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math.NA2026
Compositional Approximation Can Strictly Outperform Superpositional Approximation
Dennis Elbrächter, Philipp Petersen
Many classically studied function classes are known to be approximated optimally by superpositional methods, i.e. with approximants constructed as the linear combination of element…
math.NA2026
Certified and accurate computation of function space norms of deep neural networks
Johannes Gründler, Moritz Maibaum, Philipp Petersen
Neural network methods for PDEs require reliable error control in function space norms. However, trained neural networks can typically only be probed at a finite number of point va…