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Advances in Continuous and Discrete Models

Theory and Modern Applications

Figure 1 | Advances in Continuous and Discrete Models

Figure 1

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

Figure 1

Exemplary numerical realization of the Deep Ritz Method for a Cahn–Hilliard functional with right-hand sides given through \(f=\chi _{B_{r}(0,-1/2)} - \chi _{B_{r}(0,1/2)}\) with \(r=0.1\) for the left plot and \(r=0.4\) for the right plot. The value of ε is set to 0.01. We used zero Neumann boundary conditions and fully connected feed-forward networks with three hidden layers of width 16 and tanh activation. The number of trainable parameters is 609

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