The disturbance storm time (Dst) index is an important and useful measurement in space weather research. It has been used to characterize the size and intensity of a geomagnetic storm. A negative Dst value means that the Earth's magnetic field is weakened, which happens during storms. In this paper, we present a novel deep learning method, called the Dst Transformer, to perform short-term, 1-6 hour ahead, forecasting of the Dst index based on the solar wind parameters provided by the NASA Space Science Data Coordinated Archive. The Dst Transformer combines a multi-head attention layer with Bayesian inference, which is capable of quantifying both aleatoric uncertainty and epistemic uncertainty when making Dst predictions. Experimental results show that the proposed Dst Transformer outperforms related machine learning methods in terms of the root mean square error and R-squared. Furthermore, the Dst Transformer can produce both data and model uncertainty quantification results, which can not be done by the existing methods. To our knowledge, this is the first time that Bayesian deep learning has been used for Dst index forecasting.

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In this chapter, the authors have proposed a SIT model to eradicate the pest population. It has been assumed that the females after mating with wild males grow logistically. Pest population is being controlled with the release of sterile insects in their habitat. The model is formulated with the system of differential equations, and the authors have discussed the local stability analysis of deterministic logistic growth rate model. Further, they have also obtained a potential function by incorporating one-dimensional insect release with an invasion on patch size L, which has a toxic exterior as its surrounding. It has been obtained that, in the presence of spatial spread over a finite patch size, the sterile release of the insects produces a sudden declination of the pest population. Finally, the authors have obtained the optimal production of sterile male population using Pontryagin's maximum principle. The applicability of the proposed model is finally illustrated through numerical solution.