Fast and precise inference on diffusivity in interacting particle systems.

Area of Science:

• Computational Biology
• Statistical Physics
• Agent-Based Modeling

Background:

• Particle systems are widely used to model biological phenomena, from cellular behavior to herd dynamics.
• Brownian motion is a common model for random particle movement, with diffusion coefficient estimated via mean squared displacement.
• The mean squared displacement method struggles with sparse data and frequent agent interactions.

Purpose of the Study:

• To develop an efficient inference method for diffusion coefficients in large, interacting particle systems.
• To address limitations of the mean squared displacement method in complex scenarios.
• To accurately account for emergent effects like anomalous diffusion.

Main Methods:

• Derivation of a conjugate relationship in the diffusion term for large interacting particle systems.
• Application of the novel method to an agent-based model with numerous interacting particles.
• Comparison of the new method against a naive mean squared displacement approach.

Main Results:

• The developed method accurately models anomalous diffusion arising from mechanical interactions.
• Significant performance improvements were observed compared to the naive mean squared displacement method.
• The new method demonstrates superior accuracy in estimating diffusion coefficients.

Conclusions:

• The derived conjugate relationship offers an efficient inference method for diffusion coefficients.
• This approach enhances the analysis of particle systems, particularly in biological applications.
• The method provides improved diffusion coefficient estimates over existing techniques for systems exhibiting Brownian motion.