Sparse and nonparametric estimation of equations governing dynamical systems with applications to biology
This work addresses the challenge of data-driven model discovery for complex biological systems, offering a method to capture nonlinearities that existing parametric approaches like Sindy cannot, though it appears incremental as it builds on established sparse estimation techniques.
The authors tackled the problem of accurately modeling nonlinearities in dynamical systems, particularly in biology, by integrating sparse parametric estimation with nonparametric techniques, achieving improved representation without requiring prior knowledge of functional forms.
Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology, where the complex nature of these systems often makes a bottom up approach to modeling unfeasible. In recent years, sparse estimation techniques have gained prominence in system identification, primarily using parametric paradigms to efficiently capture system dynamics with minimal model complexity. In particular, the Sindy algorithm has successfully used sparsity to estimate nonlinear systems by extracting from a library of functions only a few key terms needed to capture the dynamics of these systems. However, parametric models often fall short in accurately representing certain nonlinearities inherent in complex systems. To address this limitation, we introduce a novel framework that integrates sparse parametric estimation with nonparametric techniques. It captures nonlinearities that Sindy cannot describe without requiring a priori information about their functional form. That is, without expanding the library of functions to include the one that is trying to be discovered. We illustrate our approach on several examples related to estimation of complex biological phenomena.