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Symplectic Geometry
Symplectic Geometry and Structure-Preserving Neural Networks
Learn physics-informed neural networks that preserve energy and symplectic structure. Covers HNN, LNN, SympNet, symplectic integrators, and four classical experiments.
PDE and Machine Learning (5): Symplectic Geometry and Structure-Preserving Networks
Standard neural networks violate conservation laws. This article derives Hamiltonian mechanics, symplectic integrators, HNNs, LNNs, and SympNets from the geometry of phase space.