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Found 5 papers, 1 papers with code
Achieving High Accuracy with PINNs via Energy Natural Gradients
We propose energy natural gradient descent, a natural gradient method with respect to a Hessian-induced Riemannian metric as an optimization algorithm for physics-informed neural networks (PINNs) and the deep Ritz method.
The Deep Ritz Method for Parametric $p$-Dirichlet Problems
We establish error estimates for the approximation of parametric $p$-Dirichlet problems deploying the Deep Ritz Method.
A parameter study on optimal scaffolds in a simple model for bone regeneration
We propose a simple model for scaffold aided bone regeneration.
Error Estimates for the Deep Ritz Method with Boundary Penalty
Our results apply to arbitrary sets of ansatz functions and estimate the error in dependence of the optimization accuracy, the approximation capabilities of the ansatz class and -- in the case of Dirichlet boundary values -- the penalization strength $\lambda$.
Deep Ritz revisited
In this notes we use the notion of $\Gamma$-convergence to show that ReLU networks of growing architecture that are trained with respect to suitably regularised Dirichlet energies converge to the true solution of the Poisson problem.
