UC Santa Barbara

Nonlinear systems can be decomposed into observable and unobservable subsystems in theory, but achieving this decomposition in a data-driven framework is challenging. Koopman operators enable us to embed nonlinear dynamical systems in high-dimensional function spaces. In this talk, we will explore how the observable decomposition of linear Koopman models relates to the observable decomposition of nonlinear systems and show how this decomposition can be achieved in a data-driven setting.

In a model biological soil bacterium, Pseudomonas putida, we use a deep neural network approach to learn Koopman operator representations to model the gene expression-phenotype dynamics. Using Koopman observable decomposition, we identified 15 genes out of 5564 genes in Pseudomonas putida, which impact the growth phenotype of the bacterium in soil simulant media conditions. Using CRISPRi, we construct synthetic strains that suppress the expression of these target genes and show that 80% of the gene targets have the predicted impact on the fitness of the bacterium Pseudomonas putida.

Our results provide a novel framework called Koopman observable decomposition, which functions as a machine learning tool for detecting critical states that generate desired outcomes in complex, high-dimensional nonlinear dynamical systems.