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cs.LG2026
Learning from the Descent Direction: Adaptive Gradient Descent under One-Sided Hölder Regularity
Arzu Ahmadova, Ismail Huseynov
We study adaptive gradient descent for continuously differentiable, possibly nonconvex objectives under one-sided Hölder regularity. Unlike classical Hölder- or Lipschitz-gradient…
cs.LG2026
Reliable Error Estimation for PINNs: Lower and Upper A Posteriori Bounds
Ismail Huseynov, Arzu Ahmadova, Agamirza Bashirov
Physics-informed neural networks (PINNs) combine machine learning with physical laws to solve differential equations. While existing results provide rigorous \emph{a posteriori} up…