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Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning.
Electrons and phonons: the theory of transport phenomena in solids
John M Ziman · 2001
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A class of globally convergent optimization methods based on conservative convex separable approximations
Krister Svanberg · 2002
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Colloquium: Phononics: Manipulating heat flow with electronic analogs and beyond
Nianbei Li, Jie Ren, Lei Wang, Gang Zhang, Peter Hänggi, and Baowen Li · 2012
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Heat flux manipulation with engineered thermal materials
Supradeep Narayana and Yuki Sato · 2012
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DEAP: Evolutionary algorithms made easy
Félix-Antoine Fortin, François-Michel De Rainville, Marc-André Gardner, Marc Parizeau, and Christian Gagné · 2012
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Metamaterials beyond electromagnetism
Muamer Kadic, Tiemo Bückmann, Robert Schittny, and Martin Wegener · 2013
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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
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Review of multi-fidelity models
M Giselle Fernández-Godino, Chanyoung Park, Nam-Ho Kim, and Raphael T Haftka · 2016
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Self-normalizing neural networks
Günter Klambauer, Thomas Unterthiner, Andreas Mayr, and Sepp Hochreiter · 2017
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almabte: A solver of the space–time dependent boltzmann transport equation for phonons in structured materials
Jesús Carrete, Bjorn Vermeersch, Ankita Katre, Ambroise van Roekeghem, Tao Wang, Georg KH Madsen, and Natalio Mingo · 2017
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Evolutionary computation 1: Basic algorithms and operators
Thomas Bäck, David B Fogel, and Zbigniew Michalewicz · 2018
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Maziar Raissi, Paris Perdikaris, and George E Karniadakis · 2019
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fpinns: Fractional physics-informed neural networks
Guofei Pang, Lu Lu, and George Em Karniadakis · 2019
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Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
Dongkun Zhang, Lu Lu, Ling Guo, and George Em Karniadakis · 2019
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Lu Lu, Pengzhan Jin, and George Em Karniadakis · 2019
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Gmls-nets: A framework for learning from unstructured data
Nathaniel Trask, Ravi G Patel, Ben J Gross, and Paul J Atzberger · 2019
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Perspective on ab initio phonon thermal transport
Lucas Lindsay, Ankita Katre, Andrea Cepellotti, and Natalio Mingo · 2019
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Physics-informed neural networks for inverse problems in nano-optics and metamaterials
Yuyao Chen, Lu Lu, George Em Karniadakis, and Luca Dal Negro · 2020
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Systems biology informed deep learning for inferring parameters and hidden dynamics
Alireza Yazdani, Lu Lu, Maziar Raissi, and George Em Karniadakis · 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
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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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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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Extraction of mechanical properties of materials through deep learning from instrumented indentation
Lu Lu, Ming Dao, Punit Kumar, Upadrasta Ramamurty, George Em Karniadakis, and Subra Suresh · 2020
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Physics-informed machine learning
Error estimates for DeepOnets: A deep learning framework in infinite dimensions
Samuel Lanthaler, Siddhartha Mishra, and George Em Karniadakis · 2021
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Convergence rate of DeepONets for learning operators arising from advection-diffusion equations
Beichuan Deng, Yeonjong Shin, Lu Lu, Zhongqiang Zhang, and George Em Karniadakis · 2021
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Exponential convergence of deep operator networks for elliptic partial differential equations
Carlo Marcati and Christoph Schwab · 2021
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Physics-enhanced deep surrogates for pdes
Raphaël Pestourie, Youssef Mroueh, Chris Rackauckas, Payel Das, and Steven G Johnson · 2021
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Inverse design in photonics by topology optimization: tutorial
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George Em Karniadakis, Ioannis G Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang · 2021
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Deepxde: A deep learning library for solving differential equations
Lu Lu, Xuhui Meng, Zhiping Mao, and George Em Karniadakis · 2021
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Physics-informed neural networks with hard constraints for inverse design
Lu Lu, Raphael Pestourie, Wenjie Yao, Zhicheng Wang, Francesc Verdugo, and Steven G Johnson · 2021
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Gradient-enhanced physics-informed neural networks for forward and inverse pde problems
Jeremy Yu, Lu Lu, Xuhui Meng, and George Em Karniadakis · 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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Lu Lu, Xuhui Meng, Shengze Cai, Zhiping Mao, Somdatta Goswami, Zhongqiang Zhang, and George Em Karniadakis · 2021
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A physics-informed operator regression framework for extracting data-driven continuum models
Ravi G Patel, Nathaniel A Trask, Mitchell A Wood, and Eric C Cyr · 2021
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Deepm&mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks
Shengze Cai, Zhicheng Wang, Lu Lu, Tamer A Zaki, and George Em Karniadakis · 2021
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Rasmus E Christiansen and Ole Sigmund · 2021
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Efficient calculations of the mode-resolved ab-initio thermal conductivity in nanostructures
Giuseppe Romano · 2021
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Openbte: a solver for ab-initio phonon transport in multidimensional structures
Giuseppe Romano · 2021
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Mitchell Daneker, Zhen Zhang, George Em Karniadakis, and Lu Lu · 2022
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Nonlocal kernel network (nkn): a stable and resolution-independent deep neural network
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Mionet: Learning multiple-input operators via tensor product
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Christian Moya, Shiqi Zhang, Meng Yue, and Guang Lin · 2022
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Scalable uncertainty quantification for deep operator networks using randomized priors
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Forecasting solar-thermal systems performance under transient operation using a data-driven machine learning approach based on the deep operator network architecture
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Simulating progressive intramural damage leading to aortic dissection using deeponet: an operator–regression neural network
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Minglang Yin, Enrui Zhang, Yue Yu, 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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