodic pattern with some channels filled with electrolyte, easing the transportation of lithium ions.
To improve ionic transport and reduce voltage drop during high charging rates, Sui et al. [129] proposed a bio-inspired vascularized electrode design.The proposed structure reduces the transport resistance near the separator, reducing voltage drop.Comparing the capacities of homogenous, vertical channel electrodes, two-branched and four-branched vascularized electrodes confirmed this hypothesis, with the vascularized electrodes showing the highest capacity.An artificial neural network was employed to find the optimal geometry.Based on 11 geometric parameters of the vasculature channels, a training dataset was generated.Each parameter combination represented a unique vascularized structure.COMSOL Multiphysics was employed to solve an electrochemical model with the finite element method (FEM).The final ANN model was 84 times more computationally efficient than the conventional FEM.By using the trained ANN's efficient prediction capability, a library of useful information was created to store charging curves, channel structure, charging rates, capacity, and porosity, as well as some electrochemical data, such as energy density, average voltage, and power density.Using this library, the optimal electrode structure design can be determined by defining manufacturing and operation limitations (channel radius, C-rate, and power density) and performance objectives.After successfully applying the vascularized graphite anode, the proposed structure was also applied to the cathode.The full cell vascularized structure showed a 66 % charging capacity enhancement compared to traditional homogenous electrodes.
The effectiveness of ML techniques in optimizing LIB designs for improved energy and power is a new and exciting frontier in LIB research.There is a clear synergy between physics-based models, ML algorithms, and optimization strategies in enhancing battery performance, providing novel insights into designing electrodes, electrolyte channels, and active material distributions.Such integrations enable the efficient exploration of vast design spaces, resulting in significant enhancements in LIB performance metrics, as demonstrated by these studies.However, as this field develops and expands, it is reasonable to assume that the digital LIB experimental space will transcend physical laboratory experimentation, leading to challenges in verifying results obtained digitally.Therefore, it is imperative that validation with physical experimentation is maintained to validate promising digital developments.

Improved thermal management
A nail penetration model, ML regressor algorithm, and genetic algorithm were used in Yamanaka et al.'s [130] study to identify battery design parameters for higher safety.Through nail penetration simulations within the range of input variables, including cell design parameters, test conditions, and performance indicators, the training database was created.By multiplying the finite element parameters by 0.5 and 1.5, upper and lower limits were set for the design and test parameters.This method generated 368 datasets.Descriptors include electrical, Fig. 9. workflow of integration of physics-based modeling and machine learning for LIB design applications.electrochemical, and dimensional parameters, and battery test conditions such as nail velocity, position, and diameter, while predictors include combustion volume, capacity, and averaged internal resistance.By analyzing the relationship between descriptors and predictors, correlation factors were calculated that indicate parameter dependency.For each predictor, a GPR algorithm was constructed.Using regression models, the values were predicted with high accuracy with a R 2 of 0.9 or greater.To find the design parameters leading to better performance, a genetic algorithm was used.Cell width, cell height, cell thickness, negative electrode layer thickness, negative active material diameter, negative porosity, and negative active material Li + diffusion coefficient were optimized, which resulted in 3.3 times greater capacity and 0.78 times lower internal resistance as well as a minimized combustion volume.
Li et al. [131] used a multilayer perceptron neural network to find the optimal battery pack configuration for enhancing battery thermal management.A 3D electrochemical model was used to simulate battery pack temperature distribution and heat transfer to the ambient environment.Nine pack configurations with variations in the gaps among battery pairs were formed.Each configuration's temperature distribution was analyzed under various operating conditions to create 130 datasets of inputs and outputs for the ANN.The inputs to the ANN included gap dimensions in two directions as the configuration parameters and air velocity and ambient temperatures as the operating conditions.The model outputs are the maximum temperature of a battery cell and the difference between its highest and lowest temperature.The developed hybrid model calculated 6,250,000 data of different battery configurations under various operating conditions and identified the optimal configuration.A 1.9 % reduction in maximum temperature and a 4.5 % reduction in maximum temperature difference improved battery cooling efficiency and performance.
The efficacy of ML approaches linked with LIB modelling methods has been shown to improve thermal management within LIB designs.This allows the improvement of LIB designs to optimize safety, temperature distribution, and cooling efficiency within LIBs.Although the application of ML-driven approaches demonstrates their potential in enhancing thermal management strategies, offering insights into optimal battery designs for improved safety and performance, further research should focus on improving the accuracy of these methods.In addition, there is still a requirement for these approaches to be applied to the knowledge gained from LIBs used in real-world applications considering the various climates and environments LIBs are routinely used in.

Mesoscale design
In their study, Takagishi et al. [132] developed a physicochemical based data-driven approach to find the mesoscale structure of LIB electrodes, resulting in lower specific resistance and higher capacity and power.A simplified physicochemical model was used to simulate the specific resistance during charge-discharge processes for 2100 randomly generated 3D structures.Analyzing the model's results, the relationship between active material volume ratio, particle radius, matrix binder conductivity, additives volume ratio, and pressure in the compaction process was constructed.To create regressions between process parameters and total specific resistance, an ANN algorithm was developed.A Bayesian optimization method was used to find the optimal electrode structure.Electrodes with a 50 % volume ratio and a binder/additive volume ratio less than 0.1 % give lower total specific resistance than other electrode structures.
Kabra et al. [133] used physics-constrained ML algorithms to characterize electrode microstructural properties.A dataset of 17,000 electrode microstructures was generated by varying ellipsoidal particle shapes, sizes, orientations, and active material and binder phase composition.A 3D physics-based pore-scale simulation method was used to characterize these electrode structures.Electrode properties included effective electronic conductivity, tortuosity of the pore network in three directions representing Li + transport in the pore network, and volume-specific surface area, which represents the interfacial area for electrochemical reactions.The method was also applied to a graphite cathode, but it can be applied to other porous electrode materials as well.Based on the created dataset, linear regression, lasso regression, elasticnet, ridge regression, decision tree, adaboost, and gradient boost algorithms were trained to map physical descriptors (inputs) to electrode properties (outputs).Predictions of different properties were more than 90 % accurate.
A summary of hybrid methods used in research for LIB design applications on a variety of scales and objectives is presented in Table 2.
Optimizing electrode structures at the mesoscale is a promising route for improved LIB performance, where ML-driven modelling approaches are effective (see Table 3).The integration of physics-based models and ML algorithms has provided insights into the relationships between electrode structure and performance metrics in LIBs.However, there is a limitation in the validation of some approaches.Designing intricate structural changes digitally can yield performance gains but can be difficult to verify experimentally if there structure is not straightforward to engineer using current technologies.Although the state-ofthe-art demonstrates the potential for ML techniques to guide the design of mesoscale electrode structures, thereby enhancing specific resistance, capacity, and power in lithium-ion batteries, there is still the requirement for further physical verification of these findings.

Hybrid modelling roadmap
Designing batteries utilizing hybrid modelling methods involving physics-based models and machine learning is an emerging field and requires a comprehensive approach.The authors suggest the following concise roadmap based on current research and future prospects.
Data collection and preprocessing is required to gather diverse datasets encompassing battery characteristics, performance, and aging under various conditions.It is imperative to ensure data quality, standardisation, and compatibility for subsequent modelling stages, allowing the adaptation of modelling results between fields.Physicsbased modelling must be developed or refined into simpler models based on electrochemical principles, incorporating material properties, kinetics, and thermodynamics.These must be simplified so they can be integrated with machine learning algorithms for improved accuracy and efficiency in real-time.Machine learning integration into hybrid models requires the identification of appropriate machine learning techniques (e.g., neural networks, ensemble methods) for coupling with physicsbased models.The machine learning methods must then be trained using the combined datasets (use by both the physics-based models and machine learning), leveraging machine learning to enhance predictive capabilities and model robustness.
Hybrid model validation and optimization using experimental and usage data to assess their accuracy and reliability.This can be challenging for designs that are not yet developed physically, and therefore lacking experimental data.This can be alleviated by optimizing the hybrid models iteratively, fine-tuning parameters and architectures for better performance.Following this, the application and scaling of hybrid models can be performed.This will involve the implementation of the validated hybrid models in practical scenarios for battery design, optimization, and predictive maintenance.This will also open opportunities for the models to be applied to broader applications across different battery chemistries and configurations.This will result in robust hybrid models that may give insight into designs of batteries that have not yet been validated experimentally.
Future research directions should focus on investigating novel datadriven techniques and advancements in machine learning for further improving hybrid modelling accuracy and efficiency.This includes the exploration of the integration of AI-driven optimization algorithms for advanced battery design, control, and monitoring.To achieve this, it will be required that many scientific disciplines collaborate in a multidisciplinary manner to address challenges in scalability, interpretability, and transferability of hybrid models.An essential requirement for this knowledge transfer and collaboration will include establishing knowledge-sharing platforms, workshops, and collaborations to disseminate findings and facilitate cross-disciplinary interactions in Lithium-ion battery hybrid modelling.
This field of research is rapidly evolving and advancing, and this roadmap should adapt to evolving research, technological advancements, and emerging challenges in battery technology, ensuring flexibility to incorporate novel methodologies and insights as they arise.

Future outlook and conclusions
More efficient deployment of LIBs is essential for a carbon emissionfree future.For this to be achieved, more improvements must be made to develop and engineer high-performing LIBs.Employing digital tools for LIB research and development can accelerate the discovery of more effective battery designs by providing the opportunity to virtually test the impact of new design ideas on battery performance during its whole lifetime and under various working conditions.By evolving from simple empirical and ECMs to precise electrochemical models, simulations of LIBs have reached a high level of maturity.It is now possible to develop realistic 3D digital models of LIBs that consider the effect of degradation modes, heat generation, and material inhomogeneities and can closely imitate an actual battery's behavior.Such high-precision models can provide valuable information regarding how internal battery parameters are affected throughout a battery's life.However, the high computational cost of these models is the primary obstacle to their widespread use.Physics-informed machine learning has been proven to perform well as a surrogate for complicated physics-based battery models by reducing computation costs while maintaining accuracy.The application of physics-informed ML within the field of LIBs has primarily focused on developing fast models suitable for battery monitoring and state estimation during operation.It has also been proven that physicsinformed ML surrogates can be used to achieve the optimal design leading to improved performance from pack to mesoscale level.
Despite this, some aspects of the current research can be improved to maximize the potential of hybrid methods.The models used in research for training dataset generation are not the most accurate and suffer from shortcomings.Integrating more precise multi-physics models with intensive details that simulate battery electrochemical reactions, thermal, aging, and mechanical behavior during the system's operation with ML algorithms can lead to more reliable results.In addition, large datasets of synthetic data are used to train ML algorithms to find the mapping between the LIB structure and property.Including the physics of the system more precisely by enforcing physical constraints to the loss  function can increase the reliability of the results by reducing the risk of producing physically unfeasible data when extrapolating beyond the training data [134].Using a database of previous experiments or simulations of novel LIB structures can be useful for the model parameterization process and ML training [135].Including experimental data in the training process of ML can increase the accuracy of the results by considering the effect of battery processes that might not be captured in the multi-physics model [136].Also, when trying to find the optimal design of a battery component such as electrodes, it would be more accurate to extract the initial parameters of the multi-physics model from the performance curves of similar structures.There are some challenges involved in developing a hybrid digital framework for LIB design.Development and parameterization of the multi-physics battery models are challenging due to the complexities involved in the system and large sets of required parameters.There are several coupled partial differential equations describing the behavior of the battery that must be solved simultaneously.It might be difficult to add all these equations to the loss function.Given that the challenges are addressed, combining three elements of high-fidelity multi-physics modeling, intelligent ML algorithms, and large experimental and simulation data can lead to developing a computationally efficient LIB simulation framework that can be used as a digital battery lab.Using this tool, electrode structures that satisfy different performance criteria simultaneously (e.g., high energy and power density, reduced lithium plating, and increased safety) can be obtained, leading to the development of the next generation of LIBs.
Verifying advanced digital LIB hybrid models through physical verification poses significant challenges due to the complexity and fidelity of digital designs.Recreating these digitally developed models in a laboratory setting can be difficult due to complexity of designs, high dimensionality and multivariate nature, resource and time constraints, accuracy and calibration challenges, and the dynamic and evolving nature of the LIB research and development field.To overcome these challenges, interdisciplinary collaborations involving experts in modelling, experimental analysis, and ML are essential.By combining aspects of hybrid modelling with targeted physical experiments can provide validation and refinement of digital results.Moreover, advancements in technology and innovative experimental techniques are continuously sought, and can prove to bridge the gap between digital models and physical verification in advanced LIB research.This procedure can be enhanced by collecting and sharing multiple datasets from various studies in a standard and interpretable manner, providing researchers with valuable information derived from both simulations and experiments.
With the need to electrify the energy sector with renewable energy to prevent climate change, batteries will play a significant role.The work presented here is of particular importance to the development of highperformance LIBs.By leveraging digital tools for LIB experimentation, it will allow research in the field of LIBs to progress faster than through traditional laboratory-based experimentation.At minimum, digital tools for battery experimentation can help guide further research in the laboratory to reduce development time.By expediting development of LIBs using digital tools, battery properties (e.g., power and energy) can be improved in a shorter time-frame.This is of interest for batteries used in transport applications, where battery size and mass are of importance.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.Illustration of the interdependence of multiscale battery parameters across the entire battery lifecycle.
M.N.Amiri et al.
The work gives clear gaps and perspectives of the field where focus on future studies and opportunities can lead to innovation

Table 1
A summary of machine learning approaches for lithium-ion batteries applications.

Table 2
Summary of works on hybrid methods for battery controlling applications.

Table 3
Summary of works on hybrid methods for battery design applications.