# emgr - The Empirical Gramian Framework

arXiv: https://arxiv.org/abs/1611.00675 · HTML: https://mlsanity.com/paper/1611.00675/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2016.

## Built on by (most cited first, 3 of 3)

- [Data-Driven Observability Analysis for Nonlinear Stochastic Systems](https://mlsanity.com/paper/2302.11979/) (2023)
- [GHOST: Unmasking Phantom States in Mamba2 via Grouped Hidden-state Output-aware Selection & Truncation](https://mlsanity.com/paper/2602.11408/) (2026)
- [Information-Guided Safe Reinforcement Learning for Autonomous Gas Source Localization using sUAS](https://mlsanity.com/paper/2609.05569/) (2026)

## Abstract (arXiv)

System Gramian matrices are a well-known encoding for properties of input-output systems such as controllability, observability or minimality. These so-called system Gramians were developed in linear system theory for applications such as model order reduction of control systems. Empirical Gramian are an extension to the system Gramians for parametric and nonlinear systems as well as a data-driven method of computation. The empirical Gramian framework - emgr - implements the empirical Gramians in a uniform and configurable manner, with applications such as Gramian-based (nonlinear) model reduction, decentralized control, sensitivity analysis, parameter identification and combined state and parameter reduction.