Learning stochastic process-based models of dynamical systems from knowledge and data.

Area of Science:

• Systems biology
• Computational modeling
• Data-driven science

Background:

• Addressing structural and parameter uncertainty in model identification is critical for systems biology but underexplored.
• Existing methods often handle parameter uncertainty but neglect structural uncertainty or oversimplify it.
• Process-based modeling offers flexibility for structural uncertainty but is limited to deterministic models.

Purpose of the Study:

• To extend process-based modeling to inductively learn stochastic models from both knowledge and data.
• To develop a unified approach for modeling dynamical systems that integrates structural and parameter uncertainty.
• To enable automated induction of model structure and parameters from diverse data sources.

Main Methods:

• Combining process-based modeling for structural uncertainty with stochastic modeling benefits.
• Implementing a search strategy across plausible model structures guided by the parsimony principle.
• Integrating parameter estimation to identify optimal model structure and parameters simultaneously.

Main Results:

• Successfully reconstructed gene regulatory network structures and parameters from synthetic data.
• Accurately identified epidemic outbreak models from real-world, sparse, and noisy epidemiological data.
• Demonstrated the method's utility across four distinct stochastic modeling tasks in two domains.

Conclusions:

• The developed method provides a unified framework for dynamical systems modeling.
• It allows flexible formalization of candidate model structures and handles both deterministic and stochastic dynamics.
• The approach automates the induction of model structure and parameters, reconstructing models from both synthetic and real data.