Piecewise Interpolation Direct Entries

class ionworkspipeline.direct_entries.BaseInterpolation(base_parameter_name: str, smoothing: float, source: str, print_precision: int = 6)

Base class for piecewise interpolation direct entries.

Provides common functionality for 1D and 2D interpolation.

Extends: ionworkspipeline.direct_entries.direct_entry.DirectEntry

run(parameter_values: ParameterValues) → ParameterValues

Create the piecewise interpolation function.

Parameters

parameter_valuesiwp.ParameterValues

ParameterValues containing the parameter values at each breakpoint.

Returns

iwp.ParameterValues

ParameterValues with the base parameter name mapped to the interpolation function.

class ionworkspipeline.direct_entries.PiecewiseInterpolation1D(base_parameter_name: str, breakpoint_values: list[float], breakpoint_parameter_name: str, smoothing: float = 0.0001, formulation: str = 'knots', **kwargs)

A direct entry that creates a piecewise linear interpolation function for a parameter that varies with respect to a breakpoint parameter (e.g., SOC, temperature, voltage).

This uses smooth heaviside functions to create a continuous, differentiable interpolation that can be used in PyBaMM models.

Parameters

base_parameter_namestr

The name of the parameter to create (e.g., “Particle diffusion time [s]”)

breakpoint_valueslist[float]

List of breakpoint values at which the parameter is defined (e.g., [0.0, 0.5, 1.0])

breakpoint_parameter_namestr

Name of the breakpoint parameter (e.g., “SOC”, “Temperature [K]”, “Voltage [V]”)

smoothingfloat, optional

Smoothing parameter for heaviside transitions (default: 1e-4). Larger values create smoother transitions.

formulationstr, optional

Parameterization formulation: “knots” (default) or “slopes”. - “knots”: Fit the parameter values at each breakpoint - “slopes”: Fit the initial value and slopes between breakpoints

Example

>>> # Create a SOC-dependent diffusivity with knots mode
>>> calc = PiecewiseInterpolation1D(
...     base_parameter_name="Particle diffusion time [s]",
...     breakpoint_values=[0.0, 0.5, 1.0],
...     breakpoint_parameter_name="SOC",
...     smoothing=1e-4,
...     formulation="knots"
... )
>>> # Provide parameter values for each breakpoint
>>> param_values = {
...     "Particle diffusion time at SOC 0 [s]": 500.0,
...     "Particle diffusion time at SOC 0.5 [s]": 1000.0,
...     "Particle diffusion time at SOC 1 [s]": 2000.0,
... }
>>> result = calc.run(param_values)
>>> # result["Particle diffusion time [s]"] is now a function that interpolates

>>> # Create a SOC-dependent diffusivity with slopes mode
>>> calc = PiecewiseInterpolation1D(
...     base_parameter_name="Particle diffusion time [s]",
...     breakpoint_values=[0.0, 0.5, 1.0],
...     breakpoint_parameter_name="SOC",
...     smoothing=1e-4,
...     formulation="slopes"
... )
>>> # Provide initial value and slopes for each segment
>>> param_values = {
...     "Particle diffusion time at SOC 0 [s]": 500.0,
...     "Particle diffusion time slope from SOC 0 to 0.5 [s]": 1000.0,
...     "Particle diffusion time slope from SOC 0.5 to 1 [s]": 2000.0,
... }
>>> result = calc.run(param_values)

Extends: ionworkspipeline.direct_entries.piecewise_interpolation.BaseInterpolation

property input_param_names

Returns the list of input parameters needed for this calculation.

In ‘knots’ formulation: Returns parameter names for all breakpoint values. In ‘slopes’ formulation: Returns parameter name for initial value and all slopes.

to_config() → dict

Convert to a config dict that can round-trip through the parser.

class ionworkspipeline.direct_entries.PiecewiseInterpolation2D(base_parameter_name: str, breakpoint1_values: list[float], breakpoint1_parameter_name: str, breakpoint2_values: list[float], breakpoint2_parameter_name: str, smoothing1: float = 0.0001, smoothing2: float = 0.0001, formulation: str = 'knots', **kwargs)

A direct entry that creates a 2D piecewise bilinear interpolation function for a parameter that varies with respect to two breakpoint parameters (e.g., SOC and Temperature).

This uses smooth heaviside functions to create a continuous, differentiable interpolation that can be used in PyBaMM models.

Parameters

base_parameter_namestr

The name of the parameter to create (e.g., “Particle diffusion time [s]”)

breakpoint1_valueslist[float]

List of first breakpoint values (e.g., [0.0, 0.5, 1.0] for SOC)

breakpoint1_parameter_namestr

Name of the first breakpoint parameter (e.g., “SOC”)

breakpoint2_valueslist[float]

List of second breakpoint values (e.g., [273.15, 298.15, 323.15] for Temperature)

breakpoint2_parameter_namestr

Name of the second breakpoint parameter (e.g., “Temperature [K]”)

smoothing1float, optional

Smoothing parameter for first dimension heaviside transitions (default: 1e-4). Larger values create smoother transitions.

smoothing2float, optional

Smoothing parameter for second dimension heaviside transitions (default: 1e-4). Larger values create smoother transitions. Use different smoothing values when the two dimensions have very different scales.

formulationstr, optional

Parameterization formulation: “knots” (default) or “slopes”. - “knots”: Fit the parameter values at each 2D grid point - “slopes”: Fit the initial value and slopes along each dimension

Example

>>> # Create a SOC and Temperature-dependent diffusivity with knots mode
>>> entry = PiecewiseInterpolation2D(
...     base_parameter_name="Diffusivity [m2.s-1]",
...     breakpoint1_values=[0.0, 0.5, 1.0],
...     breakpoint1_parameter_name="SOC",
...     breakpoint2_values=[273.15, 298.15],
...     breakpoint2_parameter_name="Temperature [K]",
...     smoothing1=1e-4,
...     smoothing2=0.1,  # Temperature has larger scale, so use larger smoothing
...     formulation="knots"
... )
>>> # Provide parameter values for each 2D breakpoint
>>> params = {
...     "Diffusivity at SOC 0, Temperature [K] 273.15 [m2.s-1]": 1e-14,
...     "Diffusivity at SOC 0, Temperature [K] 298.15 [m2.s-1]": 2e-14,
...     "Diffusivity at SOC 0.5, Temperature [K] 273.15 [m2.s-1]": 3e-14,
...     "Diffusivity at SOC 0.5, Temperature [K] 298.15 [m2.s-1]": 4e-14,
...     "Diffusivity at SOC 1, Temperature [K] 273.15 [m2.s-1]": 2e-14,
...     "Diffusivity at SOC 1, Temperature [K] 298.15 [m2.s-1]": 3e-14,
... }
>>> result = entry.run(params)
>>> # result["Diffusivity [m2.s-1]"] is now a function that takes two arguments

Extends: ionworkspipeline.direct_entries.piecewise_interpolation.BaseInterpolation

property input_param_names

Returns the list of input parameters needed for this calculation.

In ‘knots’ formulation: Returns parameter names for all 2D grid points. In ‘slopes’ formulation: Returns parameter name for initial value and all slopes.

to_config() → dict

Convert to a config dict that can round-trip through the parser.