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math.NA2021★ 2 cited
Three Ways to Solve Partial Differential Equations with Neural Networks -- A Review
Jan Blechschmidt, Oliver G. Ernst
Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three importa…
math.NA2019
Error estimation for second-order PDEs in non-variational form
Jan Blechschmidt, Roland Herzog, Max Winkler
Second-order partial differential equations in non-divergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton-Jacobi-Bellman…