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The term `surrogate modeling' in computational science and engineering refers to the development of computationally efficient approximations for expensive simulations, such as those arising from numerical solution of partial differential equations (PDEs).
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Nonlinear approximation
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Spectral methods in MATLAB
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Fe2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre sic/ti composite materials
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Understanding the difficulty of training deep feedforward neural networks
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Principles of multiscale modeling
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Numerical solution of partial differential equations by the finite element method
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Spectral methods in fluid dynamics
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A stochastic newton mcmc method for large-scale statistical inverse problems with application to seismic inversion
James Martin, Lucas C Wilcox, Carsten Burstedde, and Omar Ghattas · 2012
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Analysis of Finite Difference Schemes: For Linear Partial Differential Equations with Generalized Solutions
Boško S Jovanović and Endre Süli · 2013
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Wolfgang Hackbusch · 2013
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Multidisciplinary design optimization: a survey of architectures
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Dynamic mode decomposition: Theory and applications
Jonathan H Tu · 2013
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The gnat method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
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The theoretical foundation of reduced basis methods
Ronald A DeVore · 2014
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Multilevel monte carlo methods
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TensorFlow: Large-scale machine learning on heterogeneous systems, 2015
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Delving deep into rectifiers: Surpassing human-level performance on imagenet classification
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2015
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Ian Goodfellow, Yoshua Bengio, and Aaron Courville · 2016
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Train faster, generalize better: Stability of stochastic gradient descent
Moritz Hardt, Ben Recht, and Yoram Singer · 2016
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Su2: An open-source suite for multiphysics simulation and design
Thomas D Economon, Francisco Palacios, Sean R Copeland, Trent W Lukaczyk, and Juan J Alonso · 2016
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Cyber-physical systems: foundations, principles and applications
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Data-driven operator inference for nonintrusive projection-based model reduction
Benjamin Peherstorfer and Karen Willcox · 2016
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Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
Julia Ling, Andrew Kurzawski, and Jeremy Templeton · 2016
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Inverse boundary value problem for the Helmholtz equation: quantitative conditional Lipschitz stability estimates
Elena Beretta, Maarten V De Hoop, Florian Faucher, and Otmar Scherzer · 2016
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Modal analysis of fluid flows: An overview
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Data assimilation in reduced modeling
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Physics-informed machine learning approach for reconstructing reynolds stress modeling discrepancies based on dns data
Jian-Xun Wang, Jin-Long Wu, and Heng Xiao · 2017
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Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the koopman operator
Qianxiao Li, Felix Dietrich, Erik M Bollt, and Ioannis G Kevrekidis · 2017
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Deep neural networks as gaussian processes
Jaehoon Lee, Yasaman Bahri, Roman Novak, Samuel S Schoenholz, Jeffrey Pennington, and Jascha Sohl-Dickstein · 2017
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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
Jiequn Han, Arnulf Jentzen, et al · 2017
Solving electrical impedance tomography with deep learning
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Learning constitutive relations from indirect observations using deep neural networks
Daniel Z Huang, Kailai Xu, Charbel Farhat, and Eric Darve · 2020
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Model reduction and neural networks for parametric pdes
Kaushik Bhattacharya, Bamdad Hosseini, Nikola B Kovachki, and Andrew M Stuart · 2021
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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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A variational approach to probing extreme events in turbulent dynamical systems
Mohammad Farazmand and Themistoklis P Sapsis · 2017
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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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Optimization methods for large-scale machine learning
Léon Bottou, Frank E Curtis, and Jorge Nocedal · 2018
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Eldad Haber, Felix Lucka, and Lars Ruthotto · 2018
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Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework
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Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics
Linfeng Zhang, Jiequn Han, Han Wang, Roberto Car, and E Weinan · 2018
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Deep dynamical modeling and control of unsteady fluid flows
Jeremy Morton, Freddie D Witherden, Antony Jameson, and Mykel J Kochenderfer · 2018
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Exponential convergence for multiscale linear elliptic pdes via adaptive edge basis functions
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Exponentially convergent multiscale methods for high frequency heterogeneous helmholtz equations
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Solving and learning nonlinear pdes with gaussian processes
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Mesh sampling and weighting for the hyperreduction of nonlinear petrov–galerkin reduced-order models with local reduced-order bases
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Data-driven balancing of linear dynamical systems
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A computationally tractable framework for nonlinear dynamic multiscale modeling of membrane woven fabrics
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Learning constitutive relations using symmetric positive definite neural networks
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Convergence rates for learning linear operators from noisy data
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