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Operator learning frameworks, because of their ability to learn nonlinear maps between two infinite dimensional functional spaces and utilization of neural networks in doing so, have recently emerged as one of the more pertinent areas in the field of applied machine learning.
Predicting the output from a complex computer code when fast approximations are available
MC Kennedy and A O’Hagan · 2000
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Multi-fidelity design of stiffened composite panel with a crack
Roberto Vitali, Raphael T Haftka, and Bhavani V Sankar · 2002
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Multi-fidelity optimization via surrogate modelling
Alexander IJ Forrester, András Sóbester, and Andy J Keane · 2007
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Multifidelity surrogate modeling of experimental and computational aerodynamic data sets
Yuichi Kuya, Kenji Takeda, Xin Zhang, and Alexander IJ Forrester · 2011
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Multi-fidelity methods in aerodynamic robust optimization
Andres S Padron, Juan J Alonso, and Michael S Eldred · 2016
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A surrogate based multi-fidelity approach for robust design optimization
Souvik Chakraborty, Tanmoy Chatterjee, Rajib Chowdhury, and Sondipon Adhikari · 2017
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Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling
Paris Perdikaris, Maziar Raissi, Andreas Damianou, Neil D Lawrence, and George Em Karniadakis · 2017
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Inferring solutions of differential equations using noisy multi-fidelity data
Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2017
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Deep uq: Learning deep neural network surrogate models for high dimensional uncertainty quantification
Rohit K Tripathy and Ilias Bilionis · 2018
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Adaptive multi-fidelity polynomial chaos approach to bayesian inference in inverse problems
Liang Yan and Tao Zhou · 2019
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Multi-fidelity physics-constrained neural network and its application in materials modeling
Dehao Liu and Yan Wang · 2019
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Lu Lu, Pengzhan Jin, and George Em Karniadakis · 2019
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A multifidelity framework and uncertainty quantification for sea surface temperature in the massachusetts and cape cod bays
H Babaee, C Bastidas, M DeFilippo, C Chryssostomidis, and GE Karniadakis · 2020
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Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics
Casey M Fleeter, Gianluca Geraci, Daniele E Schiavazzi, Andrew M Kahn, and Alison L Marsden · 2020
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A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse pde problems
Xuhui Meng and George Em Karniadakis · 2020
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A latent variable approach to gaussian process modeling with qualitative and quantitative factors
Yichi Zhang, Siyu Tao, Wei Chen, and Daniel W Apley · 2020
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On transfer learning of neural networks using bi-fidelity data for uncertainty propagation
Subhayan De, Jolene Britton, Matthew Reynolds, Ryan Skinner, Kenneth Jansen, and Alireza Doostan · 2020
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Fourier neural operator for parametric partial differential equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2020
Deep capsule encoder-decoder network for surrogate modeling and uncertainty quantification
Akshay Thakur and Souvik Chakraborty · 2022
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Neural network training using l1-regularization and bi-fidelity data
Subhayan De and Alireza Doostan · 2022
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Nonlocal kernel network (nkn): a stable and resolution-independent deep neural network
Huaiqian You, Yue Yu, Marta D’Elia, Tian Gao, and Stewart Silling · 2022
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A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data
Lu Lu, Xuhui Meng, Shengze Cai, Zhiping Mao, Somdatta Goswami, Zhongqiang Zhang, and George Em Karniadakis · 2022
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Bi-fidelity modeling of uncertain and partially unknown systems using deeponets
Subhayan De, Malik Hassanaly, Matthew Reynolds, Ryan N King, and Alireza Doostan · 2022
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Neural operator: Graph kernel network for partial differential equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2020
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Multi-fidelity deep neural network surrogate model for aerodynamic shape optimization
Xinshuai Zhang, Fangfang Xie, Tingwei Ji, Zaoxu Zhu, and Yao Zheng · 2021
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Data-driven physics-informed constitutive metamodeling of complex fluids: A multifidelity neural network (mfnn) framework
Mohammadamin Mahmoudabadbozchelou, Marco Caggioni, Setareh Shahsavari, William H Hartt, George Em Karniadakis, and Safa Jamali · 2021
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Latent map gaussian processes for mixed variable metamodeling
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Transfer learning based multi-fidelity physics informed deep neural network
Souvik Chakraborty · 2021
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Transfer learning on multi-fidelity data
Dong H Song and Daniel M Tartakovsky · 2021
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A multi-fidelity surrogate modeling method based on variance-weighted sum for the fusion of multiple non-hierarchical low-fidelity data
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Lu Lu, Raphaël Pestourie, Steven G Johnson, and Giuseppe Romano · 2022
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Multifidelity deep operator networks
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Multi-fidelity cost-aware bayesian optimization
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Data fusion with latent map gaussian processes
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Xin-Yang Liu, Hao Sun, and Jian-Xun Wang · 2022
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Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems
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A wavelet neural operator based elastography for localization and quantification of tumors
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Fault detection and isolation using probabilistic wavelet neural operator auto-encoder with application to dynamic processes
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