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arXiv Machine Learning By Andrew M. Stuart, Margaret Trautner

Enforcing Dirichlet Boundary Conditions in Operator Learning

Read the original on arXiv Machine Learning →

The paper introduces a neural operator architecture that inherently satisfies homogeneous Dirichlet boundary conditions by constraining each layer’s output to lie within the span of selected Dirichlet eigenfunctions of the Laplacian. This design works for any bounded domain with a Lipschitz boundary and any discretization, avoiding the restrictions of previous methods. The authors prove universal approximation for their architecture and demonstrate its effectiveness on Darcy flow and Helmholtz equation problems.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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