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We provide convergence guarantees for the Deep Ritz Method for abstract variational energies.
Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik
Ritz, W. (1909) · 1909
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Free energy of a nonuniform system. i. interfacial free energy
Cahn, J. W. and Hilliard, J. E. (1958) · 1958
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Neural algorithm for solving differential equations
Lee, H. and Kang, I. S. (1990) · 1990
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Variational Methods
Struwe, M. (1990) · 1990
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Linear Functional Analysis
Alt, H. W. (1992) · 1992
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Neural-network-based approximations for solving partial differential equations
Dissanayake, M. and Phan-Thien, N. (1994) · 1994
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Neural network representation of finite element method
Takeuchi, J. and Kosugi, Y. (1994) · 1994
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Artificial neural networks for solving ordinary and partial differential equations
Lagaris, I. E., Likas, A., and Fotiadis, D. I. (1998) · 1998
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Two-layer neural networks for partial differential equations: Optimization and generalization theory
Luo, T. and Yang, H. (2020) · 2006
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Nichtlineare Funktionalanalysis: Eine Einführung
Růžička, M. (2006) · 2006
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Finite elements: Theory, fast solvers, and applications in solid mechanics
Braess, D. (2007) · 2007
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Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning
Han, J., Jentzen, A., et al. (2020) · 2008
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Functional Analysis, Sobolev Spaces and Partial Differential Equations
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Xu, J. (2020) · 2010
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An overview on deep learning-based approximation methods for partial differential equations
Beck, C., Hutzenthaler, M., Jentzen, A., and Kuckuck, B. (2020) · 2012
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Norm-resolvent convergence in perforated domains
Cherednichenko, K., Dondl, P., and Rösler, F. (2018) · 2018
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The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems
E, W. and Yu, B. (2018) · 2018
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DGM: A deep learning algorithm for solving partial differential equations
Sirignano, J. and Spiliopoulos, K. (2018) · 2018
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Robin Pre-Training for the Deep Ritz Method
Courte, L. and Zeinhofer, M. (2021) · 2021
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Convergence rate analysis for deep ritz method
Duan, C., Jiao, Y., Lai, Y., Lu, X., and Yang, Z. (2021) · 2021
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E, W., Han, J., and Jentzen, A. (2017) · 2017
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Lu, Y., Chen, H., Lu, J., Ying, L., and Blanchet, J. (2021b)
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