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Keyword

parametric partial differential equations

Description: Partial differential equations whose coefficients, inputs, or boundary conditions depend on parameters, studied in numerical analysis and scientific computing.
OpenAlex ID: keywords/parametric-partial-differential-equations
Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
2021 · Sifan Wang, Hanwen Wang, et al. · Science Advances · 836
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PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain
2020 · Han Gao, Luning Sun, et al. · Journal of Computational Physics · 621
Physics-Informed Neural Operator for Learning Partial Differential Equations
2024 · Zongyi Li, Hongkai Zheng, et al. · ACM / IMS Journal of Data Science · 393
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Model Reduction And Neural Networks For Parametric PDEs
2021 · Kaushik Bhattacharya, Bamdad Hosseini, et al. · SMAI Journal of Computational Mathematics · 328
Data-Driven Identification of Parametric Partial Differential Equations
2019 · Samuel Rudy, Alessandro Alla, et al. · SIAM Journal on Applied Dynamical Systems · 301
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Approximation of high-dimensional parametric PDEs
2015 · Albert Cohen, Ronald DeVore · Acta Numerica · 268
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Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs
2011 · Christoph Schwab, Claude Jeffrey Gittelson · Acta Numerica · 260
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Fourier Neural Operator for Parametric Partial Differential Equations
2021 · Zongyi Li, Nikola B. Kovachki, et al. · CaltechAUTHORS (California Institute of Technology) · 214
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Wavelet Neural Operator for solving parametric partial differential equations in computational mechanics problems
2022 · Tapas Tripura, Souvik Chakraborty · Computer Methods in Applied Mechanics and Engineering · 206
High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs
2013 · Abdellah Chkifa, Albert Cohen, et al. · Foundations of Computational Mathematics · 199
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Solving parametric PDE problems with artificial neural networks
2020 · YUEHAW KHOO, JIANFENG LU, et al. · European Journal of Applied Mathematics · 194
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Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs
2014 · Abdellah Chkifa, Albert Cohen, et al. · Journal de Mathématiques Pures et Appliquées · 179
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A Theoretical Analysis of Deep Neural Networks and Parametric PDEs
2021 · Gitta Kutyniok, Philipp Petersen, et al. · Constructive Approximation · 163
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Multipole Graph Neural Operator for Parametric Partial Differential Equations
2020 · Li, Zongyi, Kovachki, Nikola, et al. · arXiv (Cornell University) · 160
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Convergence Rates of the POD–Greedy Method
2012 · Bernard Haasdonk · ESAIM Mathematical Modelling and Numerical Analysis · 130
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Chapter 2: Reduced Basis Methods for Parametrized PDEs—A Tutorial Introduction for Stationary and Instationary Problems
2017 · Bernard Haasdonk · Society for Industrial and Applied Mathematics eBooks · 112
Data Assimilation in Reduced Modeling
2017 · Peter Binev, Albert Cohen, et al. · SIAM/ASA Journal on Uncertainty Quantification · 110
Simulation-based Anomaly Detection and Damage Localization: An application to Structural Health Monitoring
2020 · Caterina Bigoni, Jan S. Hesthaven · Computer Methods in Applied Mechanics and Engineering · 79
Multidimensional a priori hyper-reduction of mechanical models involving internal variables
2012 · David Ryckelynck, Florence Vincent, et al. · Computer Methods in Applied Mechanics and Engineering · 75
NeuralUQ: A Comprehensive Library for Uncertainty Quantification in Neural Differential Equations and Operators
2024 · Zongren Zou, Xuhui Meng, et al. · SIAM Review · 74
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Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks
2021 · Moritz Geist, Philipp Petersen, et al. · Journal of Scientific Computing · 74
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A Blackbox Reduced-Basis Output Bound Method for Noncoercive Linear Problems
2002 · Y. Maday, A.T. Patera, et al. · Studies in mathematics and its applications · 73
Comparison Between Reduced Basis and Stochastic Collocation Methods for Elliptic Problems
2013 · Peng Chen, Alfio Quarteroni, et al. · Journal of Scientific Computing · 64
Deep-learning of parametric partial differential equations from sparse and noisy data
2021 · Hao Xu, Dongxiao Zhang, et al. · Physics of Fluids · 62
GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs
2023 · Yanlai Chen, Shawn Koohy · Finite Elements in Analysis and Design · 60
Works count: 494
Citation count: 7,685
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