Enhancing generalizability of model discovery across parameter space with multi-experiment equation learning for...

Area of Science:

• Computational Biology
• Systems Biology
• Mathematical Modeling

Background:

• Agent-based modeling (ABM) is crucial for studying self-organizing biological systems but is computationally demanding and lacks analytical tractability.
• Equation learning (EQL) derives continuum models from ABM data, yet requires extensive simulations per parameter set, limiting generalizability.

Purpose of the Study:

• To extend EQL to Multi-experiment equation learning (ME-EQL) for improved model generalizability and interpretability.
• To introduce and evaluate two novel ME-EQL methods: one-at-a-time ME-EQL (OAT ME-EQL) and embedded structure ME-EQL (ES ME-EQL).

Main Methods:

• Developed OAT ME-EQL to learn individual models per parameter set, connected via interpolation.
• Developed ES ME-EQL to construct a unified model library across parameter sets.
• Applied ME-EQL methods to a noisy birth-death mean-field model and an on-lattice ABM of birth, death, and migration.

Main Results:

• Both ME-EQL methods significantly reduced relative error in parameter recovery from ABM simulations.
• OAT ME-EQL demonstrated superior generalizability across the parameter space.
• The methods successfully learned continuum models from complex spatial agent-based models.

Conclusions:

• ME-EQL enhances the efficiency and generalizability of deriving continuum models from ABM data.
• These methods offer a powerful approach for analyzing complex biological systems and interpreting simulation results.
• Future work can leverage ME-EQL for broader applications in computational biology and systems science.