Seminar in Numerical Analysis: Carsten Gräser (FAU Erlangen-Nürnberg)

PDE-regularized learning

We consider the regularization of a supervised learning problem by partial differential equations (PDEs). For the resulting regularized problem we derive error bounds in terms of a PDE error term and a data error term. These error contributions
quantify the accuracy of the PDE model used for regularization and the data coverage.

Furthermore, the discretization of the PDE-regularized learning problem by generalized Galerkin methods including finite elements and neural networks approaches is investigated. A nonlinear version of Céa's lemma allows to derive errors bounds for both classes of discretizations and gives first insights into error analysis of variational neural network discretizations of PDEs.

For further information about the seminar, please visit this webpage.

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