Hyperfastrl: Hypernetwork-based reinforcement learning for unified control of parametric chaotic PDEs

2026-04-07

AI Summary

This work addresses the challenge of controlling parametric chaotic partial differential equations (PDEs), which exhibit extreme sensitivity to parameters, rendering traditional adjoint-based optimization impractical due to the need for separate controllers per operating condition. To overcome this, the authors propose hyperFastRL, a novel framework that integrates hypernetworks with reinforcement learning to directly map physical parameters to control policy weights, thereby constructing a unified parametric control manifold that enables parameter adaptation decoupled from spatial feedback. The approach incorporates distributional reinforcement learning and pessimistic value estimation to handle the high variance of chaotic rewards and leverages large-scale parallel simulation for improved training efficiency. Evaluated on the Kuramoto–Sivashinsky equation, KAN-based hypernetworks demonstrate superior generalization to unseen parameters, achieve a 37% reduction in wall-clock training time, and maintain both robustness and computational efficiency.

Abstract

Spatiotemporal chaos in fluid systems exhibits severe parametric sensitivity, rendering classical adjoint-based optimal control intractable because each operating regime requires recomputing the control law. We address this bottleneck with hyperFastRL, a parameter-conditioned reinforcement learning framework that leverages Hypernetworks to shift from tuning isolated controllers per-regime to learning a unified parametric control manifold. By mapping a physical forcing parameter μ directly to the weights of a spatial feedback policy, the architecture cleanly decouples parametric adaptation from spatial boundary stabilization. To overcome the extreme variance inherent to chaotic reward landscapes, we deploy a pessimistic distributional value estimation over a massively parallel environment ensemble. We evaluate three Hypernetwork functional forms, ranging from residual MLPs to periodic Fourier and Kolmogorov-Arnold (KAN) representations, on the Kuramoto-Sivashinsky equation under varying spatial forcing. All forms achieve robust stabilization. KAN yields the most consistent energy-cascade suppression and tracking across unseen parametrizations, while Fourier networks exhibit worse extrapolation variability. Furthermore, leveraging high-throughput parallelization allows us to intentionally trade a fraction of peak asymptotic reward for a 37% reduction in training wall-clock time, identifying an optimal operating regime for practical deployment in complex, parameter-varying chaotic PDEs.

Problem

• spatiotemporal chaos
• parametric sensitivity
• optimal control
• chaotic PDEs
• parameter-varying systems

Innovation

• Hypernetworks
• Reinforcement Learning
• Chaotic PDE Control
• Distributional Value Estimation
• Kolmogorov-Arnold Networks