[2506.18812] Learning Physical Systems: Symplectification via Gauge Fixing in Dirac Structures

Computer Science > Robotics arXiv:2506.18812 (cs) [Submitted on 23 Jun 2025 (v1), last revised 5 Mar 2026 (this version, v2)] Title:Learning Physical Systems: Symplectification via Gauge Fixing in Dirac Structures Authors:Aristotelis Papatheodorou, Pranav Vaidhyanathan, Natalia Ares, Ioannis Havoutis View a PDF of the paper titled Learning Physical Systems: Symplectification via Gauge Fixing in Dirac Structures, by Aristotelis Papatheodorou and 2 other authors View PDF HTML (experimental) Abstract:Physics-informed deep learning has achieved remarkable progress by embedding geometric priors, such as Hamiltonian symmetries and variational principles, into neural networks, enabling structure-preserving models that extrapolate with high accuracy. However, in systems with dissipation and holonomic constraints, ubiquitous in legged locomotion and multibody robotics, the canonical symplectic form becomes degenerate, undermining the very invariants that guarantee stability and long-term prediction. In this work, we tackle this foundational limitation by introducing Presymplectification Networks (PSNs), the first framework to learn the symplectification lift via Dirac structures, restoring a non-degenerate symplectic geometry by embedding constrained systems into a higher-dimensional manifold. Our architecture combines a recurrent encoder with a flow-matching objective to learn the augmented phase-space dynamics end-to-end. We then attach a lightweight Symplectic Network (SympNet) ...