AI weather models may simulate the atmosphere via particle positions in latent space whose updates follow gradient flow on a learned free energy functional rather than conventional physical equations.
arXiv preprint arXiv:2309.01213 , year=
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SGD on multiclass cross-entropy loss alternates between curvature-driven oscillations and stable regimes but self-stabilizes to enable best-iterate convergence with large learning rates for linear and two-layer models.
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The physics of AI weather models
AI weather models may simulate the atmosphere via particle positions in latent space whose updates follow gradient flow on a learned free energy functional rather than conventional physical equations.
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SGD at the Edge of Stability: Stochastic Stabilization with Large Learning Rates
SGD on multiclass cross-entropy loss alternates between curvature-driven oscillations and stable regimes but self-stabilizes to enable best-iterate convergence with large learning rates for linear and two-layer models.