Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.14332 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Many real-life applications involve controlling high-dimensional multi-agent systems in real-time. Existing optimal control solvers often suffer from the curse-of-dimensionality and require complete rerunning for each new problem setting. We target nonconvex, nonlinear problems in 100s of dimensions by introducing PI-SONet (Physics-Informed Symplectic Operator Network), a structure-preserving operator learning framework for solving parameterized families of optimal control problems and their Pontraygin Maximum Principle (PMP) systems. PI-SONet combines a latent right-space solver with a conditional symplectic operator to produce tractable Hamiltonian trajectories in a computationally efficient auxiliary space and transform them back to physical space. This decomposition yields a \textit{single} trained operator that approximates the PMP solution map, inherently preserves Hamiltonian structure, and generalizes across unseen problem configurations. Unlike existing methods, which are fundamentally single-instance solvers, PI-SONet achieves sub-second inferences on new problem instances, equating to up to 10,000x speedup over representative baselines. These results suggest that structure-preserving neural operators provide a practical route toward reusable, real-time surrogates for high-dimensional optimal control.