Goal-Agnostic Control for PDEs Using Joint-Embedding Predictive Architecture.

Researchers have developed a novel goal-agnostic control framework for Partial Differential Equations (PDEs), leveraging a Joint-Embedding Predictive Architecture (JEPA). This system employs a small 2D Vision Transformer (ViT) encoder and action-conditioned latent dynamics, which are trained offline without any specific reward or downstream goal. Once trained, these components are frozen and subsequently utilized by a Model-Predictive Path Integral (MPPI) controller. A key finding is that control objectives are more effectively applied to explicit physical observables, provided they are injective, rather than simply minimizing raw Euclidean distance in the learned latent space. For instance, when a learned linear kinetic-energy (KE) probe is applied to frozen latent rollouts, it accurately reproduces held-out trajectories with high fidelity. This approach requires no modifications to the underlying world model. On the PDE Control Gym 2D Navier-Stokes benchmark, using KE-probe planning significantly improved the native reward and lowered the velocity-field RMSE compared to latent-L2 planning. The same frozen model also successfully supported controls for stabilizing around a steady configuration by directly regulating kinetic energy. While the latent probe showed some brittleness to measurement noise and missing pixels, the results strongly suggest that latent dynamics can remain both dynamic and goal-agnostic, with calibrated observables offering a superior objective for state control.