3 papers
math.OC2024
Optimal control of partial differential equations in PyTorch using automatic differentiation and neural network surrogates
Denis Khimin, Julian Roth, Alexander Henkes +1
The take-home message of this paper is that solving optimal control problems can be computationally straightforward, provided that differentiable partial differential equation (PDE…
cs.LG2024
Generalization capabilities of MeshGraphNets to unseen geometries for fluid dynamics
Robin Schmöcker, Alexander Henkes, Julian Roth +1
This works investigates the generalization capabilities of MeshGraphNets (MGN) [Pfaff et al. Learning Mesh-Based Simulation with Graph Networks. ICML 2021] to unseen geometries for…
math.NA2024
A monolithic space-time temporal multirate finite element framework for interface and volume coupled problems
Julian Roth, Martyna SoszyÅska, Thomas Richter +1
In this work, we propose and computationally investigate a monolithic space-time multirate scheme for coupled problems. The novelty lies in the monolithic formulation of the multir…