# Convergence of weak-SINDy Surrogate Models

@article{Russo2022ConvergenceOW, title={Convergence of weak-SINDy Surrogate Models}, author={Benjamin P. Russo and M. Paul Laiu}, journal={ArXiv}, year={2022}, volume={abs/2209.15573} }

. 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 nonlinear 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 linear system to recover coeﬃcients. We illuminate the structural…

## One Citation

### Asymptotic consistency of the WSINDy algorithm in the limit of continuum data

- Mathematics, Computer ScienceArXiv
- 2022

It is shown that in general the WSINDy estimator is only conditionally asymptotically consistent, yielding discovery of spurious terms with probability one if the noise level is above some critical threshold and the nonlinearities exhibit suﬃciently fast growth.

## References

SHOWING 1-10 OF 28 REFERENCES

### Weak SINDy For Partial Differential Equations

- Computer ScienceJ. Comput. Phys.
- 2021

### Weak SINDy: Galerkin-Based Data-Driven Model Selection

- Computer ScienceMultiscale Model. Simul.
- 2021

A weak formulation and discretization of the system discovery problem from noisy measurement data that combines the ease of implementation of the SINDy algorithm with the natural noise-reduction of integration to arrive at a more robust and user-friendly method of sparse recovery that correctly identifies systems in both small- noise and large-noise regimes.

### Reduced operator inference for nonlinear partial differential equations

- Computer ScienceSIAM J. Sci. Comput.
- 2022

We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear…

### The Occupation Kernel Method for Nonlinear System Identification

- Mathematics
- 2019

This manuscript presents a novel approach to nonlinear system identification leveraging densely defined Liouville operators and a new "kernel" function that represents an integration functional over…

### Approximation results for orthogonal polynomials in Sobolev spaces

- Mathematics
- 1982

We analyze the approximation properties of some interpolation operators and some L2-orthogonal projection operators related to systems of polynomials which are orthonormal with respect to a weight…

### Dynamic Mode Decomposition for Continuous Time Systems with the Liouville Operator

- MathematicsJournal of Nonlinear Science
- 2021

An approach to DMD is developed that treats continuous time dynamics directly through the Liouville operator, which allows for the incorporation of data that is sampled at high frequencies without producing models with excessively large rank.

### Dynamic mode decomposition - data-driven modeling of complex systems

- Computer Science
- 2016

This first book to address the DMD algorithm presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development, and blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses.

### Regression Shrinkage and Selection via the Lasso

- Computer Science
- 1996

A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.

### Occupation Kernels and Densely Defined Liouville Operators for System Identification

- Mathematics2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

The combination of Liouville operators and occupation kernels over reproducing kernel Hilbert spaces allow for the embedding of a dynamical system into a RKHS, where function theoretic tools may be leveraged for the examination of such systems.

### An Introduction to the Theory of Reproducing Kernel Hilbert Spaces

- Mathematics
- 2016

Reproducing kernel Hilbert spaces have developed into an important tool in many areas, especially statistics and machine learning, and they play a valuable role in complex analysis, probability,…