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Deep learning is a promising approach to early DRV (Design Rule Violation) prediction. However, non-deterministic parallel routing hampers model training and degrades prediction accuracy. In this work, we propose a stochastic approach, called LGC-Net, to solve this problem. In this approach, we develop new techniques of Gaussian random field layer and focal likelihood loss function to seamlessly integrate Log Gaussian Cox process with deep learning. This approach provides not only statistical regression results but also classification ones with different thresholds without retraining. Experimental results with noisy training data on industrial designs demonstrate that LGC-Net achieves significantly better accuracy of DRV density prediction than prior arts. 

The Earth's magnetosheath and cusps emit soft X‐rays due to the charge exchange between highly charged solar wind ions and exospheric hydrogen atoms. The Lunar Environment Heliospheric X‐ray Imager and Solar wind Magnetosphere Ionosphere Link Explorer missions are scheduled to image the Earth's dayside magnetosphere system in soft X‐rays to investigate global‐scale magnetopause reconnection modes under varying solar wind conditions. The exospheric neutral hydrogen density distribution, especially the value of this density at the subsolar magnetopause is of particular interest for understanding X‐ray emissions near this boundary. This paper estimates the exospheric density during solar minimum using the X‐ray Multimirror Mission (XMM) astrophysics observatory. We selected an event on 12 November 2008 from the XMM data archive, which detects soft X‐rays of magnetosheath origin while solar wind and interplanetary magnetic field conditions are relatively constant. During the event the location of the magnetopause was measured in situ by the THEMIS mission, thus the location of the solar wind ions responsible for the magnetosheath emission is well constrained by observation. We estimated the exospheric density using the Open Geospace Global Circulation Model (OpenGGCM) and a spherically symmetric exosphere model. The ratio of the magnetosheath plasma flux between the OpenGGCM model and the THEMIS, was nearly 1, which means the magnetohydrodynamic model reasonably reproduces the magnetosheath plasma conditions. The OpenGGCM magnetosheath parameters were used to deconvolve soft X‐rays of exospheric origin from the XMM signal. The lower‐limit of the exospheric density of this solar minimum event is 36.8 ± 11.7 cm⁻³at 10 R_Esubsolar location.