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Piecewise interpolants produce smooth, differentiable functions of one or two breakpoint variables — useful for SOC-dependent diffusivities, temperature-dependent transport, and OCP curves. For the math (smooth heaviside, knots vs slopes, blending), see the Piecewise Interpolants Guide.

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1D piecewise interpolant

import ionworks_schema as iws

D_neg = iws.direct_entries.PiecewiseInterpolation1D(
    base_parameter_name="Negative particle diffusivity [m2.s-1]",
    breakpoint_values=[0.0, 0.3, 0.7, 1.0],
    breakpoint_parameter_name="SOC",
    smoothing=1e-4,
)

values = iws.direct_entries.DirectEntry(
    parameters={
        "Negative particle diffusivity at SOC 0 [m2.s-1]": 3.9e-14,
        "Negative particle diffusivity at SOC 0.3 [m2.s-1]": 5.2e-14,
        "Negative particle diffusivity at SOC 0.7 [m2.s-1]": 4.8e-14,
        "Negative particle diffusivity at SOC 1 [m2.s-1]": 3.5e-14,
    },
)

pipeline = iws.Pipeline({"D_neg values": values, "D_neg": D_neg})
The interpolant reads one parameter per breakpoint (the names follow "<base> at <breakpoint_parameter_name> <value> [units]") and produces a smooth function of the breakpoint variable.

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2D piecewise interpolant

For parameters varying with two variables (e.g. SOC and temperature): 
import ionworks_schema as iws

D_neg = iws.direct_entries.PiecewiseInterpolation2D(
    base_parameter_name="Negative particle diffusivity [m2.s-1]",
    breakpoint1_values=[0.0, 0.5, 1.0],
    breakpoint1_parameter_name="SOC",
    breakpoint2_values=[273.15, 298.15, 323.15],
    breakpoint2_parameter_name="Temperature [K]",
    smoothing1=1e-4,
    smoothing2=0.1,
)
Use different smoothing parameters when the two axes have very different scales (SOC ∈ [0, 1] vs Temperature ∈ [273, 323] K).

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OCP interpolants

SchemaWhat it builds
iws.calculations.OCPDataInterpolant(electrode=...)Smooth interpolant from half-cell OCP measurements
iws.calculations.OCPMSMRInterpolant(electrode=...)Evaluates the MSMR model over a voltage range to create an interpolant
iws.calculations.OCPDataInterpolantMSMRExtrapolation(electrode=...)Blends measured data inside the data range with MSMR extrapolation outside
import ionworks_schema as iws

ocp_pos = iws.calculations.OCPDataInterpolantMSMRExtrapolation(electrode="positive")

pipeline = iws.Pipeline({"ocp_pos": ocp_pos})
The blended interpolant is the recommended option whenever a simulation might access stoichiometries outside the measured data range — MSMR provides thermodynamically consistent extrapolation at the extremes.

Piecewise Interpolants (theory)

Smooth heaviside math, knot vs slope parameterisation, MSMR blending.

Pipelines overview

How interpolants chain with direct entries and data fits.