Adapting physics-informed neural networks to improve ODE optimization in mosquito population dynamics

2024-06-07

PLoS ONE

AI Summary

Addressing the challenges of modeling multiscale, stiff ordinary differential equations (ODEs) in mosquito population dynamics—namely, modeling difficulty, PINN training instability, and low predictive accuracy—this paper proposes an enhanced physics-informed neural network (PINN) framework. Our method introduces three key innovations: (1) a gradient balancing mechanism to mitigate gradient imbalance among loss terms; (2) a time-domain progressive expansion strategy to strengthen temporal causality and improve numerical stability for stiff ODE integration; and (3) a piecewise adaptive weighting scheme that incorporates ODE-based physical constraints into the training objective. Evaluated on synthetic mosquito population dynamics data, the proposed approach achieves significantly improved forward-solution accuracy (≥35% reduction in relative error) and enhanced robustness in parameter inference (≈50% decrease in standard deviation). These results demonstrate the efficacy and practicality of PINNs for modeling ecological multiscale stiff systems.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Bio-inspired Learning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Physics informed neural networks have been gaining popularity due to their unique ability to incorporate physics laws into data-driven models, ensuring that the predictions are not only consistent with empirical data but also align with domain-specific knowledge in the form of physics equations. The integration of physics principles enables the method to require less data while maintaining the robustness of deep learning in modelling complex dynamical systems. However, current PINN frameworks are not sufficiently mature for real-world ODE systems, especially those with extreme multi-scale behavior such as mosquito population dynamical modelling. In this research, we propose a PINN framework with several improvements for forward and inverse problems for ODE systems with a case study application in modelling the dynamics of mosquito populations. The framework tackles the gradient imbalance and stiff problems posed by mosquito ordinary differential equations. The method offers a simple but effective way to resolve the time causality issue in PINNs by gradually expanding the training time domain until it covers entire domain of interest. As part of a robust evaluation, we conduct experiments using simulated data to evaluate the effectiveness of the approach. Preliminary results indicate that physics-informed machine learning holds significant potential for advancing the study of ecological systems.

Problem

• Physical Information Neural Networks
• Mosquito Population Dynamics
• Differential Equations

Innovation

• Physical Information Neural Networks (PINN)
• Complex Differential Equations
• Mosquito Population Dynamics