Convergence of Weak-SINDy Surrogate Models
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 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).
- Research Organization:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- Grant/Contract Number:
- AC05-00OR22725
- OSTI ID:
- 2502143
- Journal Information:
- SIAM Journal on Applied Dynamical Systems, Journal Name: SIAM Journal on Applied Dynamical Systems Journal Issue: 2 Vol. 23; ISSN 1536-0040
- Publisher:
- Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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