Interface IMultiScalePDEGradient<T>

Namespace

AiDotNet.PhysicsInformed.Interfaces

Assembly

AiDotNet.dll

Provides gradient information for multi-scale PDE residuals.

public interface IMultiScalePDEGradient<T> : IMultiScalePDE<T>, IPDESpecification<T>

Type Parameters

T

The numeric type.

Inherited Members

IMultiScalePDE<T>.NumberOfScales

IMultiScalePDE<T>.ScaleCharacteristicLengths

IMultiScalePDE<T>.ComputeScaleResidual(int, T[], T[], PDEDerivatives<T>)

IMultiScalePDE<T>.ComputeScaleCoupling(int, int, T[], T[], T[], PDEDerivatives<T>, PDEDerivatives<T>)

IMultiScalePDE<T>.GetScaleLossWeight(int)

IMultiScalePDE<T>.GetScaleOutputDimension(int)

IPDESpecification<T>.ComputeResidual(T[], T[], PDEDerivatives<T>)

IPDESpecification<T>.InputDimension

IPDESpecification<T>.OutputDimension

IPDESpecification<T>.Name

Methods

ComputeScaleCouplingGradient(int, int, T[], T[], T[], PDEDerivatives<T>, PDEDerivatives<T>)

Computes gradients of the coupling term.

(PDEResidualGradient<T> coarseGradient, PDEResidualGradient<T> fineGradient) ComputeScaleCouplingGradient(int coarseIndex, int fineIndex, T[] inputs, T[] coarseOutputs, T[] fineOutputs, PDEDerivatives<T> coarseDerivatives, PDEDerivatives<T> fineDerivatives)

Parameters

coarseIndex int

The coarser scale index.

fineIndex int

The finer scale index.

inputs T[]

The coordinates.

coarseOutputs T[]

Solution at coarse scale.

fineOutputs T[]

Solution at fine scale.

coarseDerivatives PDEDerivatives<T>

Derivatives at coarse scale.

fineDerivatives PDEDerivatives<T>

Derivatives at fine scale.

Returns

(PDEResidualGradient<T> coarseGradient, PDEResidualGradient<T> fineGradient)

Tuple of gradients for (coarse scale, fine scale).

ComputeScaleResidualGradient(int, T[], T[], PDEDerivatives<T>)

Computes gradients of the scale residual with respect to outputs and derivatives.

PDEResidualGradient<T> ComputeScaleResidualGradient(int scaleIndex, T[] inputs, T[] outputs, PDEDerivatives<T> derivatives)

Parameters

scaleIndex int

The scale index.

inputs T[]

The coordinates.

outputs T[]

The solution at this scale.

derivatives PDEDerivatives<T>

The derivatives at this scale.

Returns

PDEResidualGradient<T>

Gradients for backpropagation.