Domain Equation Condition

class DomainEquationCondition(domain, equation)

Bases: ConditionInterface

The class DomainEquationCondition defines a condition based on a domain and an equation. This condition is typically used in physics-informed problems, where the model is trained to satisfy a given equation over a specified domain. The domain is used to sample points where the equation residual is evaluated and minimized during training.

Example:

>>> from pina.domain import CartesianDomain
>>> from pina.equation import Equation
>>> from pina import Condition

>>> # Equation to be satisfied over the domain: # x^2 + y^2 - 1 = 0
>>> def dummy_equation(pts):
...     return pts["x"]**2 + pts["y"]**2 - 1

>>> domain = CartesianDomain({"x": [0, 1], "y": [0, 1]})
>>> condition = Condition(domain=domain, equation=Equation(dummy_equation))

Initialization of the DomainEquationCondition class.

Parameters:

• domain (DomainInterface) – The domain over which the equation is defined.

• equation (EquationInterface) – The equation to be satisfied over the specified domain.