4 papers
Generalized symmetries of remarkable (1+2)-dimensional Fokker-Planck equation
Dmytro R. Popovych, Serhii D. Koval, Roman O. Popovych
Using an original method, we find the algebra of generalized symmetries of a remarkable (1+2)-dimensional ultraparabolic Fokker-Planck equation, which is also called the Kolmogorov…
Algebraic method of group classification for semi-normalized classes of differential equations
Celestin Kurujyibwami, Dmytro R. Popovych, Roman O. Popovych
We generalize the notion of semi-normalized classes of systems of differential equations, study properties of such classes and extend the algebraic method of group classification t…
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…
Generalized symmetries of Burgers equation
Dmytro R. Popovych, Alex Bihlo, Roman O. Popovych
Despite the number of relevant considerations in the literature, the algebra of generalized symmetries of the Burgers equation has not been exhaustively described. We fill this gap…