Convergence of weak-SINDy Surrogate Models

09/30/2022
by   Benjamin Russo, et al.
Oak Ridge National Laboratory
0

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).

READ FULL TEXT

page 30

page 31

page 33

03/08/2022

Online Weak-form Sparse Identification of Partial Differential Equations

This paper presents an online algorithm for identification of partial di...
01/22/2021

Surrogate Models for Optimization of Dynamical Systems

Driven by increased complexity of dynamical systems, the solution of sys...
11/06/2022

WeakIdent: Weak formulation for Identifying Differential Equations using Narrow-fit and Trimming

Data-driven identification of differential equations is an interesting b...
03/13/2023

Reduced order model of a convection-diffusion equation using Proper Orthogonal Decomposition

In this work, a numerical simulation of 1D Burgers' equation is develope...
06/12/2019

Model Order Reduction by Proper Orthogonal Decomposition

We provide an introduction to POD-MOR with focus on (nonlinear) parametr...
06/09/2023

Active-Learning-Driven Surrogate Modeling for Efficient Simulation of Parametric Nonlinear Systems

When repeated evaluations for varying parameter configurations of a high...
05/27/2023

Scalable Transformer for PDE Surrogate Modeling

Transformer has shown state-of-the-art performance on various applicatio...

Please sign up or login with your details

Forgot password? Click here to reset