Levi-Civita Coordinates Improve Dynamics, Worsen Optimization in AI Dynamics Study

Researchers have explored the use of Levi--Civita coordinates for learned Hamiltonian dynamics, comparing them to Cartesian formulations in a perturbed Kepler system. While Levi--Civita coordinates demonstrated superior stability and accuracy, particularly at high eccentricities, they introduced challenges in raw-basis optimization conditioning. The study found that exact-feature controls and orthogonalization could restore baseline fitting for L-BFGS, but small MLPs still struggled with rollout errors even after gauge symmetrization, indicating that accurate neural residual learning for these dynamics remains an open problem. AI

IMPACT This research explores advanced coordinate systems for Hamiltonian dynamics, potentially improving the accuracy and stability of learned models in complex physical simulations.

RANK_REASON The cluster contains an academic paper detailing a computational physics study. [lever_c_demoted from research: ic=1 ai=1.0]

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• Cartesian coordinate system
• Kepler problem
• Levi--Civita coordinates
• Limited-memory BFGS

• paper
• other

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