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Constructing fast numerical solvers for partial differential equations (PDEs) is crucial for many scientific disciplines.
The multi-grid method for the diffusion equation with strongly discontinuous coefficients
Alcouffe, R. E., Brandt, A., Dendy, J. E., and Painter, J. W · 1981
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Black box multigrid
Dendy (Jr.), J. E · 1982
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Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
de Zeeuw, P. M · 1990
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Artificial neural networks for solving ordinary and partial differential equations
Lagaris, I. E., Likas, A., and Fotiadis, D. I · 1998
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The black box multigrid numerical homogenization algorithm
Moulton, J. D., Dendy, J. E., and Hyman, J. M · 1998
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A multigrid tutorial
Briggs, W. L., Henson, V. E., and McCormick, S. F · 2000
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Multigrid
Trottenberg, U., Oosterlee, C., and Schüller, A · 2001
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Solving partial differential equations in real-time using artificial neural network signal processing as an alternative to finite-element analysis
Sun, M., Yan, X., and Sclabassi, R. J · 2003
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Practical Fourier analysis for multigrid methods
Wienands, R. and Joppich, W · 2004
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An introduction to algebraic multigrid
Falgout, R. D · 2006
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Artificial neural networks approach for solving stokes problem
Baymani, M., Kerayechian, A., and Effati, S · 2010
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Han, J., Jentzen, A., and Weinan, E · 2017
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Deep multigrid: learning prolongation and restriction matrices
Katrutsa, A., Daulbaev, T., and Oseledets, I · 2017
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Study on a poisson’s equation solver based on deep learning technique
Tang, W., Shan, T., Dang, X., Li, M., Yang, F., Xu, S., and Wu, J · 2017
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Geodesic convolutional shape optimization
Baque, P., Remelli, E., Fleuret, F., and Fua, P · 2018
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Learning across scales—multiscale methods for convolution neural networks
Haber, E., Ruthotto, L., Holtham, E., and Jun, S.-H · 2018
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Solving high-dimensional partial differential equations using deep learning
Han, J., Jentzen, A., and Weinan, E · 2018
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On cell-centered multigrid methods and local Fourier analysis for PDEs with random coefficients
Kumar, P., Rodrigo, C., Gaspar, F. J., and Oosterlee, C. W · 2018
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A machine learning framework for data driven acceleration of computations of differential equations
Mishra, S · 2018
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Dgm: A deep learning algorithm for solving partial differential equations
Sirignano, J. and Spiliopoulos, K · 2018
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A unified deep artificial neural network approach to partial differential equations in complex geometries
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Fourier analysis of periodic stencils in multigrid methods
Bolten, M. and Rittich, H · 2018
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Local Fourier analysis of BDDC-like algorithms
Brown, J., He, Y., and Maclachlan, S · 2018
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Multi-level residual networks from dynamical systems view
Chang, B., Meng, L., Haber, E., Tung, F., and Begert, D · 2018
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General solutions for nonlinear differential equations: a deep reinforcement learning approach
Wei, S., Jin, X., and Li, H · 2018
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Neural ordinary differential equations
Chen, R., Rubanova, Y., Bettencourt, J., and Duvenaud, D · 2019
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Learning neural PDE solvers with convergence guarantees
Hsieh, J., Zhao, S., Eismann, S., Mirabella, L., and Ermon, S · 2019
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Residual learning without normalization via better initialization
Zhang, H., Dauphin, Y. N., and Ma, T · 2019
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