Results 11 to 20 of about 3,581,525 (255)
Transformer for Partial Differential Equations' Operator Learning [PDF]
Trans. Mach. Learn. Res., 2022 Data-driven learning of partial differential equations' solution operators has recently emerged as a promising paradigm for approximating the underlying solutions.
Zijie Li, Kazem Meidani, A. Farimani
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In-context operator learning with data prompts for differential equation problems [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 2023 Significance This paper presents In-Context Operator Networks (ICON), a neural network approach that can learn new operators from prompted data during the inference stage without requiring any weight updates.
Liu Yang +3 more
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Super-Resolution Neural Operator [PDF]
Computer Vision and Pattern Recognition, 2023 We propose Super-resolution Neural Operator (SRNO), a deep operator learning framework that can resolve high-resolution (HR) images at arbitrary scales from the low-resolution (LR) counterparts.
Min Wei, Xuesong Zhang
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Physics-Informed Neural Operator for Learning Partial Differential Equations [PDF]
ACM / IMS Journal of Data Science, 2021 In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric Partial Differential Equations (PDE).
Zong-Yi Li +7 more
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Kernel Methods are Competitive for Operator Learning [PDF]
Journal of Computational Physics, 2023 We present a general kernel-based framework for learning operators between Banach spaces along with a priori error analysis and comprehensive numerical comparisons with popular neural net (NN) approaches such as Deep Operator Net (DeepONet) [Lu et al ...
Pau Batlle +3 more
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LNO: Laplace Neural Operator for Solving Differential Equations [PDF]
arXiv.org, 2023 We introduce the Laplace neural operator (LNO), which leverages the Laplace transform to decompose the input space. Unlike the Fourier Neural Operator (FNO), LNO can handle non-periodic signals, account for transient responses, and exhibit exponential ...
Qianying Cao, S. Goswami, G. Karniadakis
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International mathematics research notices, 2021 Let $\Omega \subset{{\mathbb{R}}}^{n+1}$, $n\geq 2$, be an open set with Ahlfors regular boundary that satisfies the corkscrew condition. We consider a uniformly elliptic operator $L$ in divergence form associated with a matrix $A$ with real, merely ...
Jonas Azzam +3 more
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Operator learning with PCA-Net: upper and lower complexity bounds [PDF]
Journal of machine learning research, 2023 PCA-Net is a recently proposed neural operator architecture which combines principal component analysis (PCA) with neural networks to approximate operators between infinite-dimensional function spaces.
S. Lanthaler
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Physics-Informed Deep Neural Operator Networks [PDF]
arXiv.org, 2022 Standard neural networks can approximate general nonlinear operators, represented either explicitly by a combination of mathematical operators, e.g., in an advection-diffusion-reaction partial differential equation, or simply as a black box, e.g., a ...
S. Goswami +3 more
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Generic bounds on the approximation error for physics-informed (and) operator learning [PDF]
Neural Information Processing Systems, 2022 We propose a very general framework for deriving rigorous bounds on the approximation error for physics-informed neural networks (PINNs) and operator learning architectures such as DeepONets and FNOs as well as for physics-informed operator learning ...
T. D. Ryck, Siddhartha Mishra
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