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Reinforcement Learning with PDEs
- PDEs, unlike ODEs, require more complex modelling and simulation methods due to higher dimensions.
- PDEs are typically solved across grids, where the PDE is simplified to an algebraic equation at each grid point.
- Grid generation plays a crucial role in solving PDEs, and computation time can be extensive.
- Controlling PDEs is more challenging than ODEs due to higher dimensionality and lack of comprehensive control theory.
- Reinforcement learning has emerged as a significant area of research for understanding and controlling PDE systems.
- Various control strategies have been developed for PDEs, including analytical adjoint-based methods and machine learning approaches.
- Reinforcement learning was applied to diffusion and Kuramoto-Sivashinsky (K-S) equations for control problems.
- Diffusion equation, a simple linear PDE, displayed stable dynamics and was controlled using reinforcement learning.
- K-S equation, a complex nonlinear PDE describing flame behavior, showed sensitivity to domain size and grid points.
- Machine learning and PDEs research offer potential for improved control efficiency and understanding of complex physical systems.
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