4 papers
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-gradien…
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…
Partially Exact Controllability of Semilinear Heat Exchanger Systems
Ismail Huseynov, Arzu Ahmadova, Agamirza E. Bashirov
In this paper, we study two semilinear systems describing a monotubular and a two-stream heat exchanger. Neither system is exactly controllable; however, for each we specify a subs…
Design of Optimal Controls in Acausal LQG Problems
Arzu Ahmadova, Agamirza E. Bashirov
In control theory, a system which has output depending only on the present and past values of the input is said to be causal (or nonanticipative). Respectively, a system is acausal…