Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie)
“Numerical Methods and Programming” is a peer-reviewed scientific research journal, which was founded and is published by the Research Computing Center of Lomonosov Moscow State University (RCC MSU). The journal publishes the results of new scientific, practical and theoretical studies obtained in the field of computational mathematics, mathematical modeling, software for computing machines, complexes and networks, as well as their applications. The editorial board of the journal accepts for consideration author's materials of high quality, prepared in the form of an original article or review. The novelty and scientific significance of the work are verified by reviewers and editors. The journal is published with a periodicity of 4 issues per year. Publication of articles is free of charge. The published papers are publicly available to all Internet users. The journal “Numerical Methods and Programming” is registered as a scientific electronic periodical by the Federal Service for Supervision of Communications, Information Thechnology, and Mass Media (certificate of registration No. 77-4356, ISSN 1726-3522). The journal is included in the RSCI bibliographic database (Russian Science Citation Index), in “The White List” of the Russian Center of Scientific Information, in the core of the Russian Science Citation Index and in All-Russian Mathematical Portal MathNet.Ru. The journal belongs to category K1 of the Higher Attestation Commission List (Russian Federation) of leading peer-reviewed scientific journals and publications recommended for the publication of the main results of dissertations for the degree of doctor of science and PhD. Bibliographic information on published papers is placed in the scientific citation database of the RSCI. Articles published in the journal are assigned doi (since 2015). Full texts of all articles of the journal are placed in pdf-format in the Scientific Electronic Library of the Russian Federation (elibrary.ru) for free access. [more]
Научно-Исследовательский Вычислительный Центр Московского Государственного Университета имени М. В. Ломоносова
Optimal investment in S&P 500 using SDDP and the implied-calibrated ARMA–GARCH model
We study a dynamic portfolio optimization problem in which probabilistic forecasts of the S&P 500 index are derived from option market prices. To overcome the limitations of classical approaches to reconstructing implied density from option prices which fail to generate conditional multi-period return distributions, we propose a method that involves calibrating the discrete-time ARMA–GARCH model from the observed call option prices in a risk-neutral measure with subsequent transition to a physical measure using a representative-agent framework. The calibrated model provides conditional multi-period distributions of asset returns, which are used to construct scenario lattices in multi-stage stochastic optimization. The resulting portfolio optimization problem is formulated as a multi-stage stochastic programming problem. At each stage, a weighted combination of the expected negative objective value for the next stage and the Conditional Value-at-Risk (CVaR) is minimized. The optimization is performed by means of the Stochastic Dual Dynamic Programming (SDDP) method. Historical simulations over the period 2019–2023 demonstrate that the proposed option-calibrated ARMA–GARCH–SDDP method consistently outperforms benchmark approaches based on static implied densities, equal-probability scenarios, and buy-and-hold investment. The results underscore the economic value of using option-implied information in portfolio management.
Methods and algorithms of computational mathematics and their applications
stochastic dual dynamic programming (SDDP)
Copyright (c) 2026 П.А. Арбузов, Д.Ю. Голембиовский https://creativecommons.org/licenses/by/4.0
Estimation of three-phase relative permeabilities from the results of two-phase pore-scale numerical simulation
The article presents a parallel algorithm for numerical simulation of two-phase flows in digital rock images. The algorithm is based on the phase-field method and the finite-difference approach, which includes solving the Poisson equation using conjugate gradients with a spectral preconditioner. The domain decomposition method and CUDA and MPI technologies are used to parallelize the algorithm. The algorithm is applied to calculate the relative phase permeabilities using the steady-state method for oil and water, oil and CO2 in a supercritical form. Based on the calculated two-phase permeabilities, ternary relative permeability diagrams are constructed for a three-phase system using the Stone I, Stone II, and Baker models. The justification of the choice of liquid parameters for two-phase modeling is carried out.
Copyright (c) 2026 Д.И. Прохоров, В.Д. Чепеленкова, В.В. Лисица https://creativecommons.org/licenses/by/4.0
Finding optimal vertex on polytope of feasible solutions to linear programming problem
A new scalable AlEM algorithm for linear programming on cluster computing systems is presented. Unlike the classical simplex method, the AlEM algorithm, at each step, examines all edges coming from the current vertex of the polytope of feasible solutions, which guarantees the construction of a suboptimal path and completely prevents circling in degenerate problems. A formalized description of the algorithm and its parallel implementation using the MPI library is given.The scalability of the parallel version of the algorithm on real and synthetic linear programming problems has been experimentally investigated. The results of computational experiments confirm the high parallel efficiency of the AlEM algorithm, which remains at least 46% when using up to 200 processor nodes. It is shown that the AlEM algorithm is a possible alternative to existing linear programming methods for high-performance computing.
Copyright (c) 2026 А. Э. Жулев, Леонид Борисович Соколинский https://creativecommons.org/licenses/by/4.0
Adaptation of octree meshes for modeling supersonic airfoils and calculating tip vortex
Solutions to problems of supersonic flow around the X-43 experimental aircraft and wingtip vortex modeling are presented using a unique adaptive mesh design based on the octree principle and an irregular base mesh. Unlike traditional adaptive Cartesian meshes, the base mesh cells can be shaped not only as cubes and parallelopipeds, but also as arbitrary oblique hexagons and can be connected in any way. This allows the geometry and known features of the solution to be taken into account in the base mesh, while adaptation is used only for unknown features. While maintaining the same accuracy, the mesh size is significantly smaller than with the traditional approach. The mesh manipulation tools are implemented as a library of functions using MPI, independent of the aerodynamics portion of the program.
Copyright (c) 2026 А.Е. Луцкий, А.В. Северин https://creativecommons.org/licenses/by/4.0
Software for solving gas dynamics problems using completely conservative difference schemes with adaptive artificial viscosity
An approach to the numerical solution of the equations of gas dynamics with usage of completely conservative difference schemes with adaptive artificial viscosity is considered. Computational algorithms were developed and software implementing the proposed method within a client-server architecture was created. The client part is written in JavaScript (React), the server part is realized in Go, and the computing core is implemented in C++. Such an organization provides convenient web access, scalability, and high performance in solving hyperbolic tasks. To verify the accuracy and stability of the implemented method, numerical experiments were carried out on classical test problems of gas dynamics — on the Sod and Einfeldt problems. The obtained results confirmed the correct reproduction of shock waves, contact discontinuities and the absence of instabilities. The developed software can serve as a basic platform for further extension to spatially multidimensional formulations and the inclusion of additional physical effects.
Parallel software tools and technologies
completely conservative difference scheme
Copyright (c) 2026 Х. Чжан https://creativecommons.org/licenses/by/4.0
High-performance implementation of exponential functions for RISC-V processors
The development of a high-performance vector library for standard mathematical functions represents a significant objective for the advancement of HPC on platforms based on the RISC-V architecture. This paper presents a detailed implementation of the exp, exp2, and expm1 functions for double-precision, single-precision, and half-precision floating-point types. Special attention is paid to aspects of computational accuracy and performance. A detailed comparison with other existing vector math libraries for the RISC-V architecture is provided.
01.02.EW COMPUTER SCIENS, SOFTWARE ENGINEERING
Copyright (c) 2026 Е. А. Панова, В. Д. Волокитин, Е.А. Козинов, И.Б. Мееров https://creativecommons.org/licenses/by/4.0
Three-dimensional time-dependent multiphase model of local melting processes for stationary and moving continuous bodies
A multiphase mathematical model has been developed and verified to describe the dynamics of stationary and moving continuous bodies undergoing local melting under gravity and surface tension forces. The key element is a modified acceleration source that enables imposing target translational or rotational velocities on the object. Its action smoothly diminishes within the first-order phase transition zone and becomes spatially localized near the phase interface through the introduction of temperature-dependent and phase-based multipliers. The model is adapted to work with arbitrary volumetric heat sources. A series of computational experiments established optimal ranges for the calibration parameters, ensuring a balance between high accuracy, numerical stability, and acceptable computational cost. Verification was confirmed through agreement with analytical solutions. The model is applicable for numerical analysis of welding, cladding, induction melting, and similar processes.
Copyright (c) 2025 Р. С. Рубля, С. А. Никифоров, И. В. Шварц, А. Х. Гильмутдинов https://creativecommons.org/licenses/by/4.0
Modifications of the ant colony matrix method for parametric optimization using CUDA-based GPUs
This article focuses on the development and investigation of the matrix-based modifications of the Ant Colony Optimization (ACO) method for solving parametric optimization problems using CUDA-based Graphics Processing Units (GPUs). Unlike most existing studies focusing on the Traveling Salesman Problem (TSP), the proposed method is specialized for finding optimal values of independent parameters, which leads to a different graph structure and requires the development of novel parallelization schemes. Original parallelization strategies are proposed, including a three-stage decomposition of the algorithm and introduction of “parameter-level” parallelism in the problem dimensions. Various strategies for parallelization and memory management were developed and tested: from the basic MatrixACO-Basic modification to the optimized versions of MatrixACO-Optimization (featuring warp reduction and optimized hash-table handling) and MatrixACO-Transported (utilizing transposed data storage). Experiments were conducted on NVIDIA Tesla V100 16GB SXM2 GPU, the Jetson ORIN platform, and various personal computers using multi-dimensional test functions. Results demonstrate that for a problem with 128 parameters the optimized version of MatrixACO-Optimization provides an execution time of 0.13 ms per graph layer, which corresponds to a speed-up of more than 30 times compared to the optimized CPU implementation based on OpenMP, and in the case of a very large-scale problem with 65536 parameters it speeds up by almost 45 times. For a problem with 512 parameters, the GPU realization shows 76% higher energy efficiency compared to the CPU version, as well as an almost eightfold (7.9 times) reduction in Energy-Delay Product. The study confirms the necessity of developing specialized GPU implementations for parametric tasks and reveals the excellent scalability of the proposed algorithms.
Copyright (c) 2026 Ю.П. Титов https://creativecommons.org/licenses/by/4.0
Review of methods for describing the structure of algorithms
Algorithms are the basis of the entire computational process within the traditional chain “problem–method–algorithm–implementation”, and the effective use of their properties, structure, features and characteristics can provide a multiple reduction in the time of their implementation on a specific computing system. This review paper examines the methods used to describe the structure of computational algorithms. It also examines collections of algorithm descriptions available online, providing a brief description of the areas from which algorithms are described and how they are described.
01.02.EX COMPUTER SCIENS, THEORY & METHODS
Copyright (c) 2025 А. С. Антонов https://creativecommons.org/licenses/by/4.0
Numerical solution of determining the initial condition problem in Cauchy problem for hyperbolic equation with small parameter
The textconsiders the inverse problem of determining theinitialcondition fora singularly perturbed hyperbolic equation with a small parameter. This involves finding an unknown odd function using additional information about the derivative of the solution at a fixed spatial point. The main result of the text is to reduce the ill-posed initial problem to a Volterra integral equation of the second kind. An iterative method has been developed for numerically solving this equation. Computational experiments were conducted to test the effectiveness of this algorithm.
Copyright (c) 2026 Д.С. Андрианов https://creativecommons.org/licenses/by/4.0
New approaches for automatic analysis of HPC application performance using the TASC software suite
This paper presents new automatic analysis approaches for identifying performance issues and useful properties in jobs running on a supercomputer. Methods for detecting problematic application classes, such as “hung” programs and jobs with underutilized nodes, are proposed. New assessments for automatic preliminary evaluation of GPU processors and memory usage efficiency are developed and tested as well. These approaches extend the functionality of the existing TASC software suite designed for conducting comprehensive analysis of usage quality of modern supercomputers.
01.02.ET COMPUTER SCIENS, INFORMATION SYSTEMS
Copyright (c) 2025 В. А. Матвеев, А. В. Сетяев, В. В. Воеводин https://creativecommons.org/licenses/by/4.0
Two decades of algorithmic Feynman integral reduction
We present a historiographical review of algorithms and computer codes developed for solving integration-by-parts relations for Feynman integrals. This procedure is one of the key steps in the evaluation of Feynman integrals, since it enables to express integrals belonging to a given family as linear combinations of master integrals. In this review, we restrict ourselves to considering general algorithms which can, in principle, be applied to any family of Feynman integrals.
Copyright (c) 2025 А. В. Смирнов, В. А. Смирнов https://creativecommons.org/licenses/by/4.0
Computational efficiency and adaptation of radiation transfer module within Large-eddy simulation model
This paper examines the results of integrating the Rapid Radiative Transfer Model for GCMs (RRTMG) into the Large-Eddy simulation model developed by the Lomonosov Moscow State University Research Computing Center (RCC MSU). To test the integrated radiative transfer module, we conducted conduct analysis of the influence of turbulent aerosol particle transport on the diurnal dynamics of the atmospheric boundary layer under clear-sky conditions and in experiments modeling cold air bursts in the Arctic. A study of the sensitivity of the modeling results to the synchronization frequency of the radiative module with the dynamics core of the model revealed that the modeling results are within the ensemble spread for synchronization times much shorter than the characteristic turbulent time of the flow. This finding coupled with an analysis of the scalability of the overall computational algorithm, demonstrates that the combined models can be effectively applied to numerical analysis of direct and indirect aerosols effects, as well as to modeling cloud feedbacks.
Copyright (c) 2025 А. В. Дебольский, Е. В. Мортиков, А. А. Полюхов https://creativecommons.org/licenses/by/4.0
Scalability study of parallel algorithm for numerical modeling of plasma confinement in open magnetic traps using simulation modeling methods
This article presents a methodology for evaluating the scalability of parallel algorithms. Instead of conducting costly experiments on supercomputers, we propose using a specialized simulation model. The methodology involves studying and developing the communication and computation scheme of the tested algorithm, creating a simulation model based on the actor model, configuring for a specific supercomputer architecture, and investigating its scalability. The article demonstrates the application of this methodology to a numerical modeling problem for plasma confinement in open magnetic traps. The results indicate 85% scaling efficiency of the algorithm for thousands of cores.
01.01.PO Mathematics, Interdisciplinary Applications
Copyright (c) 2025 И. Г. Черных, Д. В. Винс, В. А. Вшивков, М. А. Боронина https://creativecommons.org/licenses/by/4.0
A method for constructing fully interpretable linear regressions with statistically significant estimates according to the Student’s criterion and insignificant intercorrelation coefficients
The article is devoted to the urgent problem of constructing interpretable machine learning models, namely, multiple linear regression models. To estimate their unknown parameters, ordinary least squares is used. A probabilistically-statistical definition of fully interpretable linear regression is formulated. Its construction involves selecting the optimal number of most informative regressors based on determination coefficients in order to ensure consistency between the signs of regression coefficients and the substantive meanings of variables. Additionally, estimates are ensured to be significant and intercorrelation coefficients insignificant by using Student’s t-test. To construct fully interpretable regressions, we propose a method that uses mixed 0-1 integer linear programming. Both strict and non-strict versions of this method are considered. Computational experiments were carried out, which in most cases showed the effectiveness of the proposed method compared to the generating all subsets method.
01.02.EP Computer science, artificial intelligence
Copyright (c) 2025 М. П. Базилевский https://creativecommons.org/licenses/by/4.0
Numerical algorithm to estimate formation factor of digital rocks
The paper presents a numerical algorithm of estimating the formation factor for digital rock samples constructed using microtomographic images. The algorithm is based on the numerical solution of the three-dimensional Poisson equation with rapidly changing high-contrast coefficients. The arising system of linear algebraic equations turns out to be ill-conditioned, so to speed up the convergence it is necessary to use a preconditioner. The conjugate gradient method is applied to solve the system and the preconditioner is constructed as the inverse Laplace operator corresponding to the homogeneous model. In its turn, the spectral decomposition of two tridiagonal matrices appearing in the approximation of one-dimensional derivatives is used for inversion. The resulting series of one dimensional problems is solved by the Thomas algorithm. The used preconditioner can be effectively applied both to the original problem with rapidly changing high-contrast coefficients and to the problem, in which the solution is calculated only in the pore space. In the latter case, the method provides the same accuracy of results as the original one for inhomogeneous models, but it converges almost twice as fast. Implementation using graphics processors allows solving problems up to 109 unknowns with a single GPU.
Copyright (c) 2025 А. А. Манаев, Т. С. Хачкова, В. В. Лисица https://creativecommons.org/licenses/by/4.0
Acceleration of numerical simulation of seismic data for monitoring the burial of CO₂ using a neural network
Seismic monitoring of greenhouse gases accumulations and injection in reservoir is critical for evaluating the safety and efficiency of injection and preventing leakage. Small changes in reservoir properties caused by fluid displacement lead to changes in seismic attributes. At the same time, modelling of seismic wavefield propagation is resource-consuming due to the need to solve the problem for a series of seismogeological models of the medium corresponding to different stages of fluid injection. The paper presents an algorithm for seismic modelling using a finite-difference method and a neural network to suppress numerical errors in seismograms when applied to the problem of seismic monitoring of greenhouse gas disposal. The algorithm speeds up calculations up to 4 times due to the application of the neural network to rapidly calculated seismograms using a coarse computational grid.
01.02.EP COMPUTER SCIENS, ARTIFICIAL INTELLIGENCE
Copyright (c) 2025 Е. А. Гондюл, В. В. Лисица, Д. М. Вишневский https://creativecommons.org/licenses/by/4.0
Applying Composable Parallelism in Programs Using Parallel
As the number of computational cores and the threads utilizing them increases, the overhead associated with thread scheduling, creation, and destruction grows, while the amount of computation performed by each individual thread decreases. Multilevel parallelism is a way to address this issue. One potential source of such parallelism is the optimization of functions within libraries called from parallel programs. However, this approach may require additional support at the level of parallel programming models. In our study, we propose an alternative implementation of the OpenMP runtime library and evaluate its efficiency using the OpenBLAS library and the High Performance Linpack (HPL) benchmark on Arm-based systems.
Copyright (c) 2025 А. С. Колганов, Н. А. Катаев, В. А. Бахтин, Д. А. Захаров, А. А. Смирнов, А. А. Малахов https://creativecommons.org/licenses/by/4.0
Numerical method for modeling multiscale dynamics of gas-dispersed media with two relaxation parameters based on Smoothed Particle Hydrodynamics
In some applications, it is advisable to simulate the dynamics of gas-dispersed media using the particle method. In this case, when using the particle-particle approach to calculate the interphase interaction, there is a problem of excess dissipation when solving problems with a small parameter. It is known that the particle-mesh approach solves this problem in the case of one relaxation process (momentum exchange). The work is an experimental study of the possibilities of extending this approach to the case of two relaxation processes (momentum and thermal energy exchange). The test problem is the problem of the motion of a plane sound wave, which has a reference solution for small-amplitude waves. The modes are considered in which the relaxation times are significantly longer, comparable, and significantly shorter than the wave period. It is found that the method under consideration does not introduce dissipation into the solution even with a small number of particles in a cell, but introduces excess counting dispersion in the mode when the relaxation times are comparable to the wave period. To reduce the level of dispersion, it is necessary to increase the number of particles in the cell (up to 5 in the one-dimensional case) and select the time step according to the Courant condition, in which the length scale is the distance from the particle to its nearest neighbor.
Copyright (c) 2025 Т.А. Савватеева https://creativecommons.org/licenses/by/4.0
Algorithm for applying the structural adaptation criterion to solve problems using adaptive mesh refinement
Adaptive mesh refinement (AMR) is widely used in solving modern mathematical modeling problems. The specifics of the implementation of numerical methods for AMR require compliance with certain ratios between the linear sizes of adjacent elements, which are called the structural criterion. Structural criterion allows creation of buffer layer of cells between regions, which cell division level difference is greater than two. In this paper we discuss the algorithm for buffer layer generation for tree-based adaptive mesh refinement on distributed computational system. Estimates of the algorithmic complexity and efficiency of the algorithm on distributed computational system are obtained. Experiments have shown the possibility of algorithm for forming a buffer layer in areas of complex shape, but at the same time its poor scalability with an increasing number of processes.
Copyright (c) 2025 С. К. Григорьев, П. А. Кучугов https://creativecommons.org/licenses/by/4.0
Improved method of recognizing marine and coastal system objects based on combination of local binary pattern method and neural network technologies
The work proposes a hybrid model LBP+PSPNet to increase the accuracy of oil spill segmentation on RGB-images of remote sensing of the Earth, especially in conditions of low contrast between pollution and marine background. The model combines local texture feature extraction (LBP) with global context analysis based on Pyramid Scene Parsing Network (PSPNet). LBP enhances the detail of the texture features of oil film, which are often masked by solar flares or small spots. PSPNet provides large-scale image analysis, which allows for the precise segmentation of both large spills and low-level pollution. Experiments showed that LBP integration increases the IoU metric by 4.6% compared to the basic PSPNet architecture. The proposed model reaches F1-measure 0.85 when tested on low contrast scenarios, demonstrating resistance to noise and atmospheric distortions. The results confirm the effectiveness of synthesis of classical methods of texture analysis and deep learning for environmental monitoring tasks.
01.01.PO MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Copyright (c) 2025 А. И. Сухинов, Д. А. Соломаха https://creativecommons.org/licenses/by/4.0
Modified axisymmetric contact smoothed particle hydrodynamics method with the possibility of modeling surface tension
The conservation accuracy of total momentum and total energy is important in modeling many physical problems, including capillary phenomena, since non-physical acceleration can lead to incorrect deformation of free surfaces. Because the standard axisymmetric CSPH method of Parshikov does not satisfy the conservation laws, a modified axisymmetric CSPH method is considered to improve the accuracy of preserving the total momentum and the total energy. An external pressure boundary condition is proposed for the CSPH method. This boundary condition is used for surface tension modeling with the new axisymmetric CSPH method. The verification of the surface tension model is performed for three test cases: modeling the establishment of Laplace pressure in a water droplet, modeling small oscillations of a water droplet (comparing the period of small oscillations with Rayleighʼs formula), and modeling the effect of surface tension on a thin film (comparing the velocity of propagation of rims created by surface tension with Taylor-Culickʼs formula). A simulation of the development of Rayleigh-Plateau instability is conducted.
Copyright (c) 2025 Г. Д. Рублев https://creativecommons.org/licenses/by/4.0
Control of the Gasoline Catalytic Reforming Process Based on a Kinetic Model Using an Artificial Neural Network
This study presents an approach to accelerated modeling of one of the key processes in the oil refining industry — catalytic reforming of gasoline — using a deep neural network. The product of catalytic reforming constitutes the majority of commercial gasoline and determines its octane number. In addition, aromatic hydrocarbons are formed during the process, the content of which can be regulated by adjusting the reaction conditions. The aim of the study was to develop a model capable of replacing resource-intensive direct calculations for evaluating the output parameters of the process, thereby enabling real-time analysis and control. Traditional methods require significant time and computational resources, making them unsuitable for rapid deployment in industrial environments. The training dataset was generated based on the results of direct simulations performed in MATLAB. A significant reduction in data generation time was achieved through the use of parallel computing. Optimal hyperparameters for the neural network were identified. Model training was carried out using the minimization of the mean squared error (MSE) and the coefficient of determination (R²). The developed model demonstrates high prediction accuracy with minimal computational time, which makes it especially suitable for implementation in automated control systems at oil refineries. The resulting neural network approximation effectively acts as a simulator capable of instantaneously estimating key parameters of the catalytic reforming process, including reformate yield, content of aromatic hydrocarbons and benzene, and the octane number of the mixture.
01.02.EV COMPUTER SCIENS, INTERDISCIPLINARY APPLICATIOONS
Copyright (c) 2025 К. Ф. Коледина, Р. Р. Минигалиев, С. Н. Коледин https://creativecommons.org/licenses/by/4.0
A software system for automated assessment of stereoscopic distortions in VR180 videos
The paper presents a comprehensive software system for automatically evaluating stereoscopic distortions in VR180 video. The proposed approach takes into account the most common types of artifacts: color mismatches, differences in sharpness, geometric distortions (vertical shift, rotation, scaling), and channel mismatches. Specialized algorithms have been developed for each type of distortion, based on disparity maps, motion vectors and their confidence maps, as well as neural network regression or classification methods. The proposed solutions have been successfully tested on several datasets, demonstrating high accuracy in detecting various types of distortions in VR180 video. The system can be integrated into standard post-processing pipelines and provides automated generation of detailed reports, allowing stereoscopic content creators to quickly identify and eliminate stereoscopic distortions before releasing their products to a wide audience.
Copyright (c) 2025 С.В. Лаврушкин https://creativecommons.org/licenses/by/4.0
Structure-oriented smoothing for wave propagation modelling by beam method with frequency dependence
This paper considers an empirical method for obtaining a frequency-dependent velocity model using structure-oriented smoothing. Smoothing is performed depending on the source position, frequency, and time field. Three smoothing methods are implemented: smoothing along a locally flat wavefront, smoothing by anisotropic diffusion and volumetric smoothing in the Fresnel zone. Anisotropic diffusion smoothing time is compared with the frequency of the smoothing in the Fresnel zone. A comparison of smoothing methods is carried out, showing that volumetric smoothing in the Fresnel zone provides the most stable solution.
Copyright (c) 2025 А. Д. Штейн, М. И. Протасов https://creativecommons.org/licenses/by/4.0
A structural two-level neural network approach to joint inversion of gravitational and magnetic fields
The paper proposes a new two-level neural network approach to joint inversion of gravitational and magnetic fields in the problem of mineral exploration. The lower level uses two neural networks with equivalent architecture. The first network calculates the distribution of gravitational field sources in a given domain based on measurements of this field on a certain remote surface. The second one finds the distribution of magnetic field sources in the same area based on magnetic field measurements. At the upper level, a structural residual between the two obtained source distributions is calculated, which determines the “degree of difference” of their geometries. The resulting neural network is trained to minimize this structural discrepancy. As a result, this two-level system implements a computational algorithm that finds geometrically close sources of fields of different nature. Test simulations demonstrate the high quality of joint inversion of model gravitational and magnetic fields within the proposed aproach.
joint processing of gravitational and magnetic fields
Copyright (c) 2025 Янфей Ван, Д. В. Чурбанов, Р. Л. Аргун, А. В. Горбачев, А. С. Леонов, Д. В. Лукьяненко https://creativecommons.org/licenses/by/4.0
Constructor of soil carbon dynamic models
This paper introduces a carbon cycle model constructor (CCMC) — a software framework for specifying and solving systems of equations in soil carbon cycle models. The CCMC is based on the structure of a generalized system of ordinary differential equations with a multiplicative representation of mass transfer rates between pools. Most known carbon cycle models found in the literature are special cases of this system. The current implementation allows users to select a model from established formulations (INMCM soil block, SOCS, RothC), provide external environmental state variables, and define a spatial–temporal grid to simulate the evolution of soil carbon content. The CCMC enables subject-matter experts in biology, ecology, soil science, and Earth system dynamics to utilize the implemented mathematical models without requiring specialized knowledge in computational mathematics or programming.
Copyright (c) 2025 Г. М. Файкин, В. М. Степаненко, А. И. Медведев, С. К. Шангареева, И. М. Рыжова, В. А. Романенков, И. Т. Хусниев https://creativecommons.org/licenses/by/4.0
Application of the nudging technique to produce initial states for the INM RAS climate model seasonal hindcasts
This study examines the implementation of nudging in the INM RAS global coupled climate model to improve the initial states for seasonal hindcasts. We compare results of three nudging experiments with both reanalyses data and ensemble of CMIP6 historical experiments. The results show that nudging significantly reduces model biases in atmosphere and ocean fields. The experiment with nudging excluding lower atmospheric levels yields the best performance by minimizing the impact of the relaxation procedures on the model physics in the atmosphere boundary layer. We compare the quality of the hindcasts for November–March obtained with different initialization techniques. The initialization approach using nudging outperforms other initialization methods for hindcasts of the Northern Hemisphere winter season with one-month lead time. However, for the first forecast month the full field initialization demonstrates the best results. The study highlights that nudging in the ocean model is essential to maintain hindcast skill over longer lead times and proposes nudging as a promising approach for initialization of the annual-to-decadal climate predictions.
01.02.EV Computer Science, Interdisciplinary Applications
01.05.QQ METEOROLOGY & ATMOSPHERIC SCIENCES
Copyright (c) 2025 М. А. Тарасевич, Е. М. Володин https://creativecommons.org/licenses/by/4.0
Systematic numerical search of steady-state solutions for the system of coupled Nonlinear Schrodinger Equations with additional double-well potential
We study stationary solutions of a system of coupled Nonlinear Schrodinger equations with additional double-well potential. In the theory of Bose-Einstein Condensate (BEC) these equations are called the Gross-Pitaevskii equations and the system describes the dynamics of a sigar-shape BEC cloud that consists of atom of two types. Stationary solutions of the system (called also "nonlinear modes") satisfy a system of two non-autonomous ODEs. The problem is stated as follows: it is necessary (i) to find all localized (i.e., that vanish at plus and minus infinity) solutions of this ODE system that coexist for given parameter values and (ii) to justify the completeness of the search conducted. For this purpose, we employed the method of "filtering out" solutions with singularities developed by our team previously. It consists in scanning of some area in the space of initial data for the Cauchy problem for the system. While this procedure, the solutions that have singularities (i.e., that tend to infinity at a finite value of argument) are detected and excluded from consideration. The diagnostics of the singularities and the criterium for the scanning to stop are based on rigorous mathematical statements. As a result, we identify the parameter regions where nonlinear modes of different types exist ("bright-dark solitons", "dark-dark solitons" etc.)
Copyright (c) 2025 Н.А. Куценко, Г.Л. Алфимов https://creativecommons.org/licenses/by/4.0
Scheme of solution of the heat and mass transfer problem in the hydration model of cement composite
The paper presents a developed model of related physical and chemical processes in reacting medium, according to which a cement composite is considered as a heterogeneous mixture of reagents and filler with specified concentrations and porosity. Water filtration due to capillary and thermocapillary forces ensures convective heat and mass transfer. The heat and mass transfer problem is presented as a two-temperature non-stationary nonlinear boundary value problem of heat conductivity of the frame and liquid phase with heat sources of chemical nature and sinks caused by water evaporation. Verification of the adequacy of the developed scheme for solving the boundary value problem of thermal conductivity is realized by solving a test one-dimensional problem with constant coefficients. The convergence of the problem solution scheme is confirmed in the process of modeling the hydration process of a cement composite at different steps in time and space.
1.02.EV “Computer sciens, interdisciplinary applications”
Copyright (c) 2025 М.А. Дмитриева, В.Н. Лейцин, А.Д. Когай https://creativecommons.org/licenses/by/4.0