# Sensitivity analysis on chaotic dynamical system by Non-Intrusive Least Square Shadowing (NILSS)

arXiv: https://arxiv.org/abs/1611.00880 · HTML: https://mlsanity.com/paper/1611.00880/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2016.

## Built on by (most cited first, 6 of 6)

- [Gradients are Not All You Need](https://mlsanity.com/paper/2111.05803/) (2021)
- [Differentiable Programming for Earth System Modeling](https://mlsanity.com/paper/2208.13825/) (2022)
- [Low-Variance Gradient Estimation in Unrolled Computation Graphs with ES-Single](https://mlsanity.com/paper/2304.11153/) (2023)
- [Gradient-free optimization of chaotic acoustics with reservoir computing](https://mlsanity.com/paper/2106.09780/) (2021)
- [OGF: An Online Gradient Flow Method for Optimizing the Statistical Steady-State Time Averages of Unsteady Turbulent Flows](https://mlsanity.com/paper/2507.05149/) (2025)
- [Divergence-kernel method for linear responses of densities and generative models](https://mlsanity.com/paper/2509.03992/) (2025)

## Abstract (arXiv)

This paper develops the non-intrusive formulation of the Least-squares shadowing (LSS) method, for computing the sensitivity of long-time averaged objectives in chaotic dynamical systems. This non-intrusive formulation constrains the computation to only the unstable subspace, greatly reducing the cost of LSS for many problems; moreover, it reparametrizes the LSS problem, requiring only minor modifications to existing tangent solvers. NILSS is demonstrated on a chaotic flow over a backward-facing step simulated with a mesh of 12e3 cells.