Bi-level identification of governing equations for nonlinear physical systems

Area of Science:

• Nonlinear dynamics
• Machine learning
• Systems biology

Background:

• Identifying governing equations from observational data is vital for understanding complex nonlinear systems.
• Overfitting poses a significant challenge in equation discovery from data.

Purpose of the Study:

• To introduce a novel framework, Bi-Level Identification of Equations (BILLIE), for simultaneous equation discovery and validation.
• To leverage reinforcement learning for robust equation identification.

Main Methods:

• Implementation of a bi-level optimization strategy using policy gradient algorithms from reinforcement learning.
• Testing the BILLIE framework on canonical nonlinear systems, including turbulent flows and three-body systems.
• Application of BILLIE to discover RNA and protein velocity equations from single-cell sequencing data.

Main Results:

• BILLIE demonstrated superior performance compared to baseline methods in identifying equations for nonlinear systems.
• The framework successfully discovered RNA and protein velocity equations from single-cell data.
• Identified equations outperformed empirical models in predicting cellular differentiation states.

Conclusions:

• The BILLIE framework offers a powerful approach for discovering and validating governing equations from observational data.
• BILLIE shows significant potential for revealing fundamental physical laws across diverse scientific fields, including systems biology.