Bayesian uncertainty quantification for data-driven equation learning.

Area of Science:

• Computational Science
• Systems Biology
• Data Science

Background:

• Equation learning infers differential equation models from observational data.
• Previous studies focused on noise-free or low-noise data for accurate model identification.
• The impact of observation noise on the uncertainty of learned differential equation models is largely unexplored.

Purpose of the Study:

• To investigate the relationship between observation noise and uncertainty in learned differential equation models.
• To develop methods for quantifying uncertainty in equation learning using multiple datasets.
• To draw mechanistic conclusions about underlying differential equations from noisy data.

Main Methods:

• Employed equation learning techniques combined with Bayesian inference.
• Utilized simulation data from an agent-based model (ABM) with a known partial differential equation description.
• Applied Bayesian inference to obtain posterior parameter distributions for uncertainty quantification.

Main Results:

• Noisy datasets lead to substantial variations in both the structure and parameter values of learned differential equation models.
• The proposed approach effectively quantifies uncertainty in learned models by leveraging multiple datasets.
• Demonstrated the ability to extract mechanistic insights into the target differential equations.

Conclusions:

• Observation noise significantly impacts the reliability of differential equation models learned from data.
• Combining multiple datasets with Bayesian inference provides a robust framework for uncertainty quantification in equation learning.
• This methodology enables more reliable model discovery and mechanistic understanding from complex, noisy data.