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Directional oil well drilling requires high precision of the wellbore positioning inside the productive area. However, due to specifics of engineering design, sensors that explicitly determine the type of the drilled rock are located farther than 15m from the drilling bit. As a result, the target area runaways can be detected only after this distance, which in turn, leads to a loss in well productivity and the risk of the need for an expensive re-boring operation.We present a novel approach for identifying rock type at the drilling bit based on machine learning classification methods and data mining on sensors readings. We compare various machine-learning algorithms, examine extra features coming from mathematical modeling of drilling mechanics, and show that the real-time rock type classification error can be reduced from 13.5% to 9%. The approach is applicable for precise directional drilling in relatively thin target intervals of complex shapes and generalizes appropriately to new wells that are different from the ones used for training the machine learning model.

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Change points are abrupt alterations in the distribution of sequential data. A change-point detection (CPD) model aims at quick detection of such changes. Classic approaches perform poorly for semi-structured sequential data because of the absence of adequate data representation learning. To deal with it, we introduce a principled differentiable loss function that considers the specificity of the CPD task. The theoretical results suggest that this function approximates well classic rigorous solutions. For such loss function, we propose an end-to-end method for the training of deep representation learning CPD models. Our experiments provide evidence that the proposed approach improves baseline results of change point detection for various data types, including real-world videos and image sequences, and improve representations for them. * This work is supported by the Russian Science Foundation (project 20-71-10135) Preprint. Under review.

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Abstract. In this paper we generalize the Deuring theorem on a reduction of elliptic curve with complex multiplication. More precisely, for an Abelian variety A, arising after reduction of an Abelian variety with complex multiplication by a CM field K over a number field at a pace of good reduction. We establish a connection between a decomposition of the first truncated Barsotti-Tate group scheme A[p] and a decomposition of pO K into prime ideals. In particular, we produce these explicit relationships for Abelian varieties of dimensions 1, 2 and 3.