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A data-driven model augmentation framework, referred to as Weakly-coupled Integrated Inference and Machine Learning (IIML), is presented to improve the predictive accuracy of physical models. In contrast to parameter calibration, this work seeks corrections to the structure of the model by a) inferring augmentation fields that are consistent with the underlying model, and b) transforming these fields into corrective model forms. The proposed approach couples the inference and learning steps in a weak sense via an alternating optimization approach. This coupling ensures that the augmentation fields remain learnable and maintain consistent functional relationships with local modeled quantities across the training dataset. An iterative solution procedure is presented in this paper, removing the need to embed the augmentation function during the inference process. This framework is used to infer an augmentation introduced within a Polymer electrolyte membrane fuel cell (PEMFC) model using a small amount of training data (from only 14 training cases.) These training cases belong to a dataset consisting of high-fidelity simulation data obtained from a high-fidelity model of a first generation Toyota Mirai. All cases in this dataset are characterized by different inflow and outflow conditions on the same geometry. When tested on 1224 different configurations, the inferred augmentation significantly improves the predictive accuracy for a wide range of physical conditions. Predictions and available data for the current density distribution are also compared to demonstrate the predictive capability of the model for quantities of interest which were not involved in the inference process. The results demonstrate that the weakly-coupled IIML framework offers sophisticated and robust model augmentation capabilities without requiring extensive changes to the numerical solver.

Physics-based electrochemical battery models derived from porous electrode theory are a very powerful tool for understanding lithium-ion batteries, as well as for improving their design and management. Different model fidelity, and thus model complexity, is needed for different applications. For example, in battery design we can afford longer computational times and the use of powerful computers, while for real-time battery control (e.g. in electric vehicles) we need to perform very fast calculations using simple devices. For this reason, simplified models that retain most of the features at a lower computational cost are widely used. Even though in the literature we often find these simplified models posed independently, leading to inconsistencies between models, they can actually be derived from more complicated models using a unified and systematic framework. In this review, we showcase this reductive framework, starting from a high-fidelity microscale model and reducing it all the way down to the Single Particle Model (SPM), deriving in the process other common models, such as the Doyle-Fuller-Newman (DFN) model. We also provide a critical discussion on the advantages and shortcomings of each of the models, which can aid model selection for a particular application. Finally, we provide an overview of possible extensions to the models, with a special focus on thermal models. Any of these extensions could be incorporated into the microscale model and the reductive framework re-applied to lead to a new generation of simplified, multi-physics models., Comment: 50 pages, 9 figures

Increasing the speed of battery formation can significantly lower lithium-ion battery manufacturing costs. However, adopting faster formation protocols in practical manufacturing settings is challenging due to a lack of inexpensive, rapid diagnostic signals that can inform possible impacts to long-term battery lifetime. This work identifies the cell resistance measured at low states of charge as an early-life diagnostic feature for screening new formation protocols. We show that this signal correlates to cycle life and improves the accuracy of data-driven battery lifetime prediction models. The signal is obtainable at the end of the manufacturing line, takes seconds to acquire, and does not require specialized test equipment. We explore a physical connection between this resistance signal and the quantity of lithium consumed during formation, suggesting that the signal may be broadly applicable for evaluating any manufacturing process change that could impact the total lithium consumed during formation.

Lithium-ion batteries can last many years but sometimes exhibit rapid, nonlinear degradation that severely limits battery lifetime. In this work, we review prior work on "knees" in lithium-ion battery aging trajectories. We first review definitions for knees and three classes of "internal state trajectories" (termed snowball, hidden, and threshold trajectories) that can cause a knee. We then discuss six knee "pathways", including lithium plating, electrode saturation, resistance growth, electrolyte and additive depletion, percolation-limited connectivity, and mechanical deformation -- some of which have internal state trajectories with signals that are electrochemically undetectable. We also identify key design and usage sensitivities for knees. Finally, we discuss challenges and opportunities for knee modeling and prediction. Our findings illustrate the complexity and subtlety of lithium-ion battery degradation and can aid both academic and industrial efforts to improve battery lifetime., Comment: Submitted to the Journal of the Electrochemical Society

Predicting lithium-ion battery degradation is worth billions to the global automotive, aviation and energy storage industries, to improve performance and safety and reduce warranty liabilities. However, very few published models of battery degradation explicitly consider the interactions between more than two degradation mechanisms, and none do so within a single electrode. In this paper, the first published attempt to directly couple more than two degradation mechanisms in the negative electrode is reported. The results are used to map different pathways through the complicated path dependent and non-linear degradation space. Four degradation mechanisms are coupled in PyBaMM, an open source modelling environment uniquely developed to allow new physics to be implemented and explored quickly and easily. Crucially it is possible to see 'inside' the model and observe the consequences of the different patterns of degradation, such as loss of lithium inventory and loss of active material. For the same cell, five different pathways that can result in end-of-life have already been found, depending on how the cell is used. Such information would enable a product designer to either extend life or predict life based upon the usage pattern. However, parameterization of the degradation models remains as a major challenge, and requires the attention of the international battery community., Comment: First version submitted to Energy and Environmental Science on 15th November 2021. Second version submitted to Physical Chemistry: Chemical Physics on 25th January 2022

Fast charging of lithium-ion batteries is crucial to increase desirability for consumers and hence accelerate the adoption of electric vehicles. A major barrier to shorter charge times is the accelerated aging of the battery at higher charging rates, which can be driven by lithium plating, increased solid electrolyte interphase growth due to elevated temperatures, and particle cracking due to mechanical stress. Lithium plating depends on the overpotential of the negative electrode, and mechanical stress depends on the concentration gradient, both of which cannot be measured directly. Techniques based on physics-based models of the battery and optimal control algorithms have been developed to this end. While these methods show promise in reducing degradation, their optimization algorithms' complexity can limit their implementation. In this paper, we present a method based on the constant current constant voltage (CC-CV) charging scheme, called CC-CV$\eta \sigma$T (VEST). The new approach is simpler to implement and can be used with any model to impose varying levels of constraints on variables pertinent to degradation, such as plating potential and mechanical stress. We demonstrate the new CC-CV$\eta \sigma$T charging using an electrochemical model with mechanical and thermal effects included. Furthermore, we discuss how uncertainties can be accounted for by considering safety margins for the plating and stress constraints., Comment: In press; Modeling, Estimation and Control Conference 2021

Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the inner workings of NeuralPDE.jl and show how a formulation structured around numerical quadrature gives rise to new loss functions which allow for adaptivity towards bounded error tolerances. We describe the various ways one can use the tool, detailing mathematical techniques like using extended loss functions for parameter estimation and operator discovery, to help potential users adopt these PINN-based techniques into their workflow. We showcase how NeuralPDE uses a purely symbolic formulation so that all of the underlying training code is generated from an abstract formulation, and show how to make use of GPUs and solve systems of PDEs. Afterwards we give a detailed performance analysis which showcases the trade-off between training techniques on a large set of PDEs. We end by focusing on a complex multiphysics example, the Doyle-Fuller-Newman (DFN) Model, and showcase how this PDE can be formulated and solved with NeuralPDE. Together this manuscript is meant to be a detailed and approachable technical report to help potential users of the technique quickly get a sense of the real-world performance trade-offs and use cases of the PINN techniques., Comment: 74 pages, 20+ figures, 20+ tables

Large-scale electrification is vital to addressing the climate crisis, but several scientific and technological challenges remain to fully electrify both the chemical industry and transportation. In both of these areas, new electrochemical materials will be critical, but their development currently relies heavily on human-time-intensive experimental trial and error and computationally expensive first-principles, meso-scale and continuum simulations. We present an automated workflow, AutoMat, that accelerates these computational steps by introducing both automated input generation and management of simulations across scales from first principles to continuum device modeling. Furthermore, we show how to seamlessly integrate multi-fidelity predictions such as machine learning surrogates or automated robotic experiments "in-the-loop". The automated framework is implemented with design space search techniques to dramatically accelerate the overall materials discovery pipeline by implicitly learning design features that optimize device performance across several metrics. We discuss the benefits of AutoMat using examples in electrocatalysis and energy storage and highlight lessons learned., Comment: v1-3:4 pages, 1 figure, accepted to NeurIPS Climate Change and AI Workshop 2020, updating acknowledgements and citations v4: substantially updated content and author list, accepted to MRS Bulletin

Recent data-driven approaches have shown great potential in early prediction of battery cycle life by utilizing features from the discharge voltage curve. However, these studies caution that data-driven approaches must be combined with specific design of experiments in order to limit the range of aging conditions, since the expected life of Li-ion batteries is a complex function of various aging factors. In this work, we investigate the performance of the data-driven approach for battery lifetime prognostics with Li-ion batteries cycled under a variety of aging conditions, in order to determine when the data-driven approach can successfully be applied. Results show a correlation between the variance of the discharge capacity difference and the end-of-life for cells aged under a wide range of charge/discharge C-rates and operating temperatures. This holds despite the different conditions being used not only to cycle the batteries but also to obtain the features: the features are calculated directly from cycling data without separate slow characterization cycles at a controlled temperature. However, the correlation weakens considerably when the voltage data window for feature extraction is reduced, or when features from the charge voltage curve instead of discharge are used. As deep constant-current discharges rarely happen in practice, this imposes new challenges for applying this method in a real-world system., Comment: 7 pages, 7 figures, Submitted to American Controls Conference 2021

For many practical applications, fully coupled three-dimensional models describing the behaviour of lithium-ion pouch cells are too computationally expensive. However, owing to the small aspect ratio of typical pouch cell designs, such models are well approximated by splitting the problem into a model for through-cell behaviour and a model for the transverse behaviour. In this paper, we combine different simplifications to through-cell and transverse models to develop a hierarchy of reduced-order pouch cell models. We give a critical numerical comparison of each of these models in both isothermal and thermal settings, and also study their performance on realistic drive cycle data. Finally, we make recommendations regarding model selection, taking into account the available computational resource and the quantities of interest in a particular study.

A three-dimensional model of a single-layer lithium-ion pouch cell is presented which couples conventional porous electrode theory describing cell electrochemical behaviour with an energy balance describing cell thermal behaviour. Asymptotic analysis of the model is carried out by exploiting the small aspect ratio typical of pouch cell designs. The analysis reveals the scaling that results in a distinguished limit, and highlights the role played by the electrical conductivities of the current collectors. The resulting model comprises a collection of one-dimensional models for the through-cell electrochemical behaviour which are coupled via two-dimensional problems for the Ohmic and thermal behaviour in the planar current collectors. A further limit is identified which reduces the problem to a single volume-averaged through-cell model, greatly reducing the computational complexity. Numerical simulations are presented which illustrate and validate the asymptotic results., Comment: 27 pages, 6 figures, submitted to SIAM Journal on Applied Mathematics (08/05/2020)

The standard continuum model of a lithium-ion battery, the Doyle-Fuller-Newman (DFN) model, is computationally expensive to solve. Typically simpler models, such as the single particle model (SPM), are used to provide insight for control purposes. Recently, there has been a move to extend the SPM to include electrolyte effects, which increase the accuracy and range of applicability. However, these extended models are derived in an ad-hoc manner, which leaves open the possibility that important terms may have been neglected, resulting in the model not being as accurate as possible. In this paper, we provide a systematic asymptotic derivation of both the SPM and a correction term that accounts for the behaviour in the electrolyte. Firstly, this allows us to quantify the error in the reduced model in terms of ratios of key parameters in the model, from which the range of applicable operating conditions can be determined. Secondly, in comparing our model with the ad-hoc models from the literature, we show that previous models have neglected a key set of terms. In particular, we make the crucial distinction between writing the terminal voltage in pointwise and electrode-averaged form, which allows us to gain additional accuracy whilst maintaining the same computational complexity as the existing models., Comment: In preparation for submission to Journal of Electrochemical Society

Electrochemical and equivalent-circuit modelling are the two most popular approaches to battery simulation, but the former is computationally expensive and the latter provides limited physical insight. A theoretical middle ground would be useful to support battery management, on-line diagnostics, and cell design. We analyse a thermodynamically consistent, isothermal porous-electrode model of a discharging lead-acid battery. Asymptotic analysis of this full model produces three reduced-order models, which relate the electrical behaviour to microscopic material properties, but simulate discharge at speeds approaching an equivalent circuit. A lumped-parameter model, which neglects spatial property variations, proves accurate for C-rates below 0.1C, while a spatially resolved higher-order solution retains accuracy up to 5C. The problem of parameter estimation is addressed by fitting experimental data with the reduced-order models., Comment: Submitted to Journal of the Electrochemical Society. Second part of a two-part paper. Part I: "Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: I. Physical Model"

An isothermal porous-electrode model of a discharging lead-acid battery is presented, which includes an extension of concentrated-solution theory that accounts for excluded-volume effects, local pressure variation, and a detailed microscopic water balance. The approach accounts for three typically neglected physical phenomena: convection, pressure diffusion, and variation of liquid volume with state of charge. Rescaling of the governing equations uncovers a set of fundamental dimensionless parameters that control the battery's response. Total volume change during discharge and nonuniform pressure prove to be higher-order effects in cells where variations occur in just one spatial dimension. A numerical solution is developed and exploited to predict transient cell voltages and internal concentration profiles in response to a range of C-rates. The dependence of discharge capacity on C-rate deviates substantially from Peukert's simple power law: charge capacity is concentration-limited at low C-rates, and voltage-limited at high C-rates. The model is fit to experimental data, showing good agreement., Comment: Submitted to Journal of the Electrochemical Society. First part of a two-part paper. Part II: "Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: II. Asymptotic Analysis"