{"paper":{"title":"PI-SONet: A Physics-Informed Symplectic Operator Network for Real-Time Optimal Control of Multi-Agent Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A single trained conditional symplectic operator approximates the PMP solution map for families of high-dimensional optimal control problems and delivers sub-second inferences on new instances.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alan John Varghese, George Em Karniadakis, J\\'er\\^ome Darbon, Paula Chen, Shanqing Liu, Yaochen Zhu","submitted_at":"2026-05-14T03:55:39Z","abstract_excerpt":"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 condit"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"PI-SONet achieves sub-second inferences on new problem instances, equating to up to 10,000x speedup over representative baselines.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That a single trained conditional symplectic operator can reliably approximate the PMP solution map for unseen problem configurations while inherently preserving Hamiltonian structure.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"PI-SONet trains a single structure-preserving operator network to deliver sub-second approximations to Pontryagin Maximum Principle solutions for parameterized multi-agent optimal control problems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A single trained conditional symplectic operator approximates the PMP solution map for families of high-dimensional optimal control problems and delivers sub-second inferences on new instances.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2453bd15d075e9044c9322ff5d2c047c6b614f8783fed4dfe086f346a31cf787"},"source":{"id":"2605.14332","kind":"arxiv","version":1},"verdict":{"id":"c429e02e-3e1e-464b-8bf6-bd960144f3b3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:31:50.769330Z","strongest_claim":"PI-SONet achieves sub-second inferences on new problem instances, equating to up to 10,000x speedup over representative baselines.","one_line_summary":"PI-SONet trains a single structure-preserving operator network to deliver sub-second approximations to Pontryagin Maximum Principle solutions for parameterized multi-agent optimal control problems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That a single trained conditional symplectic operator can reliably approximate the PMP solution map for unseen problem configurations while inherently preserving Hamiltonian structure.","pith_extraction_headline":"A single trained conditional symplectic operator approximates the PMP solution map for families of high-dimensional optimal control problems and delivers sub-second inferences on new instances."},"references":{"count":60,"sample":[{"doi":"","year":2005,"title":"Math´ ematiques Concr` etes","work_id":"030d0131-0895-40c1-8b3e-cab3568a61c8","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1002/9781118122631","year":2012,"title":"John Wiley & Sons, Hoboken, NJ (2012)","work_id":"fd562ea0-f3ae-4bbb-9eeb-0684aa41fd5e","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"Foderaro, G., Ferrari, S., Wettergren, T.A.: Distributed optimal control for multi-agent trajectory optimization. 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