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Learning Physical Systems: Symplectification via Gauge Fixing in Dirac Structures
Aristotelis Papatheodorou, Pranav Vaidhyanathan, Natalia Ares, Ioannis Havoutis
https://arxiv.org/abs/2506.18812

Learning Physical Systems: Symplectification via Gauge Fixing in Dirac Structures
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 predicti…