Interface IPDESpecification<T>

Namespace

AiDotNet.PhysicsInformed.Interfaces

Assembly

AiDotNet.dll

Defines the interface for specifying Partial Differential Equations (PDEs) that can be used with Physics-Informed Neural Networks.

public interface IPDESpecification<T>

Type Parameters

T

The numeric type (float, double, etc.) used for calculations.

Remarks

For Beginners: A Partial Differential Equation (PDE) is an equation that involves rates of change with respect to multiple variables. For example, the heat equation describes how temperature changes over both space and time. This interface allows you to define any PDE in a way that neural networks can learn to solve it.

Properties

InputDimension

Gets the dimension of the input space (e.g., 2 for 2D spatial problems, 3 for 2D space + time).

int InputDimension { get; }

Property Value

int

Name

Gets the name or description of the PDE (e.g., "Heat Equation", "Navier-Stokes").

string Name { get; }

Property Value

string

OutputDimension

Gets the dimension of the output space (e.g., 1 for scalar fields like temperature, 3 for vector fields like velocity).

int OutputDimension { get; }

Property Value

int

Methods

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

Computes the PDE residual at the given point. The residual is how much the PDE equation is violated at that point. For a true solution, the residual should be zero everywhere.

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

Parameters

inputs T[]

The spatial and temporal coordinates where to evaluate the PDE.

outputs T[]

The predicted solution values at those coordinates.

derivatives PDEDerivatives<T>

The derivatives of the solution (gradient, Hessian, etc.).

Returns

T

The PDE residual value (should be zero for a perfect solution).