Class PDEDerivatives<T>

Namespace

AiDotNet.PhysicsInformed.Interfaces

Assembly

AiDotNet.dll

Holds the derivatives needed for PDE computation.

public class PDEDerivatives<T>

Type Parameters

T

The numeric type.

Inheritance

object

PDEDerivatives<T>

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Remarks

For Beginners: Derivatives tell us how fast a function is changing. For PDEs, we need:

• First derivatives (gradient): How fast the solution changes in each direction
• Second derivatives (Hessian): How fast the rate of change itself is changing These are computed automatically using automatic differentiation.

Properties

FirstDerivatives

First-order derivatives (gradient) of the output with respect to each input dimension. Shape: [output_dim, input_dim]

public T[,]? FirstDerivatives { get; set; }

Property Value

T[,]

HigherDerivatives

Higher-order derivatives (4th order and above) if needed for the specific PDE.

public T[,,,]? HigherDerivatives { get; set; }

Property Value

T[,,,]

SecondDerivatives

Second-order derivatives (Hessian) of the output with respect to input dimensions. Shape: [output_dim, input_dim, input_dim]

public T[,,]? SecondDerivatives { get; set; }

Property Value

T[,,]

ThirdDerivatives

Third-order derivatives of the output with respect to input dimensions. Shape: [output_dim, input_dim, input_dim, input_dim] Used for higher-order PDEs like Korteweg-de Vries equation.

public T[,,,]? ThirdDerivatives { get; set; }

Property Value

T[,,,]