PI-SONet: A Physics-Informed Symplectic Operator Network for Real-Time Optimal Control of Multi-Agent Systems
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917494318432256 |
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| author | Varghese, Alan John Liu, Shanqing Chen, Paula Zhu, Yaochen Darbon, Jérôme Karniadakis, George Em |
| author_facet | Varghese, Alan John Liu, Shanqing Chen, Paula Zhu, Yaochen Darbon, Jérôme Karniadakis, George Em |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14332 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | PI-SONet: A Physics-Informed Symplectic Operator Network for Real-Time Optimal Control of Multi-Agent Systems Varghese, Alan John Liu, Shanqing Chen, Paula Zhu, Yaochen Darbon, Jérôme Karniadakis, George Em Optimization and Control 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. |
| title | PI-SONet: A Physics-Informed Symplectic Operator Network for Real-Time Optimal Control of Multi-Agent Systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.14332 |