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Deep neural operators, such as DeepONets, have changed the paradigm in high-dimensional nonlinear regression from function regression to (differential) operator regression, paving the way for significant changes in computational engineering applications.
The characteristics of 78 related airfoil sections from tests in the variable-density wind tunnel
Eastman N Jacobs, Kenneth E Ward, and Robert M Pinkerton · 1933
Earlier work this paper cites.
A statistical approach to some basic mine valuation problems on the witwatersrand
Daniel G Krige · 1951
Earlier work this paper cites.
Wing design by numerical optimization
Raymond M Hicks and Preston A Henne · 1978
Earlier work this paper cites.
A new optimizer using particle swarm theory
Russell Eberhart and James Kennedy · 1995
Earlier work this paper cites.
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
Tianping Chen and Hong Chen · 1995
Earlier work this paper cites.
Aerodynamic shape optimization of complex aircraft configurations via an adjoint formulation
James Reuther, Antony Jameson, James Farmer, Luigi Martinelli, and David Saunders · 1996
Earlier work this paper cites.
A conservative staggered-grid chebyshev multidomain method for compressible flows
David A. Kopriva and John H. Kolias · 1996
Earlier work this paper cites.
Studies of the continuous and discrete adjoint approaches to viscous automatic aerodynamic shape optimization
Siva Nadarajah and Antony Jameson · 2001
Earlier work this paper cites.
Optimized nonuniform rational b-spline geometrical representation for aerodynamic design of wings
Jerome Lepine, Francois Guibault, Jean-Yves Trepanier, and Francois Pepin · 2001
Earlier work this paper cites.
Aerodynamics and design for ultra-low Reynolds number flight
Peter Josef Kunz · 2003
Earlier work this paper cites.
Convergence analysis of the direct algorithm
D Finkel and Carl Tim Kelley · 2004
Earlier work this paper cites.
Airfoil shape optimization using a nonuniform rational b-splines parametrization under thickness constraint
Simon Painchaud-Ouellet, Christophe Tribes, Jean-Yves Trépanier, and Dominique Pelletier · 2006
Earlier work this paper cites.
Adjoint-based aerodynamic shape optimization on unstructured meshes
Giampietro Carpentieri, Barry Koren, and Michel JL van Tooren · 2007
Earlier work this paper cites.
Model reduction for large-scale systems with high-dimensional parametric input space
Tan Bui-Thanh, Karen Willcox, and Omar Ghattas · 2008
Earlier work this paper cites.
A compact proper orthogonal decomposition basis for optimization-oriented reduced-order models
Kevin Carlberg and Charbel Farhat · 2008
Earlier work this paper cites.
Computational geometry algorithms and applications
de Berg Mark, Cheong Otfried, van Kreveld Marc, and Overmars Mark · 2008
Earlier work this paper cites.
Parameter and state model reduction for large-scale statistical inverse problems
Chad Lieberman, Karen Willcox, and Omar Ghattas · 2010
Earlier work this paper cites.
An adjoint method for shape optimization in unsteady viscous flows
DN Srinath and Sanjay Mittal · 2010
Earlier work this paper cites.
Multimodality and global optimization in aerodynamic design
Oleg Chernukhin and David W Zingg · 2013
Earlier work this paper cites.
Reduced models in chemical kinetics via nonlinear data-mining
Eliodoro Chiavazzo, Charles W Gear, Carmeline J Dsilva, Neta Rabin, and Ioannis G Kevrekidis · 2014
Earlier work this paper cites.
A guide to the implementation of boundary conditions in compact high-order methods for compressible aerodynamics
Gianmarco Mengaldo, Daniele De Grazia, Freddie Witherden, Antony Farrington, Peter Vincent, Spencer Sherwin, and Joaquim Peiro · 2014
Earlier work this paper cites.
A data–driven approximation of the koopman operator: Extending dynamic mode decomposition
Matthew O Williams, Ioannis G Kevrekidis, and Clarence W Rowley · 2015
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A survey of projection-based model reduction methods for parametric dynamical systems
Peter Benner, Serkan Gugercin, and Karen Willcox · 2015
Cited alongside, same era.
Design optimization using hyper-reduced-order models
David Amsallem, Matthew Zahr, Youngsoo Choi, and Charbel Farhat · 2015
Cited alongside, same era.
Nektar++: An open-source spectral/hp element framework
C.D. Cantwell, D. Moxey, A. Comerford, A. Bolis, G. Rocco, G. Mengaldo, D. De Grazia, S. Yakovlev, J.-E. Lombard, D. Ekelschot, B. Jordi, H. Xu, Y. Mohamied, C. Eskilsson, B. Nelson, P. Vos, C. Biotto, R.M. Kirby, and S.J. Sherwin · 2015
Cited alongside, same era.
Certified reduced basis methods for parametrized partial differential equations
Jan S Hesthaven, Gianluigi Rozza, Benjamin Stamm, et al · 2016
Cited alongside, same era.
Gradient-based constrained optimization using a database of linear reduced-order models
Youngsoo Choi, Gabriele Boncoraglio, Spenser Anderson, David Amsallem, and Charbel Farhat · 2020
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Non-intrusive reduced-order model for predicting transonic flow with varying geometries
SUN Zhiwei, WANG Chen, Yu Zheng, BAI Junqiang, LI Zheng, XIA Qiang, and FU Qiujun · 2020
Later among the works it cites.
Nektar++: Enhancing the capability and application of high-fidelity spectral/hp element methods
David Moxey, Chris D. Cantwell, Yan Bao, Andrea Cassinelli, Giacomo Castiglioni, Sehun Chun, Emilia Juda, Ehsan Kazemi, Kilian Lackhove, Julian Marcon, Gianmarco Mengaldo, Douglas Serson, Michael Turner, Hui Xu, Joaquim Peiró, Robert M. Kirby, and Spencer J. Sherwin · 2020
Later among the works it cites.
Neural operator: Graph kernel network for partial differential equations, 2020
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2020
Later among the works it cites.
SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python
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Model reduction of parametrized systems
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Efficient aerodynamic shape optimization of transonic wings using a parallel infilling strategy and surrogate models
J Liu, W-P Song, Z-H Han, and Y Zhang · 2017
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Airfoil shape optimization using output-based adapted meshes
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Non-intrusive reduced order modeling of nonlinear problems using neural networks
Jan S Hesthaven and Stefano Ubbiali · 2018
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Yin Yu, Zhoujie Lyu, Zelu Xu, and Joaquim RRA Martins · 2018
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Automatic differentiation in machine learning: a survey
Atilim Gunes Baydin, Barak A Pearlmutter, Alexey Andreyevich Radul, and Jeffrey Mark Siskind · 2018
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Learning nonlinear operators via deeponet based on the universal approximation theorem of operators
Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis · 2021
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Cfd analysis and shape optimization of airfoils using class shape transformation and genetic algorithm—part i
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Multi-fidelity deep neural network surrogate model for aerodynamic shape optimization
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Enhanced data efficiency using deep neural networks and gaussian processes for aerodynamic design optimization
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Rapid airfoil design optimization via neural networks-based parameterization and surrogate modeling
Xiaosong Du, Ping He, and Joaquim RRA Martins · 2021
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Multi-fidelity convolutional neural network surrogate model for aerodynamic optimization based on transfer learning
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Ahmad Peyvan, Jonathan Komperda, Dongru Li, Zia Ghiasi, and Farzad Mashayek · 2021
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Subhayan De, Malik Hassanaly, Matthew Reynolds, Ryan N. King, and Alireza Doostan · 2022
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Multifidelity deep operator networks. Preprint at https://arxiv.org/abs/2204.09157
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Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport
Lu Lu, Raphaël Pestourie, Steven G. Johnson, and Giuseppe Romano · 2022
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Mionet: Learning multiple-input operators via tensor product
Pengzhan Jin, Shuai Meng, and Lu Lu · 2022
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Reliable extrapolation of deep neural operators informed by physics or sparse observations
Min Zhu, Handi Zhang, Anran Jiao, George Em Karniadakis, and Lu Lu · 2022
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On the influence of over-parameterization in manifold based surrogates and deep neural operators
Katiana Kontolati, Somdatta Goswami, Michael D Shields, and George Em Karniadakis · 2022
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Aerodynamic data-driven surrogate-assisted teaching-learning-based optimization (tlbo) framework for constrained transonic airfoil and wing shape designs
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Zongren Zou, Xuhui Meng, Apostolos F Psaros, and George Em Karniadakis · 2022
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