🤖 AI Summary
This study addresses the challenge of parameter identification in Lotka–Volterra predator–prey models under sparse and noisy observations, where conventional optimization methods often fail to converge due to irregular likelihood landscapes and numerical instability or stiffness arising from ordinary differential equation (ODE) solvers across the parameter space. To overcome these issues, the authors propose a computational framework integrating natural gradient ascent. They first employ nondimensionalization to eliminate redundant scale parameters, thereby reducing the dimensionality of the optimization problem. Additionally, they devise a component-separated adaptive ODE integration strategy that dynamically switches between two second-order equations to mitigate numerical instabilities. Experimental results demonstrate that the proposed method achieves stable convergence in fewer iterations compared to standard gradient ascent and BFGS, significantly enhancing both the reliability and efficiency of parameter estimation from sparse data.
📝 Abstract
Parameter identification from observations of dynamical systems is a fundamental problem in population biology. Mechanistic models of ecological systems rely on optimization methods that require accurate initial guesses to guarantee convergence. In ecological applications, datasets contain observation noise and are collected at sparse time points. This sparsity creates irregular likelihoods that cause standard optimization methods to struggle, while the ordinary differential equation solvers can become stiff or unstable in certain regions of the parameter space. These instabilities cause long running times or runtime errors. Here we present a computational framework for parameter identification that addresses these numerical instabilities by employing Natural Gradient Ascent, and we apply it to the classical Lotka-Volterra predator-prey model. We exploit the non-dimensionalization of the ordinary differential equations to treat scaling factors as nuisance parameters, reducing the dimensionality of the optimization problem. To prevent the solver step from becoming small, we implement an adaptive solver that switches between two independent second-order equations derived from the two components of the model. This approach allows Natural Gradient Ascent to converge in fewer iterations and with more stability than standard gradient ascent or BFGS methods. This framework provides a reliable method for parameter estimation in ecology when data is limited. The method can be generalized to other dynamical systems as long as the different components of the system do not become numerically problematic at the same time.