# Generative Neural Reparameterization for Differentiable PDE-constrained Optimization

arXiv: https://arxiv.org/abs/2410.12683 · HTML: https://mlsanity.com/paper/2410.12683/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 11 references that are in the map.
- First posted on arXiv 16 Oct 2024.

## Builds on (most cited first, 1 of 1)

- [Neural reparameterization improves structural optimization](https://mlsanity.com/paper/1909.04240/) (2019)

## Built on by (most cited first, 1 of 1)

- [Neural Operator-enabled Topology-informed Evolutionary Strategy for PDE-Constrained Optimization](https://mlsanity.com/paper/2607.07682/) (2026)

## Abstract (arXiv)

Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per optimization. Given a differentiable PDE solver, if the free parameters are reparameterized as the output of a neural network, that neural network can be trained to learn a map from a probability distribution to the distribution of optimal parameters. This proves useful in the case where there are many well performing local minima for the PDE. We apply this technique to train a neural network that generates optimal parameters that minimize laser-plasma instabilities relevant to laser fusion and show that the neural network generates many well performing and diverse minima.