Data Assimilation (DA) techniques, such as Kalman filtering, have historically been employed in engineering applications, but are rarely used by mathematical modelers or taught to mathematics students. However, because of DA's fusing of mechanistic modeling with machine-learning approaches, it holds great potential for strengthening the predictive power of deterministic mathematical models. For biological models particularly, nonlinearity and sparse, noisy data both complicate the implementation of DA methods and highlight their benefit. We present a case-study implementation of model-fitting using the Unscented Kalman Filter (UKF) on a well-known ODE system (the Lotka-Volterra Predator-Prey model) with a published data set. We compare model-fitting outcomes from UKF with model fits from two other well-understood techniques: Particle Swarm Optimization (PSO) and Delayed Rejection Adaptive Metropolis (DRAM) and examine potential complications when models grow in dimensionality and complexity. Our aim is to present a practical user's perspective on the implementation and use of UKF and to share our experiences, insights, and recommendations for fitting simple dynamical systems models in biology.
A mathematical modeling exploration of data assimilation for simple model fitting
Christina Catlett, Scripps CollegeAuthors: Christina Catlett, Lisette de Pillis, An Dela, Christina J. Edholm, Daniel Shenker, Blerta Shtylla, Rachel Wander, Maya Watanabe
2022 AWM Research Symposium
Recent Developments in Ecological and Epidemiological Modeling