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Kernel Methods in the Deep Ritz framework: Theory and practice

Announce Type: replace Abstract: In this contribution, kernel approximations are applied as ansatz functions within the Deep Ritz method. This allows to approximate weak solutions of elliptic partial differential equations with weak enforcement of boundary conditions using Nitsche's method. A priori error estimates are proven in different norms leveraging both standard results for weak solutions of elliptic equations and well-established convergence results for kernel methods.

arXiv CS 7d ago

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