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About this paper
Jonathan Gallagher, Roberto Guglielmi
An approach for controlling Partial Differential Equations introduces a goal-agnostic framework utilizing Joint-Embedding Predictive Architectures, demonstrating closed-loop control in a latent space. By integrating a physical observable, like kinetic energy, into the control objective, the method enhances tracking accuracy, achieving a 53% reduction in velocity-field RMSE for aperiodic targets in the 2D Navier-Stokes environment.
Key insights
- Joint-Embedding Predictive Architectures can learn robust, action-sensitive PDE dynamics in a latent space without explicit reward functions, enabling goal-agnostic control.
- Defining control objectives using a physical observable, estimated by a latent probe, significantly improves actual physical tracking performance over direct latent-space distance minimization.
- Planning in a reconstruction-free, low-dimensional latent space offers computational efficiency critical for online control of high-dimensional PDE systems.
Summary by alphaXiv.
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