Parameter estimation and analysis for agent-based models in biology

Prerequisites: Differential equations, linear algebra, statistics (regression models), python programming.

Outline: Agent-based models (ABMs) are widely used across several areas of biology. However, practitioners using ABMs for research encounter several challenges, both computationally and analytically, when the processes described include heterogeneity in agent behavior or complex spatial landscapes. To overcome these challenges, this project will employ recently developed machine learning techniques to derive differential equation (DE) approximations to ABMs. We will derive DE approximations for ABMs that were previously developed to describe processes in ecology, epidemiology, and cell biology, and determine whether the DEs can be used for accurate parameter estimation as well as equilibrium and stability analysis.

Objectives: Students will apply methods from machine learning to derive DE approximations to several biologically relevant ABMs and their extensions, and then use several methods for computational and mathematical analysis, including sensitivity, identifiability, equilibria and stability analysis to understand the key processes that drive the behavior of the ABMs.

Outcomes: The students will gain experience in techniques from machine learning, statistics, agent-based modeling, and python programming. All code generated will be made open-source through github for public use. We expect there to be at least one publication from the research.

References:
JT Nardini, RE Baker, MJ Simpson, KB Flores (2021) Learning differential equation models from stochastic agent-based model simulations. Journal of the Royal Society Interface 18:20200987. https://royalsocietypublishing.org/doi/10.1098/rsif.2020.0987