Research on Multi-Parameter Optimization of Coupled Models Using PINN Based on Numerical Mode

Traditional data assimilation methods may lead to erroneous parameter estimation due to system parameter compensation effects. In recent years, with the emergence of neural network technology, particularly the introduction of Physics-Informed Neural Networks (PINN), it has become possible to effectively embed physical models into neural networks to optimize biased parameters. However, the traditional PINN-RK framework is limited to solving models that couple a single physical quantity, which integrates Runge-Kutta nodes into the neural network loss function. The study introduces a novel PINN-MCS framework based on PINN-RK. The PINN-MCS can flexibly integrate neural networks with multivariable coupled models. To improve performance when optimizing multiple parameters simultaneously, we set the initial learning rate based on the sensitivity of the parameters in the physical model. This strategy has been proven in the study to accelerate the overall parameter convergence. This research conducted perfect twin and biased twin experiments on a Five Variable Coupled Climate Model. In the perfect twin experiment, system bias arises from imperfect parameter values. The experimental results show that the PINN-MCS framework can efficiently optimize parameters with various sensitivities to the true values. In the biased twin experiment, system bias arises from imperfect numerical discretization schemes. The results show that after optimizing the initial parameters using observational data generated by the imperfect dynamical core, the optimized parameters can compensate for the system bias introduced by the numerical scheme, improving the model's predictive performance.