Equation Interface

class EquationInterface

Bases: object

Abstract base class for equations.

Equations in PINA simplify the training process. When defining a problem, each equation passed to a Condition object must be either an Equation or a SystemEquation instance.

An Equation is a wrapper for a callable function, while SystemEquation wraps a list of callable functions. To streamline code writing, PINA provides a diverse set of pre-implemented equations, such as FixedValue, FixedGradient, and many others.

abstract residual(input_, output_, params_)

Abstract method to compute the residual of an equation.

Parameters:

• input (LabelTensor) – Input points where the equation is evaluated.

• output (LabelTensor) – Output tensor, eventually produced by a torch.nn.Module instance.

• params (dict) – Dictionary of unknown parameters, associated with a InverseProblem instance.

Returns:

The computed residual of the equation.

Return type:

LabelTensor