# A Certified Model Reduction Approach for Robust Parameter Optimization with PDE Constraints

arXiv: https://arxiv.org/abs/1703.01613 · HTML: https://mlsanity.com/paper/1703.01613/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2017.

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

- [Efficient PDE-Constrained optimization under high-dimensional uncertainty using derivative-informed neural operators](https://mlsanity.com/paper/2305.20053/) (2023)

## Abstract (arXiv)

We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear optimization problem has a bi-level structure due to the min-max formulation. To approximate the worst-case in the optimization problem we propose linear and quadratic approximations. However, this approach still turns out to be very expensive, therefore we propose an adaptive model order reduction technique which avoids long offline stages and provides a certified reduced order surrogate model for the parametrized PDE which is then utilized in the numerical optimization. Numerical results are presented to validate the presented approach.