miscellaneous-7

Operator learning

3260 papers • 126 benchmarks • 313 datasets

Learn an operator between infinite dimensional Hilbert spaces or Banach spaces

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Benchmarks

These leaderboards are used to track progress in operator-learning-7

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Libraries

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Use these libraries to find operator-learning-7 models and implementations

liuyangmage/in-context-operator-net…

3 papers 25

Datasets

BubbleML

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Most implemented papers

Physics-Informed Neural Operator for Learning Partial Differential Equations

K. Azizzadenesheli, Anima Anandkumar, Zong-Yi Li, Nikola B. Kovachki, Burigede Liu, Hongkai Zheng, David Jin, Haoxuan Chen•Fri Nov 05 2021

PINO is the first hybrid approach incorporating data and PDE constraints at different resolutions to learn the operator of a given family of parametric Partial Differential Equations (PDE), and achieves a high-fidelity reconstruction of the ground-truth operator.

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Convolutional Analysis Operator Learning: Dependence on Training Data

B. Adcock, Il Yong Chun, J. Fessler, David Hong•Wed Feb 20 2019

A series of results that lend insight into the impact of dataset size on the filter update in CAOL are presented, including a general deterministic bound on errors in the estimated filters, and a bound on the expected errors as the number of training samples increases.

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Convolutional Analysis Operator Learning: Acceleration and Convergence

Il Yong Chun, J. Fessler•Wed Feb 14 2018

A new convolutional analysis operator learning (CAOL) framework that learns an analysis sparsifying regularizer with the convolution perspective, and develops a new convergent Block Proximal Extrapolated Gradient method using a Majorizer (BPEG-M) to solve the corresponding block multi-nonconvex problems.

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Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers

Bryan Catanzaro, Zong-Yi Li, Anima Anandkumar, Andrew Tao, M. Mardani, John Guibas•Tue Nov 23 2021

Adaptive Fourier Neural Operator is proposed as an efficient token mixer that learns to mix in the Fourier domain that can handle a sequence size of 65k and outperforms other efficient self-attention mechanisms for few-shot segmentation in terms of both efficiency and accuracy.

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GNOT: A General Neural Operator Transformer for Operator Learning

Zhongkai Hao, Chengyang Ying, Zhengyi Wang, Hang Su, Yinpeng Dong, Songming Liu, Ze Cheng, Jun Zhu, Jian Song•Mon Feb 27 2023

This work proposes a general neural operator transformer (GNOT), a scalable and effective transformer-based framework for learning operators that is highly flexible to handle multiple input functions and irregular meshes and introduces a geometric gating mechanism which could be viewed as a soft domain decomposition to solve the multi-scale problems.

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Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere

K. Kashinath, Maximilian Baust, B. Bonev, T. Kurth, Christian Hundt, Jaideep Pathak, Anima Anandkumar•Mon Jun 05 2023

Spherical FNOs (SFNOs) are introduced, a generalization of Fourier Neural Operators on the sphere, which has important implications for machine learning-based simulation of climate dynamics that could eventually help accelerate the response to climate change.

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In-context operator learning with data prompts for differential equation problems

Liu Yang, Siting Liu, Tingwei Meng, S. Osher•Sun Apr 16 2023

Numerical results demonstrate the efficacy of ICON in solving various types of differential equation problems and generalizing to operators beyond the training distribution and has implications for artificial general intelligence in physical systems.

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An enrichment approach for enhancing the expressivity of neural operators with applications to seismology

G. Karniadakis, E. Haghighat, U. Waheed•Tue Jun 06 2023

The results indicate that En-DeepONet paves the way for real-time hypocenter localization for velocity models of practical interest, and represents a significant advancement in operator learning that is applicable to a gamut of scientific problems, including those in seismology, fracture mechanics, and phase-field problems.

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Importance Weight Estimation and Generalization in Domain Adaptation Under Label Shift

K. Azizzadenesheli•Sat Nov 28 2020

A series of methods to estimate the importance weights from labeled source to unlabeled target domain and provide confidence bounds for these estimators are proposed and deployed.

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Learning Symbolic Operators for Task and Motion Planning

L. Kaelbling, J. Tenenbaum, Tomas Lozano-Perez, Tom Silver, Rohan Chitnis•Sat Feb 27 2021

This work proposes a bottom-up relational learning method for operator learning and shows how the learned operators can be used for planning in a TAMP system, finding this approach to substantially outperform several baselines, including three graph neural network-based model-free approaches from the recent literature.

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