Toward Goal-Agnostic Joint-Embedding Predictive Control of Partial Differential Equations
The paper presents a goal-agnostic control framework for partial differential equations (PDEs) using a joint-embedding predictive architecture (JEPA). The framework trains a small 2D ViT encoder and action-conditioned latent dynamics offline without a reward or downstream goal, then freezes and reuses them with a model-predictive path integral (MPPI) controller. The control objective is better applied to an explicit physical observable (e.g., kinetic energy) rather than minimizing raw Euclidean
Analysis
TL;DR
- The paper presents a goal-agnostic control framework for partial differential equations (PDEs) using a joint-embedding predictive architecture (JEPA).
- The framework trains a small 2D ViT encoder and action-conditioned latent dynamics offline without a reward or downstream goal, then freezes and reuses them with a model-predictive path integral (MPPI) controller.
- The control objective is better applied to an explicit physical observable (e.g., kinetic energy) rather than minimizing raw Euclidean distance in the latent space, achieving superior performance on benchmarks.
- The method improves native reward and reduces velocity-field RMSE on the PDE Control Gym 2D Navier--Stokes benchmark, and stabilizes systems around steady configurations with low error.
Why It Matters
This work is relevant to AI practitioners and researchers in control systems and PDE modeling, as it demonstrates a flexible, goal-agnostic approach to controlling complex dynamical systems without requiring task-specific training. By leveraging physical observables for control planning, it offers a more robust and interpretable alternative to latent-space distance minimization, with potential applications in fluid dynamics, climate modeling, and other PDE-driven domains.
Technical Details
- The framework uses a joint-embedding predictive architecture (JEPA) with a small 2D Vision Transformer (ViT) encoder and action-conditioned latent dynamics, trained offline without rewards or goals.
- A model-predictive path integral (MPPI) controller is applied to the frozen latent dynamics for control planning.
- Instead of minimizing $L^2$ distance in latent space, the control objective is applied to a learned linear kinetic-energy (KE) probe on latent rollouts, achieving $R^2=0.989$ for trajectory reproduction.
- On the PDE Control Gym 2D Navier--Stokes benchmark, KE-probe planning improves native reward from $-12.08\pm0.86$ to $-10.90\pm0.91$ (95% CI) and reduces last-quarter velocity-field RMSE from $0.0765$ to $0.0692$.
- For three withheld aperiodic targets, KE planning lowers late field RMSE by 53% compared to latent-$L^2$ planning ($0.0220$ vs. $0.0469$) and wins all 30 paired episodes.
- The same model stabilizes systems around steady configurations via direct KE regulation, achieving 2.7% mean relative error.
Industry Insight
- The results suggest that using calibrated physical observables (e.g., kinetic energy) as control objectives can outperform latent-space distance minimization in goal-agnostic PDE control, offering a more reliable and interpretable approach for real-world applications.
- The ability to reuse a single frozen world model for diverse control tasks (e.g., trajectory tracking, stabilization) without retraining highlights the potential for efficient, modular control systems in complex dynamical environments.
- While the latent probe is sensitive to noise and missing data, the framework’s performance on physical observables underscores the importance of incorporating domain-specific knowledge into AI-driven control systems for improved robustness and generalization.
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