Interface IInverseProblemGradient<T>

Namespace

AiDotNet.PhysicsInformed.Interfaces

Assembly

AiDotNet.dll

Provides gradient information for inverse problem parameters.

public interface IInverseProblemGradient<T> : IInverseProblem<T>

Type Parameters

T

The numeric type.

Inherited Members

IInverseProblem<T>.ParameterNames

IInverseProblem<T>.NumberOfParameters

IInverseProblem<T>.InitialParameterGuesses

IInverseProblem<T>.ParameterLowerBounds

IInverseProblem<T>.ParameterUpperBounds

IInverseProblem<T>.Observations

IInverseProblem<T>.HasMeasurementNoiseLevel

IInverseProblem<T>.MeasurementNoiseLevel

IInverseProblem<T>.ValidateParameters(T[])

IInverseProblem<T>.CreateParameterizedPDE(T[])

Methods

ComputeParameterGradients(T[], T[], T[], PDEDerivatives<T>)

Computes gradients of the PDE residual with respect to the unknown parameters.

T[] ComputeParameterGradients(T[] parameters, T[] inputs, T[] outputs, PDEDerivatives<T> derivatives)

Parameters

parameters T[]

Current parameter values.

inputs T[]

The spatial and temporal coordinates.

outputs T[]

The predicted solution values.

derivatives PDEDerivatives<T>

The derivatives of the solution.

Returns

T[]

Gradient of residual with respect to each parameter.

Remarks

For Beginners: This tells us how changing each parameter affects the PDE residual.

• If dR/d(parameter) is large: parameter has strong effect on physics
• If dR/d(parameter) is small: parameter has weak effect (hard to identify)

The gradients are used to update parameters during training.