arXiv subjects

Jamie M. Foster

Publications and source records attributed to Jamie M. Foster.

12 recordsLinked to original sources

arXiv2026

Surrogate-accelerated parameterisation of physics-based Li-ion battery models

Physics-based lithium-ion battery models provide access to physically meaningful internal electrochemical states and processes, but cell-specific parameter inference from terminal current-voltage data is computationally expensive and limited by identifiability. We present a surrogate-accelerated inverse framework based on a single-particle model with electrolyte dynamics (SPMe). Its forward map uses our Artiphy surrogate framework for rapid, differentiable evaluation of voltage and selected internal states. After rescaling to remove exact structural redundancies, we infer non-redundant transport, kinetic and capacity parameter groups, including concentration-dependent solid and electrolyte diffusivities. Synthetic voltage data from a Doyle-Fuller-Newman (DFN) model under a WLTP-like current protocol provide a benchmark with known reference parameters and controlled model discrepancy. The inferred SPMe reproduces the benchmark voltage with an error of order 1 mV and recovers electrode capacities well. Positive-electrode diffusivity is recovered accurately over much of the probed stoichiometric range. Local sensitivity and Fisher-information analysis identifies correlated kinetic-Ohmic and electrolyte-transport directions, and shows how localised information and the global diffusivity parameterisation can yield narrow Fisher-curvature envelopes despite weak voltage sensitivity to negative-electrode diffusion over much of the drive cycle. These results represent a step towards rapid physics-based in-silico parameterisation and reduced reliance on destructive cell characterisation.

physics.app-ph↗

arXiv2026

Incorporating multiscale mechanics in lithium-ion battery models

Lithiation-induced swelling in lithium-ion batteries generates stresses not only within active particles, but also across the surrounding non-active matrix, electrodes, and cell stack. These stresses can modify the chemical potential of lithium and therefore influence transport, reaction kinetics, and terminal voltage. We derive a reduced-order electro-chemo-mechanical model that captures this multiscale coupling while retaining a complexity comparable to standard Doyle--Fuller--Newman models. The electrode is modelled as a periodic array of spherical active particles embedded in a homogenised elastic non-active matrix. Exploiting the small stiffness of the non-active matrix relative to the active material, together with scale separation between particles, electrodes, and the full cell, we obtain an effective mechanical correction to the active-particle chemical potential and overpotential. This correction depends on particle swelling, electrode-scale strain, and macroscopic boundary conditions such as clamping or applied pressure. The resulting formulation can be incorporated directly into DFN, SPMe, and SPM frameworks, providing a computationally efficient route to include battery-scale mechanical effects in electrochemical simulations.

physics.chem-ph↗

arXiv2024

A fast and accurate method for inferring solid-state diffusivity in lithium-ion battery active materials: improving upon the classical GITT approach

Data collected using the galvanostatic intermittent titration technique (GITT) and application of the Sand equation is a ubiquitous method for inferring the solid-state diffusivity in lithium-ion battery active materials. However, the experiment is notoriously time-consuming and the Sand equation relies on assumptions whose applicability can be questionable. We propose a novel methodology, termed Inference from a Consistent Model (ICM), which enables inference of solid-state diffusivity using the same physical model employed for prediction, and is applicable to more general and quick-to-measure data. We infer the diffusivity (as a function of inserted lithium concentration) by minimising the residual sum of squares between data and solutions to a spherically-symmetric nonlinear diffusion model in a single representative active material particle. Using data harvested from the NMC cathode of a commercial LG M50 cell we demonstrate that the ICM is robust, and yields more accurate diffusivity estimates, while relying on data that are five times faster to collect than that required by the classical approach. Moreover, there is good reason to believe that further speed ups could be achieved when other types of data are available. This work contributes towards developing faster and more reliable techniques in parameter inference for lithium-ion batteries, and the code required to deploy ICM is provided to facilitate its adoption in future research.

physics.app-ph↗

arXiv2023

Learning Optimal Forms of Constitutive Relations Characterizing Ion Intercalation from Data in Mathematical Models of Lithium-ion Batteries

Most mathematical models of the transport of charged species in battery electrodes require a constitutive relation describing intercalation of Lithium, which is a reversible process taking place on the interface between the electrolyte and active particle. The most commonly used model is the Butler-Volmer relation, which gives the current density as a product of two expressions: one, the exchange current, depends on Lithium concentration only whereas the other expression depends on both Lithium concentration and on the overpotential. We consider an inverse problem where an optimal form of the exchange current density is inferred, subject to minimum assumptions, from experimental voltage curves. This inverse problem is recast as an optimization problem in which the least-squares error functional is minimized with a suitable Sobolev gradient approach. The proposed method is thoroughly validated and we also quantify the reconstruction uncertainty. Finally, we identify the universal features in the constitutive relations inferred from data obtained during charging and discharging at different C-rates and discuss how these features differ from the behaviour predicted by the standard Butler-Volmer relation. We also identify possible limitations of the proposed approach, mostly related to uncertainties inherent in the material properties assumed known in the inverse problem. Our approach can be used to systematically improve the accuracy of mathematical models employed to describe Li-ion batteries as well as other systems relying on the Butler-Volmer relation.

physics.chem-ph↗

arXiv2022

A Continuum of Physics-Based Lithium-Ion Battery Models Reviewed

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.

physics.chem-ph↗

arXiv2022

Data-Driven Optimal Closures for Mean-Cluster Models: Beyond the Classical Pair Approximation

This study concerns the mean-clustering approach to modelling the evolution of lattice dynamics. Instead of tracking the state of individual lattice sites, this approach describes the time evolution of the concentrations of different cluster types. It leads to an infinite hierarchy of ordinary differential equations which must be closed by truncation using a so-called closure condition. This condition approximates the concentrations of higher-order clusters in terms of the concentrations of lower-order ones. The pair approximation is the most common form of closure. Here, we consider its generalization, termed the "optimal approximation", which we calibrate using a robust data-driven strategy. To fix attention, we focus on a recently proposed structured lattice model for a nickel-based oxide, similar to that used as cathode material in modern commercial Li-ion batteries. The form of the obtained optimal approximation allows us to deduce a simple sparse closure model. In addition to being more accurate than the classical pair approximation, this ``sparse approximation'' is also physically interpretable which allows us to a posteriori refine the hypotheses underlying construction of this class of closure models. Moreover, the mean-cluster model closed with this sparse approximation is linear and hence analytically solvable such that its parametrization is straightforward. On the other hand, parametrization of the mean-cluster model closed with the pair approximation is shown to lead to an ill-posed inverse problem.

physics.comp-ph↗

arXiv2021

On Uncertainty Quantification in the Parametrization of Newman-type Models of Lithium-ion Batteries

We consider the problem of parameterizing Newman-type models of Li-ion batteries focusing on quantifying the inherent uncertainty of this process and its dependence on the discharge rate. In order to rule out genuine experimental error and instead isolate the intrinsic uncertainty of model fitting, we concentrate on an idealized setting where "synthetic" measurements in the form of voltage curves are manufactured using the full, and most accurate, Newman model with parameter values considered "true", whereas parameterization is performed using simplified versions of the model, namely, the single-particle model and its recently proposed corrected version. By framing the problem in this way, we are able to eliminate aspects which affect uncertainty, but are hard to quantity such as, e.g., experimental errors. The parameterization is performed by formulating an inverse problem which is solved using a state-of-the-art Bayesian approach in which the parameters to be inferred are represented in terms of suitable probability distributions; this allows us to assess the uncertainty of their reconstruction. The key finding is that while at slow discharge rates the voltage curves can be reconstructed quite accurately, this can be achieved with some parameter varying by 300\% or more, thus providing evidence for very high uncertainty of the parameter inference process. As the discharge rate increases, the reconstruction uncertainty is reduced but at the same time the fits to the voltage curves becomes less accurate. These observations highlight the ill-posedness of the inverse problem of parameter reconstruction in models of Li-ion battery operation.In practice, using simplified model appears to be a viable and useful strategy provided that the assumptions facilitating the model simplification are truly valid for the battery operating regimes in which the data was collected.

physics.comp-ph↗

arXiv2021

DandeLiion v1: An extremely fast solver for the Newman model of lithium-ion battery (dis)charge

DandeLiion (available at dandeliion.com) is a robust and extremely fast solver for the Doyle Fuller Newman (DFN) model, the standard electrochemical model for (dis)charge of a planar lithium-ion cell. DandeLiion conserves lithium, uses a second order spatial discretisation method (enabling accurate computations using relatively coarse discretisations) and is many times faster than its competitors. The code can be used `in the cloud' and does not require installation before use. The difference in compute time between DandeLiion and its commercial counterparts is roughly a factor of 100 for the moderately-sized test case of the discharge of a single cell. Its linear scaling property means that the disparity in performance is even more pronounced for bigger systems, making it particularly suitable for applications involving multiple coupled cells. The model is characterised by a number of phenomenological parameters and functions, which may either be provided by the user or chosen from DandeLiion's library. This library contains data for the most commonly used electrolyte (LiPF6) and a number of common active material chemistries including graphite, lithium iron phosphate (LFP), nickel cobalt aluminium (NCA), and a variant of nickel cobalt manganese (NMC).

physics.app-ph↗

arXiv2018

A mathematical model for mechanically-induced deterioration of the binder in lithium-ion electrodes

This study is concerned with modeling detrimental deformations of the binder phase within lithium-ion batteries that occur during cell assembly and usage. A two-dimensional poroviscoelastic model for the mechanical behavior of porous electrodes is formulated and posed on a geometry corresponding to a thin rectangular electrode, with a regular square array of microscopic circular electrode particles, stuck to a rigid base formed by the current collector. Deformation is forced both by (i) electrolyte absorption driven binder swelling, and; (ii) cyclic growth and shrinkage of electrode particles as the battery is charged and discharged. The governing equations are upscaled in order to obtain macroscopic effective-medium equations. A solution to these equations is obtained, in the asymptotic limit that the height of the rectangular electrode is much smaller than its width, that shows the macroscopic deformation is one-dimensional. The confinement of macroscopic deformations to one dimension is used to obtain boundary conditions on the microscopic problem for the deformations in a 'unit cell' centered on a single electrode particle. The resulting microscale problem is solved using numerical (finite element) techniques. The two different forcing mechanisms are found to cause distinctly different patterns of deformation within the microstructure. Swelling of the binder induces stresses that tend to lead to binder delamination from the electrode particle surfaces in a direction parallel to the current collector, whilst cycling causes stresses that tend to lead to delamination orthogonal to that caused by swelling. The differences between the cycling-induced damage in both: (i) anodes and cathodes, and; (ii) fast and slow cycling are discussed. Finally, the model predictions are compared to microscopy images of nickel manganese cobalt oxide cathodes and a qualitative agreement is found.

physics.flu-dyn↗

arXiv2018

Binder migration during drying of lithium-ion battery electrodes: modelling and comparison to experiment

The drying process is a crucial step in electrode manufacture as it can affect the component distribution within the electrode. Phenomena such as binder migration can have negative effects in the form of poor cell performance (e.g. capacity fade) or mechanical failure (e.g. electrode delamination from the current collector). We present a mathematical model that tracks the evolution of the binder concentration in the electrode during drying. Solutions to the model predict that low drying rates lead to a favourable homogeneous binder profile across the electrode film, whereas high drying rates result in an unfavourable accumulation of binder near the evaporation surface. These results show strong qualitative agreement with experimental observations and provide a cogent explanation for why fast drying conditions result in poorly performing electrodes. Finally, we provide some guidelines on how the drying process could be optimised to offer relatively short drying times whilst simultaneously maintaining a roughly homogeneous binder distribution.

cond-mat.soft↗

arXiv2017

Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption

Bifurcations of self-similar solutions for reversing interfaces are studied in the slow diffusion equation with strong absorption. The self-similar solutions bifurcate from the time-independent solutions for standing interfaces. We show that such bifurcations occur at the bifurcation points, at which the confluent hypergeometric functions satisfying Kummer's differential equation is truncated into a finite polynomial. A two-scale asymptotic method is employed to obtain the asymptotic dependencies of the self-similar reversing interfaces near the bifurcation points. The asymptotic results are shown to be in excellent agreement with numerical computations.

nlin.PS↗

arXiv2015

Self-similar solutions for reversing interfaces in the nonlinear diffusion equation with constant absorption

We consider the slow nonlinear diffusion equation subject to a constant absorption rate and construct local self-similar solutions for reversing (and anti-reversing) interfaces, where an initially advancing (receding) interface gives way to a receding (advancing) one. We use an approach based on invariant manifolds, which allows us to determine the required asymptotic behaviour for small and large values of the concentration. We then `connect' the requisite asymptotic behaviours using a robust and accurate numerical scheme. By doing so, we are able to furnish a rich set of self-similar solutions for both reversing and anti-reversing interfaces.

math-ph↗