Physics-based electrochemical battery models

Physics-based models predict how a cell behaves outside the operating window you have tested. Empirical models, fit to measurements alone, cannot.

This page is the pillar for the DFN, SPM, and SPMe family of lithium-ion cell models. Thermal, degradation, and 3D extensions live on their own pages and link back here.

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Schematic of the Doyle-Fuller-Newman (DFN) battery model showing lithium transport through the electrolyte and intercalation into solid particles across the negative electrode, separator, and positive electrode

Doyle-Fuller-Newman model structure

What a physics-based electrochemical model is

A physics-based battery model represents the transport, reaction, and intercalation physics inside a cell from first principles, with parameters tied to real materials and geometry.

Lithium diffuses through an electrolyte, reacts at an electrode surface, and intercalates into solid particles. The model solves those equations across the electrode stack and predicts the terminal voltage as a function of current, temperature, and state of charge.

The Doyle-Fuller-Newman formulation (DFN, also called P2D or the Newman model) is the canonical form. SPM and SPMe are principled reductions of DFN that trade a small amount of accuracy for a large gain in speed.

The physics-based model family

SPM

Single particle model

One representative particle per electrode. Very fast. Accurate at low C-rate, where electrolyte gradients are small. Useful for long duty cycles, calendar studies, and first-pass scoping.

SPMe

Single particle with electrolyte

Adds electrolyte transport to SPM. Recovers near-DFN accuracy across most automotive and grid duty cycles, at a fraction of the solve time. The practical default for many studies.

DFN / P2D

Doyle-Fuller-Newman

Full porous electrode theory with electrolyte transport through the thickness of the stack. The benchmark for accuracy, and the right choice for design optimization and high-C-rate or low-temperature behavior.

+ extensions

Thermal, degradation, 3D

The base models extend to coupled thermal, degradation, pseudo-3D, and full 3D electrochemical studies using the same parameter set.

Physics-based vs. equivalent circuit

Both have their place. Which one fits depends on what the team is actually trying to predict.

Equivalent circuit model

Doyle-Fuller-Newman physics-based battery model schematic

Physics-based model (DFN)

Question	Physics-based	ECM
Extrapolate outside tested window	Yes	No
Explain why a cell behaves a certain way	Yes	No
Real-time BMS or onboard estimation	No	Yes
Fit from sparse pulse data	No	Yes
Design optimization (loading, porosity, thickness)	Yes	No

SPM, SPMe, and DFN: accuracy and speed

Model	Accuracy	Speed	Use when
SPM	Good at low C-rate	Very fast	First-pass scoping, long duty cycles, calendar aging
SPMe	Near-DFN through moderate C-rate	Fast	Most automotive and grid duty cycles
DFN	Benchmark	Slower	Design optimization, fast charge, low temperature

Parameterization is the real work

The equations are settled. What determines whether a physics-based model predicts your cell correctly is the parameter set: diffusion coefficients, reaction rate constants, transport properties, open-circuit voltages, particle sizes. Most of these cannot be measured directly on a commercial cell. Some have to be inferred from cycling data.

Identifiability matters more than raw fit quality. A model that fits one discharge curve perfectly by pushing two parameters in opposite directions will fail on the next one. The workflow has to pin parameters to data that isolates them, and flag the ones that remain coupled.

This is the Train stage in Ionworks Studio. A parameter set fit here drives every downstream study.

How Ionworks fits in

How Ionworks supports physics-based models

PyBaMM as the solver

Ionworks is built on PyBaMM, the open-source battery modeling framework maintained by the Ionworks team. Models are first-class objects: DFN, SPM, SPMe, and custom submodels all run through the same interface.

Parameters carry across the workflow

A parameter set fit in Train drives capacity curves, fast-charge studies, thermal runs, and design sweeps in Predict and Optimize. Teams do not re-fit per study.

BPX parameter exchange

Ionworks supports BPX, the community standard for physics-based battery parameter sets. Teams can import vendor-supplied BPX files or export their own for sharing with partners and suppliers.

Immutable parameterized models with provenance

Every parameterized model records which dataset it was fit to, which cells were used, and when. The model you run in a design study six months from now is the same model you shipped to your stakeholders.

Ionworks Studio Train stage: parameterization workflow fitting DFN, SPM, and SPMe models to cycling data

Parameterization in Ionworks Studio

Example questions teams answer

Energy-power tradeoff

How thick can I coat this electrode before the resulting cell cannot deliver the power the application needs?

Fast-charge limits

What is the fastest charge rate that avoids lithium plating across the temperature range this cell will see in the field?

Silicon content tradeoff

How does increasing silicon content in the anode change energy density, rate capability, and cycle life for a target duty cycle?

Frequently asked questions

The Doyle-Fuller-Newman model, also called P2D or the Newman model, is the canonical physics-based model for lithium-ion cells. It resolves lithium transport in the electrolyte and in the solid particles of both electrodes through the thickness of the electrode stack, coupled to Butler-Volmer kinetics at the particle surface. It is the benchmark against which faster reduced-order models (SPM and SPMe) are compared.

The Single Particle Model (SPM) treats each electrode as one representative particle and ignores electrolyte dynamics. It is accurate at low C-rates and runs very fast. SPMe adds electrolyte transport back in. It recovers most of the DFN accuracy at moderate C-rates while remaining much faster than the full model.

For onboard state estimation inside a BMS, for fitting sparse pulse data at a single operating point, or for problems that stay well inside the tested operating window, an equivalent circuit model is usually sufficient. Physics-based models pay off when a team needs to extrapolate, change a design variable, or attribute behavior to a specific mechanism.

At a minimum, charge and discharge curves at several C-rates and temperatures, open-circuit measurements on harvested half-cells or pseudo-OCV protocols, and ideally electrolyte transport and particle-size data from the cell vendor or literature. Ionworks Studio handles the fitting workflow in Train and supports BPX parameter exchange.

Yes. Ionworks is built on PyBaMM and treats models as first-class objects. Teams can bring custom PyBaMM models, custom submodels, or modified physics and run them through the same parameterization, simulation, and optimization workflow as the built-in DFN, SPM, and SPMe.

Use an equivalent circuit when the goal is fast inference inside a narrow operating window, for example onboard SoC or SoH tracking. Use a physics-based model when the goal is to predict what happens under conditions you have not tested, to attribute behavior to a mechanism, or to optimize a design variable like electrode thickness or loading.

See DFN, SPM, and SPMe side by side on your cell

Bring a dataset from one of your cells. We will show what each model gets right and where the accuracy-speed tradeoff lands for your workflow.

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