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Design of Loss Functions for Solving Inverse Problems using Deep Learning
Solving inverse problems is a crucial task in several applications that strongly a ffect our daily lives, including multiple engineering fields, military operations, and/or energy production. There exist different methods ...
Variational Formulations for Explicit Runge-Kutta Methods
Variational space-time formulations for partial di fferential equations have been of great interest in the last decades, among other things, because they allow to develop mesh-adaptive algorithms. Since it is known ...
Explicit-in-Time Goal-Oriented Adaptivity
Goal-oriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for partial differential equations. In time dependent problems, we seek to represent the error in the quantity of ...
Forward-in-Time Goal-Oriented Adaptivity
In goal-oriented adaptive algorithms for partial differential equations, we adapt the finite element mesh in order to reduce the error of the solution in some quantity of interest. In time-dependent problems, this adaptive ...
Time-Domain Goal-Oriented Adaptivity Using Pseudo-Dual Error Representations
Goal-oriented adaptive algorithms produce optimal grids to solve challenging engineering problems. Recently, a novel error representation using (unconventional) pseudo-dual problems for goal-oriented adaptivity in the ...