A First Step Towards Mesh-Free Probabilistic Shape Optimization
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911476238778368 |
|---|---|
| author | Schmidt, Stephan Würschmidt, Maximilian |
| author_facet | Schmidt, Stephan Würschmidt, Maximilian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01141 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A First Step Towards Mesh-Free Probabilistic Shape Optimization Schmidt, Stephan Würschmidt, Maximilian Optimization and Control Probability 49Q10, 68T07, 65C05 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. |
| title | A First Step Towards Mesh-Free Probabilistic Shape Optimization |
| topic | Optimization and Control Probability 49Q10, 68T07, 65C05 |
| url | https://arxiv.org/abs/2603.01141 |