Kernel Methods for Learning Operators with Multiple Inputs and Outputs | Paper Citation Record

Observation 22a43843-bf8c-48e3-9c1b-fb1aec3a4e1d · outbound

This paper cites Adams and J.J.F.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Adams and J.J.F

Reference 1

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This paper cites Álvarez, Lorenzo Rosasco, and Neil D.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Álvarez, Lorenzo Rosasco, and Neil D

Reference 2

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This paper cites An extension of a bound for functions in sobolev spaces, with applications to (m, s)-spline interpolation and smoothing.Numerische Mathematik, 107(2):181–211, 2007.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs An extension of a bound for functions in sobolev spaces, with applications to (m, s)-spline interpolation and smoothing.Numerische Mathematik, 107(2):181–211, 2007

Reference 3

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This paper cites Extension of sampling inequalities to sobolev semi-norms of fractional order and derivative data.Numerische Mathematik, 121(3):587–608, 2012.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Extension of sampling inequalities to sobolev semi-norms of fractional order and derivative data.Numerische Mathematik, 121(3):587–608, 2012

Reference 4

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Observation 96414081-9767-43cd-b935-db4ea6714de2 · outbound

This paper cites Theory of reproducing kernels.Transactions of the American Mathematical Society, 68:337–404, 1950.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Theory of reproducing kernels.Transactions of the American Mathematical Society, 68:337–404, 1950

Reference 5

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Unresolved cited work

Reference 6

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This paper cites Sorokin, Xianjin Yang, Théo Bourdais, Edoardo Calvello, Matthieu Darcy, Alexander Hsu, Bamdad Hosseini, and Houman Owhadi.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Sorokin, Xianjin Yang, Théo Bourdais, Edoardo Calvello, Matthieu Darcy, Alexander Hsu, Bamdad Hosseini, and Houman Owhadi

Reference 7

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Unresolved cited work

Reference 8

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Observation 8c8ba9ad-aac2-4be3-b49e-2df77c6e3cfc · outbound

This paper cites Kernel methods are competitive for operator learning.Journal of Computational Physics, 496:112549, 2024.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Kernel methods are competitive for operator learning.Journal of Computational Physics, 496:112549, 2024

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This paper cites Brezis.Functional Analysis, Sobolev Spaces and Partial Differential Equations.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Brezis.Functional Analysis, Sobolev Spaces and Partial Differential Equations

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This paper cites Vicon: Vision in- context operator networks for multi-physics fluid dynamics prediction.arXiv preprint arXiv:2411.16063, 2024.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Vicon: Vision in- context operator networks for multi-physics fluid dynamics prediction.arXiv preprint arXiv:2411.16063, 2024

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This paper cites Carmeli, E.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Carmeli, E

Reference 12

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Unresolved cited work

Reference 13

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This paper cites Conway.A Course in Functional Analysis, volume 96 ofGraduate Texts in Mathematics.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Conway.A Course in Functional Analysis, volume 96 ofGraduate Texts in Mathematics

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This paper cites Springer, New York, 3 edition, 2002.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Springer, New York, 3 edition, 2002

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This paper cites Duffy.Green’s Functions with Applications.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Duffy.Green’s Functions with Applications

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This paper cites Evans.Partial Differential Equations, volume 19 ofGraduate Studies in Mathematics.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Evans.Partial Differential Equations, volume 19 ofGraduate Studies in Mathematics

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This paper cites Cambridge University Press, 2022.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Cambridge University Press, 2022

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This paper cites Vector-valued gaussian processes for ap- proximating divergence- or rotation-free vector fields.Journal of Machine Learning Research, 27(74):1– 36, 2026.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Vector-valued gaussian processes for ap- proximating divergence- or rotation-free vector fields.Journal of Machine Learning Research, 27(74):1– 36, 2026

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Observation 01fed0f2-9252-4e79-b3d1-3ef514e19497 · outbound

This paper cites Kernel methods for bayesian elliptic inverse problems on manifolds.SIAM/ASA Journal on Uncertainty Quantification, 8(4):1414–1445, 2020.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Kernel methods for bayesian elliptic inverse problems on manifolds.SIAM/ASA Journal on Uncertainty Quantification, 8(4):1414–1445, 2020

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Poseidon: Efficient foundation models for PDEs

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Sparse learning of dynamical systems in RKHS: An operator-theoretic approach

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This paper cites Data-efficient kernel methods for learning differential equations and their solution operators: Algorithms and error analysis, 2025.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Data-efficient kernel methods for learning differential equations and their solution operators: Algorithms and error analysis, 2025

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Minimax optimal kernel operator learning via multilevel training

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Mionet: Learning multiple-input operators via tensor product

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Time-series forecasting and refine- ment within a multimodal pde foundation model.Journal of Machine Learning for Modeling and Com- puting, 6(2):77–89, 2025

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Operator-valued kernels for learning from functional response data.Journal of Machine Learning Research, 17(20):1–54, 2016

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Kernel-based operator learning: Error analysis, budget allocation, and a physics- informed extension, 2026

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Operator learning with pca-net: upper and lower complexity bounds.J

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Fourier Neural Operator for Parametric Partial Differential Equations

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Cauchy Random Features for Operator Learning in Sobolev Space

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs BCAT: A Block Causal Transformer for PDE Foundation Models for Fluid Dynamics

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Multiple Physics Pretraining for Physical Surrogate Models

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs A Multimodal PDE Foundation Model for Prediction and Scientific Text Descriptions

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Nelsen and Andrew M

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs On optimal recovery methods in hardy-sobolev spaces.Sbornik: Mathematics, 192(2):225, feb 2001

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Cam- bridge Monographs on Applied and Computational Mathematics

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Robey and J

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Towards a foundation model for partial differential equations: Multioperator learning and extrapolation.Physical Review E, 111(3):035304, 2025

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs LeMON: Learning to Learn Multi-Operator Networks

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Generalization bounds and statistical guarantees for multi-task and multiple operator learning with mno networks, 2026

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Kernel Methods for Learning Operators with Multiple Inputs and Outputs Multiple neural operators achieve near-optimal rates for multi-task learning, 2026

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Observation 60aae74c-2e43-413e-b6f2-04e2f9d0e5b1 · outbound

This paper cites A deep learning framework for multi-operator learning: Architectures and approximation theory, 2025.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs A deep learning framework for multi-operator learning: Architectures and approximation theory, 2025

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Resolution: unresolved; no resolver link, observed 2026-08-16T00:30:39.873503Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fcd4d48f-187a-4e00-9a91-8c3c16e82efa · outbound

This paper cites Cambridge Monographs on Applied and Computa- tional Mathematics.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Cambridge Monographs on Applied and Computa- tional Mathematics

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:30:40.615874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8abfe6a0-c611-451d-948a-763a2972ac50 · outbound

This paper cites In-context operator learning with data prompts for differential equation problems.Proceedings of the National Academy of Sciences, 120(39):e2310142120, 2023.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs In-context operator learning with data prompts for differential equation problems.Proceedings of the National Academy of Sciences, 120(39):e2310142120, 2023

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Resolution: unresolved; no resolver link, observed 2026-08-16T00:30:39.882492Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a244bb72-5ac6-495c-ae26-8e99470030d9 · outbound

This paper cites Fine-Tune Language Models as Multi-Modal Differential Equation Solvers.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Fine-Tune Language Models as Multi-Modal Differential Equation Solvers

Reference 56

Resolution: unresolved; no resolver link, observed 2026-08-16T00:30:39.886673Z

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Observation 2de68fda-d8a0-43b9-9441-de4656bb5170 · outbound

This paper cites Generalization guarantees for multi-input neural operator learning in sobolev spaces, 2026.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Generalization guarantees for multi-input neural operator learning in sobolev spaces, 2026

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:30:40.590562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a3962333-0536-416f-a1a0-0b0c8b66e26a · outbound

This paper cites PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations

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Resolution: unresolved; no resolver link, observed 2026-08-16T00:30:39.895777Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b278cc8-ccbb-4eb7-b3cd-41582d9f0bef · outbound

This paper cites Regularized random fourier features and finite element reconstruction for operator learning in sobolev space.Journal of Machine Learning for Modeling and Computing, 7(3):1–47, 2026.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Regularized random fourier features and finite element reconstruction for operator learning in sobolev space.Journal of Machine Learning for Modeling and Computing, 7(3):1–47, 2026

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:30:40.576453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5c2f79ca-5b22-416a-a699-669bd404464b · outbound

This paper cites Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equations.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equations

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Resolution: unresolved; no resolver link, observed 2026-08-16T00:30:39.904175Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e330d57-567b-4d35-b9e3-a6832fde2012 · outbound

This paper cites Modno: Multi-operator learning with distributed neural operators.Computer Methods in Applied Mechanics and Engineering, 431:117229, 2024.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Modno: Multi-operator learning with distributed neural operators.Computer Methods in Applied Mechanics and Engineering, 431:117229, 2024

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:30:40.563412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f5905873-5681-4aeb-9120-01ab15ad980e · outbound

This paper cites A discretization-invariant extension and analysis of some deep operator networks.Journal of Computational and Applied Mathematics, 456:116226, 2025.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs A discretization-invariant extension and analysis of some deep operator networks.Journal of Computational and Applied Mathematics, 456:116226, 2025

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:30:40.551771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0ae175da-e4d8-43cf-8b1d-d49cfae5c11b · outbound

This paper cites D2no: Efficient handling of heterogeneous input function spaces with distributed deep neural operators.Computer Methods in Applied Mechanics and Engineering, 428:117084, 2024.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs D2no: Efficient handling of heterogeneous input function spaces with distributed deep neural operators.Computer Methods in Applied Mechanics and Engineering, 428:117084, 2024

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Resolution: unresolved; no resolver link, observed 2026-08-16T00:30:39.915371Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c4f5ab1-9aa4-4caa-9d7b-a340a1e3561f · outbound

This paper cites Deeponet as a multi-operator extrapolation model: Distributed pretraining with physics-informed fine-tuning.Journal of Computa- tional Physics, page 114537, 2025.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Deeponet as a multi-operator extrapolation model: Distributed pretraining with physics-informed fine-tuning.Journal of Computa- tional Physics, page 114537, 2025

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:30:40.532860Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a6224312-a3e6-49f0-a662-4434f5052803 · outbound

This paper cites Belnet: basis enhanced learning, a mesh-free neural operator.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 479(2276):20230043, 2023.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Belnet: basis enhanced learning, a mesh-free neural operator.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 479(2276):20230043, 2023

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:30:40.519726Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c5cff3d0-d6c6-44bb-a323-fb96eba4b2a8 · outbound

This paper cites Pi-mfm: Physics-informed mul- timodal foundation model for solving partial differential equations.arXiv preprint arXiv:2512.23056, 2025.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Pi-mfm: Physics-informed mul- timodal foundation model for solving partial differential equations.arXiv preprint arXiv:2512.23056, 2025

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Resolution: unresolved; no resolver link, observed 2026-08-16T00:30:39.926092Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 84f9cd01-fee6-4695-a39a-832b09824599 · outbound

This paper cites Ifx 0∈A S, then (7)A S =x 0 + kerL.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Ifx 0∈A S, then (7)A S =x 0 + kerL

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:30:40.503017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 73de16a0-893b-43cc-9aa3-c650f1263b30 · outbound

This paper cites Define the functional Jγ :X→R, J γ(x) :=∥x∥ 2 X +γ−1∥Lx−S∥ 2 Z.

Kernel Methods for Learning Operators with Multiple Inputs and Outputs Define the functional Jγ :X→R, J γ(x) :=∥x∥ 2 X +γ−1∥Lx−S∥ 2 Z

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:30:40.488051Z

Source-reported events for the cited work

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