Parameter estimation in a nonlinear dynamic model of an aquatic ecosystem with meta-heuristic optimization

Abstract

Parameter estimation in dynamic models of ecosystems is essentially an optimization task. Due to the characteristics of ecosystems and typical models thereof, such as non-linearity, high dimensionality, and low quantity and quality of observed data, this optimization task can be very hard for traditional (derivative-based or local) optimization methods. This calls for the use of advanced meta-heuristic approaches, such as evolutionary or swarm-based methods. In this paper, we conduct an empirical comparison of four meta-heuristic optimization methods, and one local optimization method as a baseline, on a representative task of parameter estimation in a nonlinear dynamic model of an aquatic ecosystem. The five methods compared are the differential ant-stigmergy algorithm (DASA) and its continuous variant (CDASA), particle swarm optimization (PSO), differential evolution (DE) and algorithm 717 (A717). We use synthetic data, both without and with different levels of noise, as well as real measurements from Lake Bled. We also consider two different simulation approaches: teacher forcing, which makes supervised predictions one (small) time step ahead, and full (multistep) simulation, which makes predictions based on the history predictions for longer time periods. The meta-heuristic global optimization methods for parameter estimation are clearly superior and should be preferred over local optimization methods. While the differences in performance between the different methods within the class of meta-heuristics are not significant across all conditions, differential evolution yields the best results in terms of quality of the reconstructed system dynamics as well as speed of convergence. While the use of teacher forcing simulation makes parameter estimation much faster, the use of full simulation produces much better parameter estimates from real measured data.