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Introducing Operator
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arXiv AI
Jun 11
Harness In-Context Operator Learning with Chain of Operators
arXiv:2606. 12318v1 Announce Type: cross Abstract: Neural operators approximate mappings between function spaces, but often generalize poorly to other operators and usually require fine-tuning or retraining.
arXiv AI
Jul 13
Projection Methods for Operator Learning and Universal Approximation
arXiv:2406. 12264v5 Announce Type: replace-cross Abstract: We obtain a new universal approximation theorem for continuous (possibly nonlinear) operators on arbitrary Banach spaces using the Leray-Schauder mapping.
arXiv Machine Learning
1d ago
PIKFNO: An Interpretable Neural Operator Based on Physics Informed Kernel Function
arXiv:2608. 14619v1 Announce Type: new Abstract: This work proposes a new interpretable neural operator framework, termed the Physics Informed Kernel Function Neural Operator (PIKFNO), which explicitly incorporates physics informed kernel functions derived from governing equations into the neural operator architecture.
arXiv Machine Learning
Jun 30
Learned iterative networks: An operator learning perspective
arXiv:2512. 08444v2 Announce Type: replace-cross Abstract: Learned image reconstruction has become a pillar in computational imaging and inverse problems.
arXiv Machine Learning
Jun 17
From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing
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.
arXiv Machine Learning
Aug 11
Test-time Generalization for Physics through Neural Operator Splitting
arXiv:2602. 00884v2 Announce Type: replace Abstract: Neural operators have shown promise in learning solution maps of partial differential equations (PDEs), but they often struggle to generalize when test inputs lie outside the training distribution, such as novel initial conditions, unseen PDE coefficients or unseen physics.