Predicting and Reconstructing Aerosol–Cloud–Precipitation Interactions with Physics-Informed Neural Networks

Interactions between clouds, aerosol, and precipitation are crucial aspects of weather and climate. The simple Koren–Feingold conceptual model is important for providing deeper insight into the complex aerosol–cloud–precipitation system. Recently, artificial neural networks (ANNs) and physics-informed neural networks (PINNs) have been used to study multiple dynamic systems. However, the Koren–Feingold model for aerosol–cloud–precipitation interactions has not yet been studied with either ANNs or PINNs. It is challenging for pure data-driven models, such as ANNs, to accurately predict and reconstruct time series in a small data regime. The pure data-driven approach results in the ANN becoming a “black box” that limits physical interpretability. We demonstrate how these challenges can be overcome by combining a simple ANN with physical laws into a PINN model (not purely data-driven, good for the small data regime, and interpretable). This paper is the first to use PINNs to learn about the original and modified Koren–Feingold models in a small data regime, including external forcings such as wildfire-induced aerosols or the diurnal cycle of clouds. By adding external forcing, we investigate the effects of environmental phenomena on the aerosol–cloud–precipitation system. In addition to predicting the system’s future, we also use PINN to reconstruct the system’s past: a nontrivial task because of time delay. So far, most research has focused on using PINNs to predict the future of dynamic systems. We demonstrate the PINN’s ability to reconstruct the past with limited data for a dynamic system with nonlinear delayed differential equations, such as the Koren–Feingold model, which remains underexplored in the literature. The main reason that this is possible is that the model is non-diffusive. We also demonstrate for the first time that PINNs have significant advantages over traditional ANNs in predicting the future and reconstructing the past of the original and modified Koren–Feingold models containing external forcings in the small data regime. We also show that the accuracy of the PINN is not sensitive to the value of the regularization factor (λ), a key parameter for the PINN that controls the weight for the physics loss relative to the data loss, for a broad range (from λ=1×103 to λ=1×105).