Neural networks (geobrain.nn)

Not a separate mode, and not a solver. A network here is an operator you compose in front of the physics with @, which changes what the unknowns are without touching the forward model.

Piece	What is there
Reparameterization	WeightReparameterization, LatentReparameterization
Decoders	ConvDecoder2d, ConvDecoder3d, CoordinateMLP
Variational layers	LinearFlipout, Conv2dFlipout, Conv3dFlipout, BaseVariationalLayer
KL machinery	get_kl_loss, kl_regularizer, gaussian_kl, count_variational_parameters
Utilities	Reshape, ClippedLinearActivation

Three answers to “what are the unknowns?”

# sketch: runnable version in examples/00_showcase/06
explicit = seismic                                     # the image itself
network  = seismic @ WeightReparameterization(decoder, ...)
latent   = seismic @ LatentReparameterization(decoder, ...)

	The unknown is	The prior is
Explicit	the property image, one number per cell	none, so wherever the data are weak, the answer is whatever the optimiser drifted into
Network	a decoder’s weights, fed a frozen random code	whatever that architecture can draw. This is the deep image prior
Latent	the code, decoder frozen	the strongest of the three: the image cannot leave the decoder’s range

All three then go through the same InverseProblem and the same create_inverter().run(). Not one line of the forward model changes between them, and the chain reports the switch honestly: ask the network version for its trainable inputs and it answers with the decoder’s weight names.

What the comparison actually shows

The unknown count does not order the results

In the worked example the deep image prior wins with the most unknowns, and the latent run beats the explicit one with a fifth of them. The prior is not a term in the objective; it is the set of images the decoder can draw at all.

And the result is a property of that earth, not a law. A convolutional prior is built for fields that are smooth on the scale the data resolve; where bedding is finer than the wavelength, the same prior costs resolution instead of buying it. The claim worth making is narrower and more useful: trying all three cost three lines and one @ apiece, on the same physics, through the same door.

The same inversion run with the unknown as an image, as a decoder’s weights, and as its latent code. From examples/00_showcase/06_neural_network_integration.py.

See also

• examples/00_showcase/06_neural_network_integration.py: all three parameterizations on one seismic problem, scored against the truth.