Toward Goal-Agnostic Joint-Embedding Predictive Control of Partial Differential Equations
A goal-agnostic control framework for PDEs using a joint-embedding predictive architecture (JEPA) is presented. A small 2D ViT encoder and action-conditioned latent dynamics are trained offline without reward or goal, frozen, and reused by an MPPI controller. Applying the control objective to a physical observable (kinetic energy) outperforms minimizing Euclidean distance in latent space. On the 2D Navier-Stokes benchmark, KE-probe planning improves reward from -12.08 to -10.90 and reduces late-field RMSE by 53% on withheld targets. The frozen model also supports stabilization with 2.7% mean relative error.
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[Submitted on 21 Jul 2026]
Title:Toward Goal-Agnostic Joint-Embedding Predictive Control of Partial Differential Equations
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Abstract:We present a goal-agnostic control framework for partial differential equations (PDEs) built around a joint-embedding predictive architecture (JEPA). The small 2D ViT encoder and action-conditioned latent dynamics are trained offline without a reward or downstream goal, frozen, and reused by a model-predictive path integral (MPPI) controller. We find that when available, the control objective is better applied to an explicit physical observable (provided injectivity) than to minimizing raw Euclidean distance ($L^2$) in the learned latent space. For a learned linear kinetic-energy (KE) probe on frozen latent rollouts we can reproduce held-out trajectories with $R^2=0.989$, while requiring no change to the underlying world model. On the PDE Control Gym 2D Navier--Stokes benchmark, using KE-probe planning improves the matched 50-episode native reward from $-12.08\pm0.86$ for latent-$L^2$ planning to $-10.90\pm0.91$ (95\% CI), while lowering last-quarter velocity-field RMSE from $0.0765$ to $0.0692$. Across three intentionally withheld, dissimilar, aperiodic targets, KE planning lowers late field RMSE by $53\%$ relative to latent-$L^2$ planning ($0.0220$ versus $0.0469$), winning all 30 paired episodes. The same frozen model also supports controls targeting stabilization around a steady configuration via direct regulation of KE achieving $2.7\%$ mean relative error. While the latent probe is brittle to measurement noise and missing pixels, we believe the results support the claim that latent dynamics can remain both dynamic and goal-agnostic while calibrated observables (granted they guarantee unique continuation) may be a better objective for state control
Comments: Associated code will be open sourced alongside the V2 submission
Subjects:
Machine Learning (cs.LG); Systems and Control (eess.SY)
Cite as: arXiv:2607.21644 [cs.LG]
(or arXiv:2607.21644v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.21644
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Jonathan Gallagher [view email] [v1] Tue, 21 Jul 2026 20:49:07 UTC (2,679 KB)
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