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Advances in Continuous and Discrete Models

Theory and Modern Applications

Figure 2 | Advances in Continuous and Discrete Models

Figure 2

From: Uniform convergence guarantees for the deep Ritz method for nonlinear problems

Figure 2

Exemplary numerical realization of the Deep Ritz Method for the p-Laplacian with right-hand \(f=1\) and \(p=1.5\) in the left plot and \(p=10\) in the right plot. Zero Dirichlet boundary conditions are enforced through a penalty parameter \(\lambda =250\). We used fully connected feed-forward networks with three hidden layers of width 16 and GELU activation for the left plot and ReLU activation for the right plot. The number of trainable parameters is 609. Note the difference in the scaling of the axis in the two plots

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