arXiv:2601.04120v2 Announce Type: replace-cross Abstract: Optimal control of obstacle problems arises in a wide range of applications and is computationally challenging due to its nonsmoothness, nonlinearity, and bilevel structure. Classical numerical approaches rely on mesh-based discretization and typically require solving a sequence of costly subproblems. In this work, we propose a single-loop bilevel deep learning method, which is mesh-free, scalable to high-dimensional and complex domains, and avoids repeated solution of discretized subproblems. The method employs constraint-embedding neu
The increasing complexity of optimal control problems in various applications, combined with advancements in deep learning, necessitates more efficient and scalable computational methods.
This development offers a potential breakthrough for tackling computationally intensive optimal control problems, enabling new applications in complex systems by providing a mesh-free and scalable solution.
Traditional mesh-based, sequential subproblem-solving approaches for optimal control could be superseded by more efficient and scalable single-loop deep learning methods, significantly reducing computational overhead.
- · AI researchers
- · Robotics
- · Autonomous systems development
- · Industrial control systems
- · Traditional numerical optimization software vendors
- · Computational engineers reliant solely on classical methods
More complex and high-dimensional optimal control problems become computationally feasible.
Accelerated development and deployment of autonomous systems in challenging environments due to improved control algorithms.
Enhanced efficiency and autonomy across sectors like aerospace, manufacturing, and logistics, driven by robust and scalable control solutions.
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