# Simultaneous Identification and Denoising of Dynamical Systems

arXiv: https://arxiv.org/abs/2203.13837 · HTML: https://mlsanity.com/paper/2203.13837/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2022.

## Built on by (most cited first, 10 of 10)

- [Asymptotic consistency of the WSINDy algorithm in the limit of continuum data](https://mlsanity.com/paper/2211.16000/) (2022)
- [Statistical Mechanics of Dynamical System Identification](https://mlsanity.com/paper/2403.01723/) (2024)
- [Constrained or Unconstrained? Neural-Network-Based Equation Discovery from Data](https://mlsanity.com/paper/2406.02581/) (2024)
- [Ensemble WSINDy for Data Driven Discovery of Governing Equations from Laser-based Full-field Measurements](https://mlsanity.com/paper/2409.20510/) (2024)
- [Data-driven Discovery of Digital Twins in Biomedical Research](https://mlsanity.com/paper/2508.21484/) (2025)
- [Overcoming error-in-variable problem in data-driven model discovery by orthogonal distance regression](https://mlsanity.com/paper/2507.23426/) (2025)
- [Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization](https://mlsanity.com/paper/2602.13513/) (2026)
- [Exact identification of nonlinear dynamical systems by Trimmed Lasso](https://mlsanity.com/paper/2308.01891/) (2023)
- [A joint optimization approach to identifying sparse dynamics using least squares kernel collocation](https://mlsanity.com/paper/2511.18555/) (2025)
- [From STLS to Projection-based Dictionary Selection in Sparse Regression for System Identification](https://mlsanity.com/paper/2512.14404/) (2025)

## Abstract (arXiv)

In recent years there has been a push to discover the governing equations dynamical systems directly from measurements of the state, often motivated by systems that are too complex to directly model. Although there has been substantial work put into such a discovery, doing so in the case of large noise has proved challenging. Here we develop an algorithm for Simultaneous Identification and Denoising of a Dynamical System (SIDDS). We infer the noise in the state measurements by requiring that the denoised data satisfies the dynamical system with an equality constraint. This is unlike existing work where the mismatch in the dynamical system is treated as a penalty in the objective. We assume the dynamics is represented in a pre-defined basis and develop a sequential quadratic programming approach to solve the SIDDS problem featuring a direct solution of KKT system with a specialized preconditioner. In addition, we show how we can include sparsity promoting regularization using an iteratively reweighted least squares approach. The resulting algorithm leads to estimates of the dynamical system that approximately achieve the Cram'er-Rao lower bound and, with sparsity promotion, can correctly identify the sparsity structure for higher levels of noise than existing techniques. Moreover, because SIDDS decouples the data from the evolution of the dynamical system, we show how to modify the problem to accurately identify systems from low sample rate measurements. The inverse problem approach and solution framework used by SIDDS has the potential to be expanded to related problems identifying governing equations from noisy data.