# A parallel-in-time approach for accelerating direct-adjoint studies

arXiv: https://arxiv.org/abs/2004.00546 · HTML: https://mlsanity.com/paper/2004.00546/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2020.

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

- [Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems](https://mlsanity.com/paper/2606.12337/) (2026)

## Abstract (arXiv)

Parallel-in-time methods are developed to accelerate the direct-adjoint looping procedure. Particularly, we utilize the Paraexp algorithm, previously developed to integrate equations forward in time, to accelerate the direct-adjoint looping that arises from gradient-based optimization. We consider both linear and non-linear governing equations and exploit the linear, time-varying nature of the adjoint equations. Gains in efficiency are seen across all cases, showing that a Paraexp based parallel-in-time approach is feasible for the acceleration of direct-adjoint studies. This signifies a possible approach to further increase the run-time performance for optimization studies that either cannot be parallelized in space or are at their limit of efficiency gains for a parallel-in-space approach.