Handling noisy data in sparse model identification using subsampling and co-teaching

In this paper, a novel algorithm based on sparse identification, subsampling and co-teaching is developed to mitigate the problems of highly noisy data from sensor measurements in modeling of nonlinear systems. Specifically, sparse identification is combined with subsampling, a method where a fraction of the data set is randomly sampled and used for model identification, as well as co-teaching, a method that mixes noise-free data from first-principles simulations with the noisy measurements to provide a mixed data set that is less corrupted with noise for model training. The proposed method is bench-marked against sparse identification without subsampling as well as subsampling but without co-teaching using two examples, a predator-prey system and a chemical process, both of which are modeled as nonlinear systems of ordinary differential equations. It was shown that the proposed method yields better models in terms of prediction accuracy in the presence of high noise levels.