arXiv:2607. 02715v1 Announce Type: new Abstract: Recently, neural operators have shown promising outcomes for learning solution operators of differential equations directly from data.
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.
arXiv:2607. 12570v1 Announce Type: cross Abstract: Multiscale problems are notoriously difficult to tackle using traditional numerical methods, as accurately resolving fine-scale features often requires prohibitively fine discretizations.
arXiv:2505. 11766v4 Announce Type: replace Abstract: Neural Operators (NOs) are powerful architectures for learning mappings between function spaces.
The paper introduces the Frame Kernel Method, a multiscale operator learning approach for surrogate modeling of multiscale partial differential equations. It uses a novel multiscale kernel frame function approximation to cast the learning problem as one of estimating frame coefficients, enabling automatic multiscale decomposition of outputs. The authors provide interpolation proofs, error estimates, and demonstrate that the method outperforms popular neural operators on challenging PDE problems while offering a posteriori multiscale analysis.
arXiv:2606. 11963v1 Announce Type: new Abstract: Neural operators provide a powerful framework for learning solution mappings of partial differential equations directly in function space.
arXiv:2507.07292v2 Announce Type: replace Abstract: We develop a new and general encode-approximate-reconstruct operator learning model that leverages learned neural representations of bases for inpu...
arXiv:2503. 05598v2 Announce Type: replace-cross Abstract: This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation.