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 modeling 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.

翻译：物理信息神经网络因其独特能力而日益受到关注，该能力可将物理定律融入数据驱动模型，确保预测不仅与经验数据一致，而且符合以物理方程形式呈现的领域特定知识。物理原理的集成使该方法能够在保持深度学习对复杂动力系统建模鲁棒性的同时，减少对数据量的需求。然而，当前PINN框架对于现实世界常微分方程系统尚不够成熟，特别是针对具有极端多尺度行为的系统，如蚊子种群动力学建模。在本研究中，我们提出了一种改进的PINN框架，用于常微分方程系统的正演与反演问题，并以蚊子种群动力学建模为案例进行应用。该框架解决了蚊子常微分方程带来的梯度失衡与刚性难题。该方法通过逐步扩展训练时间域直至覆盖整个目标区域，提供了一种简单而有效的途径来解决PINN中的时间因果性问题。作为稳健评估的一部分，我们使用模拟数据进行了实验以评估该方法的有效性。初步结果表明，物理信息机器学习在推进生态系统研究方面具有显著潜力。