Physics Guided Neural Networks For Solar Wind Prediction

Project Summary

Solar wind modeling is categorized into empirical and physics-based models that both predict its properties in different parts of the heliosphere. Empirical models are relatively inexpensive to run and have shown great success at predicting the solar wind at the L1 Lagrange point. Physics-based models provide more sophisticated scientific modeling based on magnetohydrodynamics (MHD) codes that are computationally expensive to run. In this paper we propose to combine empirical and physics based model by developing a physics-guided neural network for solar wind prediction. To the best of our knowledge, this is the first attempt to forecast solar wind by combining data-driven methods with physics constrains. Our results shows the superiority of our physics-constrained model compared to other state-of-the-arts deep learning predictive models.

Figure:1 A plot of the modified Ohm's law relationship. Red dots, representing the values of the electrical field, plotted on the y axis, are lower than the L2 norm of the cross product of the velocity field with the magnetic field, plotted on the x axis. The equality of the two is plotted in green. This relationship is something we can take advantage of to train neural networks.

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Requirements

pyomnidata (installable with pip)
torch (pytorch.org)
numpy
matplotlib
sklearn (scikit-learn.org)

Data

The data we used for this analysis is the publicly available OMNI dataset from NASA. This dataset is available in general from the NASA website omniweb.gsfc.nasa.gov , but is more easily accessible for data science purposes through the pyomnidata module from the python package index. The notebook below goes through the process of pulling, validating and normalizing the data to prepare it for our neural networks.

While the embedded notebook shows off a good example, it is only one run of many we collected data over. To better understand the effect of different normalizations and lambda values, we show the following graphs.

Figure 2: Bar charts showing the probabilities of obtaining an R squared value of greater than 0.1 (green) or greater than 0 (orange). Reading from top left, shown are the results from our Time Based CNN, ResNet, RotateNet, GRU, and LSTM networks. On the left of each graph is the probability grouped by normalization, and on the right is the probability grouped by the weight of the physics value Lambda.

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