Parameterization

sweepx.opt's parameterizations let you optimize over a latent variable while the FWI solver still sees the physical model.

class Parameterization:
    def forward(self, latent: torch.Tensor) -> torch.Tensor:
        """latent -> physical model the solver consumes."""

    def inverse(self, physical: torch.Tensor) -> torch.Tensor:
        """Initial physical model -> latent state to optimize."""

This decouples the optimization variable from the physical bounds, which is useful for:

• enforcing velocity bounds via a sigmoid map
• working in log(velocity) space for stability
• inverting for a perturbation dv rather than absolute v
• replacing the entire model by the output of a neural network (DIP-FWI)

Available parameterizations

Name	Class	Notes
Identity	IdentityParameterization	Pass-through; the default.
Sigmoid bounds	SigmoidBounds	Smooth box constraint via logistic.
Log-velocity	LogVelocity	Latent in log(physical) space.
Perturbation from background	PerturbationFromBackground	Latent is the perturbation dv around a fixed background.
DIP-FWI	DIPParameterization (+ SmallUNet2D)	Generator network as implicit regularizer.