Fluid world models can read physics but not steer it: pre-registered tests split decodable, prominent and steerable

On two-dimensional decaying flow, a joint-embedding predictive architecture (JEPA, which predicts in a learned latent space rather than in pixels) trained to predict the flow does not organize its latent around fluid quantities by the pre-registered criteria. The usual reading was that a linear probe decoding a quantity from the latent, or a principal or slow latent direction correlating with it, shows the model learned that physical quantity; such readings lacked controls. The JEPA exceeds an untrained network of the same architecture on log enstrophy, log palinstrophy and log(1 + vortex count), but the mandatory Okubo–Weiss fraction is 0.507 against a required 0.656, so only three of five targets count and the mandatory one is not among them, giving a verdict of not supported.

What a latent contains and what can be pushed through it come apart: a supervised direction that reads spectral shape almost perfectly barely changes the rendered field when the latent is moved along it. Decodability had often stood in for evidence that the model uses a quantity, while the output change under an intervention on the latent was not measured separately. Among 84 candidate directions from 21 existing models, none moved the decoded field by even 0.1 log-units per unit of latent movement, the largest effect being 0.086; the supervised shape direction read spectral shape at 0.97–0.99.

Plain autoencoders that render the field make enstrophy prominent in their slowest unsupervised directions, and adding VICReg (variance–invariance–covariance regularization) lowers that prominence in every comparison while raising linear decodability. Predicting dynamics had been treated as the prerequisite for such structure, and the roles of the render target and the regularizer had not been tested separately. On a sealed set of 1,005 trajectories, the velocity autoencoder reaches E1 0.860 and the vorticity autoencoder 0.799, both above the untrained control plus 0.25; but for the vorticity autoencoder the plain-minus-VICReg drop misses the pre-registered 0.20, so the hypothesis is partially supported.

Routing loudness to the decoder only through a small conditioning code and degrading the content pathway's copy of spectral shape yields label-free dials for both loudness and spectral shape on sealed data. Earlier steerable directions were either not found or produced grid artefacts under strong steering and failed the realism criteria. In the final design, the loudness dial is valid in all 5 fresh seeds and the shape dial in 3 of 5, below the pre-registered bar of 4; neither control model shows a shape dial, and the untrained network shows neither kind.

All results concern periodic two-dimensional decaying Navier–Stokes flow, one simulator and initial-condition distribution, and one small convolutional encoder; neither the positive nor the negative results are claimed to transfer to three-dimensional flow, other simulators or larger models. The whole program used about 70 logged hours of compute on one consumer GPU, and the pre-registrations, deviations, code and outputs are public.

Study 2 carries a confound the design cannot remove: VICReg also made the autoencoders' rendering about 25 times worse, so how much of the drop in prominence comes from latent geometry rather than worse rendering cannot be separated. In Study 3 the shape-dial identification rule was chosen during exploration after seeing results, so only the fresh-seed confirmation tests it; the dose curve has one intermediate point and spans two decoders.