46 citations · 73 across the 7 of their papers we have counts for
7 papers
Low-rank adaptive physics-informed HyperDeepONets for solving differential equations
Etienne Zeudong, Elsa Cardoso-Bihlo, Alex Bihlo
HyperDeepONets were introduced in Lee, Cho and Hwang [ICLR, 2023] as an alternative architecture for operator learning, in which a hypernetwork generates the weights for the trunk…
Physics-informed neural networks for tsunami inundation modeling
Rüdiger Brecht, Elsa Cardoso-Bihlo, Alex Bihlo
We use physics-informed neural networks for solving the shallow-water equations for tsunami modeling. Physics-informed neural networks are an optimization based approach for solvin…
Exactly conservative physics-informed neural networks and deep operator networks for dynamical systems
Elsa Cardoso-Bihlo, Alex Bihlo
We introduce a method for training exactly conservative physics-informed neural networks and physics-informed deep operator networks for dynamical systems. The method employs a pro…
Differential invariants for a class of diffusion equations
Elsa Dos Santos Cardoso-Bihlo, Alexander Bihlo, Roman O. Popovych
We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is…
Algebraic method for finding equivalence groups
Alexander Bihlo, Elsa Dos Santos Cardoso-Bihlo, Roman O. Popovych
The algebraic method for computing the complete point symmetry group of a system of differential equations is extended to finding the complete equivalence group of a class of such…
Differential Invariants for the Korteweg-de Vries Equation
Elsa Maria Dos Santos Cardoso-Bihlo
Differential invariants for the maximal Lie invariance group of the Korteweg-de Vries equation are computed using the moving frame method and compared with existing results. Closed…