Pattern recognition (psychology)

Image (mathematics)

Noise (video)

Computer science

Gene

Probabilistic logic

Quantum mechanics

Machine learning

Biochemistry

Algorithm

Artificial intelligence

Robustness (evolution)

Statistical model

Ensemble forecasting

Leverage (statistics)

Chemistry

Ensemble learning

Physics

Nonlinear system

Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of bootstrap aggregating (bagging) to robustify the sparse identification of the nonlinear dynamics (SINDy) algorithm. First, an ensemble of SINDy models is identified from subsets of limited and noisy data. The aggregate model statistics are then used to produce inclusion probabilities of the candidate functions, which enables uncertainty quantification and probabilistic forecasts. We apply this ensemble-SINDy (E-SINDy) algorithm to several synthetic and real-world datasets and demonstrate substantial improvements to the accuracy and robustness of model discovery from extremely noisy and limited data. For example, E-SINDy uncovers partial differential equations models from data with more than twice as much measurement noise as has been previously reported. Similarly, E-SINDy learns ...

Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control