PI-SONet: A Physics-Informed Symplectic Operator Network for Real-Time Optimal Control of Multi-Agent Systems

TL;DR

PI-SONet is a physics-informed neural operator framework that efficiently solves high-dimensional, parameterized optimal control problems in real-time while preserving Hamiltonian structure.

Contribution

Introduces PI-SONet, a structure-preserving neural operator that generalizes across problem instances and achieves significant speedups in solving complex optimal control problems.

Findings

PI-SONet achieves sub-second inference times for new problem instances.

It provides up to 10,000x speedup over baseline methods.

It accurately approximates the PMP solution map while preserving Hamiltonian structure.

Abstract

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.