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.
Original language | English (US) |
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Pages (from-to) | 1462-1490 |
Number of pages | 29 |
Journal | SIAM Journal on Scientific Computing |
Volume | 45 |
Issue number | 4 |
DOIs | |
State | Published - Aug 2023 |
Keywords
- design of experiments
- noise
- nonintrusive model reduction
- operator inference
- reduced models
- scientific machine learning
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics