A First Step Towards Mesh-Free Probabilistic Shape Optimization
Optimization and Control
2026-03-03 v1 Probability
Abstract
We present an initial implementation of a probabilistic PDE-constrained shape optimization algorithm. Our method is based on a novel probabilistic representation of the shape derivative, which is evaluated using Monte Carlo sampling; and does not rely on a mesh. The underlying state is represented with a neural network-based PDE solver on point clouds. The methodology is applied throughout to a benchmark tracking problem.
Cite
@article{arxiv.2603.01141,
title = {A First Step Towards Mesh-Free Probabilistic Shape Optimization},
author = {Stephan Schmidt and Maximilian Würschmidt},
journal= {arXiv preprint arXiv:2603.01141},
year = {2026}
}
Comments
13 pages, 1 figure