# Simultaneous Single-Step One-Shot Optimization with Unsteady PDEs

arXiv: https://arxiv.org/abs/1503.00884 · HTML: https://mlsanity.com/paper/1503.00884/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2015.

## Built on by (most cited first, 2 of 2)

- [PDE-constrained Models with Neural Network Terms: Optimization and Global Convergence](https://mlsanity.com/paper/2105.08633/) (2021)
- [Stable Optimization for Large Vision Model Based Deep Image Prior in Cone-Beam CT Reconstruction](https://mlsanity.com/paper/2203.12476/) (2022)

## Abstract (arXiv)

The single-step one-shot method has proven to be very efficient for PDE-constrained optimization where the partial differential equation (PDE) is solved by an iterative fixed point solver. In this approach, the simulation and optimization tasks are performed simultaneously in a single iteration. If the PDE is unsteady, finding an appropriate fixed point iteration is non-trivial. In this paper, we provide a framework that makes the single-step one-shot method applicable for unsteady PDEs that are solved by classical time-marching schemes. The One-shot method is applied to an optimal control problem with unsteady incompressible Navier-Stokes equations that are solved by an industry standard simulation code. With the Van-der-Pol oscillator as a generic model problem, the modified simulation scheme is further improved using adaptive time scales. Finally, numerical results for the advection-diffusion equation are presented.