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ACTIVE OPERATOR INFERENCE FOR LEARNING LOW-DIMENSIONAL DYNAMICAL-SYSTEM MODELS FROM NOISY DATA.
- Source :
-
SIAM Journal on Scientific Computing . 2023, Vol. 45 Issue 4, pA1462-A1490. 29p. - Publication Year :
- 2023
-
Abstract
- Noise poses a challenge for learning dynamical-system models because already small variations can distort the dynamics described by trajectory data. This work builds on operator inference from scientific machine learning to infer low-dimensional models from high-dimensional state trajectories polluted with noise. The presented analysis shows that, under certain conditions, the inferred operators are unbiased estimators of the well-studied projection-based reduced operators from traditional model reduction. Furthermore, the connection between operator inference and projection-based model reduction enables bounding the mean-squared errors of predictions made with the learned models with respect to traditional reduced models. The analysis also motivates an active operator inference approach that judiciously samples high-dimensional trajectories with the aim of achieving a low mean-squared error by reducing the effect of noise. Numerical experiments with high-dimensional linear and nonlinear state dynamics demonstrate that predictions obtained with active operator inference have orders of magnitude lower mean-squared errors than operator inference with traditional, equidistantly sampled trajectory data. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SCIENCE education
*SAMPLING errors
Subjects
Details
- Language :
- English
- ISSN :
- 10648275
- Volume :
- 45
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Scientific Computing
- Publication Type :
- Academic Journal
- Accession number :
- 172377777
- Full Text :
- https://doi.org/10.1137/21M1439729