# Algebraic Tools for the Analysis of State Space Models

arXiv: https://arxiv.org/abs/1609.07985 · HTML: https://mlsanity.com/paper/1609.07985/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2016.

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

- [Estimate Epidemiological Parameters given Partial Observations based on Algebraically Observable PINNs](https://mlsanity.com/paper/2407.12598/) (2024)
- [Algebraically Observable Physics-Informed Neural Network and its Application to Epidemiological Modelling](https://mlsanity.com/paper/2508.04590/) (2025)

## Abstract (arXiv)

We present algebraic techniques to analyze state space models in the areas of structural identifiability, observability, and indistinguishability. While the emphasis is on surveying existing algebraic tools for studying ODE systems, we also present a variety of new results. In particular: on structural identifiability, we present a method using linear algebra to find identifiable functions of the parameters of a model for unidentifiable models. On observability, we present techniques using Gr"obner bases and algebraic matroids to test algebraic observability of state space models. On indistinguishability, we present a sufficient condition for distinguishability using computational algebra and demonstrate testing indistinguishability.