# Convergence of weak-SINDy Surrogate Models

arXiv: https://arxiv.org/abs/2209.15573 · HTML: https://mlsanity.com/paper/2209.15573/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 36 references that are in the map.
- First posted on arXiv 30 Sep 2022.

## Builds on (most cited first, 4 of 4)

- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [On the Convergence of the SINDy Algorithm](https://mlsanity.com/paper/1805.06445/) (2018)
- [Reduced operator inference for nonlinear partial differential equations](https://mlsanity.com/paper/2102.00083/) (2021)
- [The Occupation Kernel Method for Nonlinear System Identification](https://mlsanity.com/paper/1909.11792/) (2019)

## Built on by (most cited first, 11 of 11)

- [Benchmarking sparse system identification with low-dimensional chaos](https://mlsanity.com/paper/2302.10787/) (2023)
- [Asymptotic consistency of the WSINDy algorithm in the limit of continuum data](https://mlsanity.com/paper/2211.16000/) (2022)
- [Coarse-Graining Hamiltonian Systems Using WSINDy](https://mlsanity.com/paper/2310.05879/) (2023)
- [The Weak Form Is Stronger Than You Think](https://mlsanity.com/paper/2409.06751/) (2024)
- [Weak-Form Inference for Hybrid Dynamical Systems in Ecology](https://mlsanity.com/paper/2405.20591/) (2024)
- [Streaming Compression of Scientific Data via weak-SINDy](https://mlsanity.com/paper/2308.14962/) (2023)
- [Weighted Birkhoff Averages Accelerate Data-Driven Methods](https://mlsanity.com/paper/2511.17772/) (2025)
- [Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification](https://mlsanity.com/paper/2604.20141/) (2026)
- [SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study](https://mlsanity.com/paper/2403.00578/) (2024)
- [From STLS to Projection-based Dictionary Selection in Sparse Regression for System Identification](https://mlsanity.com/paper/2512.14404/) (2025)
- [Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training error](https://mlsanity.com/paper/2605.31438/) (2026)

## Abstract (arXiv)

In this paper, we give an in-depth error analysis for surrogate models generated by a variant of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an overview of a variety of non-linear system identification techniques, namely, SINDy, weak-SINDy, and the occupation kernel method. Under the assumption that the dynamics are a finite linear combination of a set of basis functions, these methods establish a matrix equation to recover coefficients. We illuminate the structural similarities between these techniques and establish a projection property for the weak-SINDy technique. Following the overview, we analyze the error of surrogate models generated by a simplified version of weak-SINDy. In particular, under the assumption of boundedness of a composition operator given by the solution, we show that (i) the surrogate dynamics converges towards the true dynamics and (ii) the solution of the surrogate model is reasonably close to the true solution. Finally, as an application, we discuss the use of a combination of weak-SINDy surrogate modeling and proper orthogonal decomposition (POD) to build a surrogate model for partial differential equations (PDEs).