An Efficient Numerical Technique for Solving the Inverse Gravity Problem of Finding a Lateral Density

The main goal of our paper is to construct a technique for the gravity inversion problem of finding a variable density in a horizontal layer on the basis of gravitational data. This technique consists of two steps: extracting the gravitational field and solving the linear integral equation of the density. After discretization and approximation of integral operator, this problem is reduced to solving large systems of linear algebraic equations. To solve these systems, we proposed a memory-efficient algorithm based on the iterative method of minimal residuals. The idea of memory optimization is based on exploiting the block-Toeplitz structure of coefficients matrix. The algorithms were parallelized and implemented using the Uran and UrFU supercomputers. A model problem with synthetic gravitational data was solved

Review of deep learning approaches in solving rock fragmentation problems

One of the most significant challenges of the mining industry is resource yield estimation from visual data. An example would be identification of the rock chunk distribution parameters in an open pit. Solution of this task allows one to estimate blasting quality and other parameters of open-pit mining. This task is of the utmost importance, as it is critical to achieving optimal operational efficiency, reducing costs and maximizing profits in the mining industry. The mentioned task is known as rock fragmentation estimation and is typically tackled using computer vision techniques like instance segmentation or semantic segmentation. These problems are often solved using deep learning convolutional neural networks. One of the key requirements for an industrial application is often the need for real-time operation. Fast computation and accurate results are required for practical tasks. Thus, the efficient utilization of computing power to process high-resolution images and large datasets is essential. Our survey is focused on the recent advancements in rock fragmentation, blast quality estimation, particle size distribution estimation and other related tasks. We consider most of the recent results in this field applied to open-pit, conveyor belts and other types of work conditions. Most of the reviewed papers cover the period of 2018-2023. However, the most significant of the older publications are also considered. A review of publications reveals their specificity, promising trends and best practices in this field. To place the rock fragmentation problems in a broader context and propose future research topics, we also discuss state-of-the-art achievements in real-time computer vision and parallel implementations of neural networks

Parallel Algorithm for Solving the Inverse Two-Dimensional Fractional Diffusion Problem of Identifying the Source Term

This paper is devoted to the development of a parallel algorithm for solving the inverse problem of identifying the space-dependent source term in the two-dimensional fractional diffusion equation. For solving the inverse problem, the regularized iterative conjugate gradient method is used. At each iteration of the method, we need to solve the auxilliary direct initial-boundary value problem. By using the finite difference scheme, this problem is reduced to solving a large system of a linear algebraic equation with a block-tridiagonal matrix at each time step. Solving the system takes almost the entire computation time. To solve this system, we construct and implement the direct parallel matrix sweep algorithm. We establish stability and correctness for this algorithm. The parallel implementations are developed for the multicore CPU using the OpenMP technology. The numerical experiments are performed to study the performance of parallel implementations