# SIMBa: System Identification Methods leveraging Backpropagation

arXiv: https://arxiv.org/abs/2311.13889 · HTML: https://mlsanity.com/paper/2311.13889/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2023.

## Built on by (most cited first, 5 of 5)

- [Learning Adaptive Hydrodynamic Models Using Neural ODEs in Complex Conditions](https://mlsanity.com/paper/2410.00490/) (2024)
- [Neural Port-Hamiltonian Models for Nonlinear Distributed Control: An Unconstrained Parametrization Approach](https://mlsanity.com/paper/2411.10096/) (2024)
- [Stable-by-Design Neural Network-Based LPV State-Space Models for System Identification](https://mlsanity.com/paper/2510.24757/) (2025)
- [Controller Design for Structured State-space Models via Contraction Theory](https://mlsanity.com/paper/2604.07069/) (2026)
- [A Novel Schur-Decomposition-Based Weight Projection Method for Stable State-Space Neural-Network Architectures](https://mlsanity.com/paper/2605.14489/) (2026)

## Abstract (arXiv)

This manuscript details and extends the SIMBa toolbox (System Identification Methods leveraging Backpropagation) presented in previous work, which uses well-established Machine Learning tools for discrete-time linear multi-step-ahead state-space System Identification (SI). SIMBa leverages linear-matrix-inequality-based free parametrizations of Schur matrices to guarantee the stability of the identified model by design. In this paper, backed up by novel free parametrizations of Schur matrices, we extend the toolbox to show how SIMBa can incorporate known sparsity patterns or true values of the state-space matrices to identify without jeopardizing stability. We extensively investigate SIMBa's behavior when identifying diverse systems with various properties from both simulated and real-world data. Overall, we find it consistently outperforms traditional stable subspace identification methods, and sometimes significantly, especially when enforcing desired model properties. These results hint at the potential of SIMBa to pave the way for generic structured nonlinear SI. The toolbox is open-sourced on https://github.com/Cemempamoi/simba.