FluidJEPA: Joint-Embedding Predictive World Models for Controlled Fluid Dynamics

Modeling controlled fluid dynamics requires predicting how a flow evolves under a prescribed action sequence. Unlike forecasting under fixed forcing, the same initial state can lead to different futures as the control changes. Accurate next-field prediction, however, does not ensure that a model's internal state can support repeated action-conditioned prediction. We introduce \method, a joint-embedding world model that learns physical-field prediction and latent dynamics together. Action-conditioned latent predictions are matched to encoded future observations. A jointly trained decoder retains physical-field supervision, and a distributional regularizer discourages representation collapse. We construct a benchmark of four two-dimensional flow environments spanning internal forcing and boundary actuation, with 8,000 trajectories organized into shared-initial-state control branches. Evaluation separates field-space feedback from latent rollout and tests control-induced changes and generalization to an action family withheld from training and validation. \method achieves competitive field accuracy. In same-architecture ablations across the four environments, latent alignment reduces 20-step mean physical-field error under latent rollout by 73.6–96.6% relative to training without this alignment. Action-family holdout produces modest degradation in periodic Navier–Stokes latent prediction relative to training on all families. The larger degradation in Pinball highlights a remaining challenge when unseen actions also change actuator coordination.