Physics-Informed Machine Learning with Autoencoders and LSTM for Probabilistic Space Weather Modeling and Forecasting

Space Weather (SW) is represented by multiple complex dynamical systems coupled together and driven by solar activity, which is difficult to predict. The uncertainty in solar activity propagates through the dynamical systems downstream to the space-atmosphere interaction region with operational and societal impacts. Characterizing the impact of input uncertainty is a crucial aspect of decision making. The computational cost of modeling the different SW dynamical systems limits our ability to accurately quantify uncertainty in nowcasts and forecasts. The cost also limits comprehensive exploration of the parameter space necessary for statistically significant scientific investigations. In this work, we demonstrate an approach for developing quasi-physical, nonlinear, reduced-order models based in physics-informed machine learning. The model encapsulate state-of-the-art physical knowledge learnt through simulation data but carries a very small fraction of the computational expense.

The main idea behind reduced order modeling is separating spatial and temporal variations. Reducing the state of the high-dimensional complex SW dynamical systems can be achieved in different ways. One such technique uses autoencoders (AEs), a type of artificial neural network (ANN). The advantage of using AEs over standard dimensionality reduction methods such as principal component analysis (PCA) is that it can embed nonlinear mappings or processes using a small number of dimensions. We build upon previous work and demonstrate the development of a nonlinear reduced order model for thermospheric mass density using simulation data from the Thermosphere Ionosphere Electrodynamics Global Circulation Model (TIE-GCM) to extract and embed state-of-the-art physical knowledge. The latent state is then married with another kind of neural network, the Long-Short Term Memory network for modeling and forecasting the temporal variations while accounting for the hysteric properties. In general, the method is widely applicable across dynamical systems and can greatly facilitate probabilistic modeling and forecasting of space weather.