3 papers
math-ph2026
Symmetry analysis and exact solutions of multi-layer quasi-geostrophic problem
Serhii D. Koval, Alex Bihlo, Roman O. Popovych
We carry out an extended symmetry analysis of the multi-layer quasi-geostrophic problem. This model is given by a system of an arbitrary number of coupled barotropic vorticity equa…
math.AP2024
Extended symmetry analysis of remarkable (1+2)-dimensional Fokker-Planck equation
Serhii D. Koval, Alexander Bihlo, Roman O. Popovych
We carry out the extended symmetry analysis of an ultraparabolic Fokker-Planck equation with three independent variables, which is also called the Kolmogorov equation and is single…
cs.LG2024
Improving physics-informed DeepONets with hard constraints
Rüdiger Brecht, Dmytro R. Popovych, Alex Bihlo +1
Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equation…