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Regularization in iws.DataFit is expressed as priors on the fit parameters. Each prior pairs a parameter name with a distribution from iws.stats. For why regularization is needed and how to choose prior strengths, see the Regularization Guide.

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Distributions

SchemaUse for
iws.stats.Normal(mean=..., std=...)Gaussian prior, additive scale
iws.stats.LogNormal(mean=..., std=...)Strictly-positive parameter spanning orders of magnitude (e.g. solid-phase diffusivities)
iws.stats.Uniform(lb=..., ub=...)Hard support; equivalent to bounds with constant density
iws.stats.MultivariateNormal(...)Correlated priors across multiple parameters

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A regularized fit

import ionworks_schema as iws
from ionworks import Ionworks

parameters = {
    "Positive particle diffusivity [m2.s-1]": iws.Parameter(
        "Positive particle diffusivity [m2.s-1]",
        initial_value=1e-14,
        bounds=(1e-16, 1e-12),
    ),
    "Negative particle diffusivity [m2.s-1]": iws.Parameter(
        "Negative particle diffusivity [m2.s-1]",
        initial_value=3e-14,
        bounds=(1e-16, 1e-12),
    ),
}

priors = {
    "Positive particle diffusivity [m2.s-1]": iws.priors.Prior(
        "Positive particle diffusivity [m2.s-1]",
        iws.stats.LogNormal(mean=-32.2, std=1.0),  # log-mean, log-std
    ),
    "Negative particle diffusivity [m2.s-1]": iws.priors.Prior(
        "Negative particle diffusivity [m2.s-1]",
        iws.stats.LogNormal(mean=-31.1, std=1.0),
    ),
}

fit = iws.DataFit(
    objectives={
        "1C": iws.objectives.CurrentDriven(
            data_input="file:.../1C.csv",
            options={"model": {"type": "SPMe"}},
        ),
    },
    parameters=parameters,
    priors=priors,
    optimizer=iws.optimizers.ScipyLeastSquares(),
)

pipeline = iws.Pipeline({"fit": fit})

client = Ionworks()
submission = client.pipeline.create(pipeline)
The priors dict adds a regularization term to the cost function so deviations from the prior mean are penalised in proportion to the prior’s inverse variance.

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Attaching priors via Parameter

Priors can also be attached directly to a Parameter rather than passed as a separate dict — useful when the prior is intrinsic to that parameter: 
diffusivity = iws.Parameter(
    "Positive particle diffusivity [m2.s-1]",
    initial_value=1e-14,
    bounds=(1e-16, 1e-12),
    prior=iws.stats.LogNormal(mean=-32.2, std=1.0),
)

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Why LogNormal for diffusivities

Solid-phase diffusivities span many orders of magnitude (often 10−1610^{-16} to 10−1010^{-10} m²/s). A Normal prior on the raw value is hard to specify — mean ± std doesn’t reflect order-of-magnitude uncertainty. A LogNormal prior treats the parameter on a log scale, so “mean ± 1 std” corresponds to a factor of ee — much more natural. The mean=-32.2 in the example above is the natural log of ∼10−14\sim 10^{-14}, so the prior is centred on a typical particle diffusivity.

Regularization (theory)

Ridge regression, MAP estimation, bias–variance tradeoff.

Data Fitting overview

Putting priors together with objectives and optimisers.