Numerical solutions of fixed points in two-dimensional Kuramoto-Sivashinsky equation expedited by reinforcement learning
On the map: Deep reinforcement learning methods → RL theory and sample complexity
Abstract (arXiv)
This paper presents a combined approach to enhancing the effectiveness of Jacobian-Free Newton-Krylov (JFNK) method by deep reinforcement learning (DRL) in identifying fixed points within the 2D Kuramoto-Sivashinsky Equation (KSE). JFNK approach entails a good initial guess for improved convergence when searching for fixed points. With a properly defined reward function, we utilise DRL as a preliminary step to enhance the initial guess in the converging process. We report new results of fixed points in the 2D KSE which have not been reported in the literature. Additionally, we explored control optimization for the 2D KSE to navigate the system trajectories between known fixed points, based on parallel reinforcement learning techniques. This combined method underscores the improved JFNK approach to finding new fixed-point solutions within the context of 2D KSE, which may be instructive for other high-dimensional dynamical systems.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods. First posted on arXiv 27 Dec 2024.
Builds on
0 of 0 references.
No references here yet.
Built on by
Not cited yet.
Similar, not cited
Close in wording, no citation either way
- 2025NFQ2.0: The CartPole Benchmark Revisited
- 2024Koopman-Assisted Reinforcement Learning
- 2024MultiSTOP: Solving Functional Equations with Reinforcement Learning
- 2025Solving nonconvex Hamilton--Jacobi--Isaacs equations with PINN-based policy iteration
- 2025Continuous-Time Value Iteration for Multi-Agent Reinforcement Learning
- 2024Data-driven optimal control of unknown nonlinear dynamical systems using the Koopman operator
- 2024Parametric PDE Control with Deep Reinforcement Learning and Differentiable L0-Sparse Polynomial Policies
- 2026Learning to Solve Stochastic Controls with Unknown Drifts and Running Rewards: Theory, Algorithms and Convergence