A New Hybrid PINN for High-Resolution Spatiotemporal Nowcasting of Stratospheric and Mesospheric States

High-precision prediction of atmospheric environmental parameters is vital for high-altitude balloon experiments, aerospace missions, and climate simulation research. While traditional numerical weather prediction (NWP) models solve atmospheric partial differential equations (PDEs), their high computational cost limits short-term forecast timeliness. Pure data-driven deep learning models improve efficiency but often violate physical laws, leading to overfitting and poor generalization.

To address these issues, Physics-Informed Neural Networks (PINNs) integrate data-driven learning with physical equations by incorporating PDEs as soft constraints in the loss function. However, standard PINNs struggle with high-dimensional spatiotemporal prediction due to training instability and convergence difficulties, especially in multi-scale, nonlinear atmospheric systems.

In response to the above issues, this study proposes a new PINN framework that combines hard constraints and soft constraints for high-resolution short-term and near-term prediction of wind, temperature, density and air pressure within an altitude range of 10 to 70 km. The core innovation lies in a novel network design that enforces symbolic constraints and the equation of state via hard constraints, while incorporating atmospheric dynamics equations through soft constraints, thereby creating a complementary optimization mechanism. Specifically, hard constraints strictly ensure the positivity of key variables (such as air pressure and temperature) by modifying the output structure of the network. Soft constraints are based on the Navier-Stokes equation in spherical coordinate form, introducing the residual terms of momentum conservation and mass conservation into the loss function as physical regularization terms. In addition, this study is the first to verify the model using actual stratospheric balloon flight test data. By comparing the observation results of the SENSORs project in the Qinghai region of China in 2019, the prediction accuracy and stability of the model in real scenarios are evaluated.

The experimental results show that the hybrid constrained PINN framework proposed in this study has achieved remarkable effects in the case of Qinghai region (90°-100°E, 30°-40°N). This method effectively suppresses non-physical oscillations while maintaining the physical consistency of the prediction results, reducing the root mean square error of short-term and near-term forecasts by approximately 28% compared to pure data-driven models. This method demonstrates superior generalization performance and stability in tasks ranging from sparse training data (0.5°×0.5°×2 km) to high-resolution predictions (0.25°×0.25°×1 km). Meanwhile, the collaborative mechanism of hard constraints and soft constraints significantly enhances the physical interpretability of the model, providing a new reliable approach for high-precision and high-efficiency numerical prediction in complex atmospheric environments.