Physics-based dynamic models (PBDMs) are simplified representations of complex dynamical systems. PBDMs take specific processes within a complex system and assign a fragment of variables and an accompanying set of parameters to depict the processes. As this often leads to suboptimal parameterisation of the system, a key challenge requires refining the empirical parameters and variables to reduce uncertainties while maintaining the model s explainability and enhancing its predictive accuracy. We demonstrate that a hybrid mosquito population dynamics model, which integrates a PBDM with Physics-Informed Neural Networks (PINN), retains the explainability of the PBDM by incorporating the PINN-learned model parameters in place of its empirical counterparts. Specifically, we address the limitations of traditional PBDMs by modelling the parameters of larva and pupa development rates using a PINN that encodes complex, learned interactions of air temperature, precipitation and humidity. Our results demonstrate improved mosquito population simulations including the difficult-to-predict mosquito population peaks. This opens the possibility of hybridisation concept application on other complex systems based on PBDMs such as cancer growth to address the challenges posed by scarce and noisy data, and to numerical weather prediction and climate modelling to overcome the gap between physics-based and data-driven weather prediction models.

翻译：基于物理的动态模型（PBDMs）是复杂动力系统的简化表示。PBDMs提取复杂系统中的特定过程，并分配一组变量及伴随的参数集来描述这些过程。由于这通常会导致系统的参数化不够理想，一个关键挑战在于需要优化经验参数和变量，以在保持模型可解释性的同时减少不确定性并提高其预测精度。我们证明，一种将PBDM与物理信息神经网络（PINN）相结合的混合蚊子种群动态模型，通过用PINN学习得到的模型参数替代其经验参数，保留了PBDM的可解释性。具体而言，我们通过使用一个编码了气温、降水和湿度之间复杂学习交互作用的PINN来建模幼虫和蛹发育速率的参数，从而解决了传统PBDMs的局限性。我们的结果表明，蚊子种群模拟得到了改进，包括难以预测的蚊子种群峰值。这为将混合概念应用于其他基于PBDM的复杂系统（如癌症生长）以应对数据稀缺和噪声带来的挑战，以及应用于数值天气预报和气候建模以弥合基于物理的模型与数据驱动的天气预报模型之间的差距，提供了可能性。