arXiv Machine Learning By Diego Marcondes

Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks

Read the original on arXiv Machine Learning →

arXiv:2605. 03542v2 Announce Type: replace-cross Abstract: The dual norm characterisation of weak solutions of second-order linear elliptic partial differential equations is mathematically natural but computationally intractable: evaluating the $H^{-1}$ norm of the residual requires a supremum over an infinite-dimensional test space.

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