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In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep learning.
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A theoretical analysis of deep neural networks and parametric PDEs
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Backflow transformations via neural networks for quantum many-body wave functions
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Adaptive deep learning for high dimensional Hamilton-Jacobi-Bellman equations
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Ab-initio solution of the many-electron Schrödinger equation with deep neural networks
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