Iterative Calculation Research Articles

Deep-learning-assisted inverse design of polarization-multiplexed structural color filters with ultrahigh saturation based on all-dielectric metasurface

Although great progress has been made for metasurface-based structural color filters, there are still significant challenges in encoding metasurfaces with complex color images, especially in high saturation or multi-channel cases, where traditional iterative optimization calculations demand substantial computational resources. Here, we proposed a dual-channel multilayered all-dielectric metasurface that can generate structural colors accounting for 224% Standard RGB space, 168% Adobe RGB space and 78% of the 1931 CIE chromaticity space under vertically-polarized incidence. A deep learning-based designing approach is introduced to significantly reduce the computing consumption while maintaining high accuracy. Numerical simulations further demonstrated that the proposed design method is effective for encoding both complementary and independent images with high saturation and wide color gamut. Therefore, the proposed color filters may find potential applications in image display, information encryption and optical anti-counterfeiting.

Internal-multiple-elimination with application to migration using two-way wave equation depth-extrapolation scheme

Internal multiple interference, affecting both seismic data processing and interpretation, has been observed for long time. Although great progress has been achieved in developing a variety of internal-multiple-elimination (IME) methods, how to increase accuracy and reduce cost of IME still poses a significant challenge. A new method is proposed to effectively and efficiently eliminate internal multiples, along with its application in internal-multiple-eliminated-migration (IMEM), addressing this issue. This method stems from two-way wave equation depth-extrapolation scheme and associated up/down wavefield separation, which can accomplish depth-extrapolation of both up-going and down-going wavefields simultaneously, and complete internal-multiple-elimination processing, adaptively and efficiently. The proposed method has several features: (1) input data is same as that for conventional migration: source signature (used for migration only), macro velocity model, and receiver data, without additional requirements for source/receiver sampling; (2) method is efficient, without need of iterative calculations (which are typically needed for most of IME algorithms); and (3) method is cost effective: IME is completed in the same depth-extrapolation scheme of IMEM, without need of a separate processing and additional cost. Several synthesized data models are used to test the proposed method: one-dimensional model, horizontal layered model, multi-layer model with one curved layer, and SEG/EAGE Salt model. Additionally, we perform a sensitivity analysis of velocity using smoothed models. This analysis reveals that although the accuracy of velocity measurements impacts our proposed method, it significantly reduces internal multiple false imaging compared to traditional RTM techniques. When applied to actual seismic data from a carbonate reservoir zone, our method demonstrates superior clarity in imaging results, even in the presence of high-velocity carbonate formations, outperforming conventional migration methods in deep strata.

POE-Based Error Modeling and Multiple Plane Constraint-Based Parameter Identification for the Kinematic Calibration of a 4-UPS/SPR Parallel External Fixator

Limb deformity is a common complaint in orthopedic surgery. Currently, gradual treatment using parallel external fixator (PEF) has become the preferred option for deformity correction. As the key medical apparatus with the special application properties of temporary assembly and direct utilization, the geometric errors generated during the manufacturing and assembly process of the PEF contribute to the post-correction residual and iatrogenic deformities. However, considering the complexity of clinical scenarios, there is a lack of an applicable solution to reduce the effect of the above error source of PEF. To overcome these problems, taking a 4-UPS/SPR PEF as the research object, this paper proposes a novel kinematic calibration method. First, the error model with the features of completeness, continuity, and minimality is first established based on the product of exponentials (POE) formula. Then, the identifiability analysis is conducted to eliminate the redundant error parameters and ensure the stability and accuracy of the iterative calculation in the process of parameter identification. Furthermore, a multiple plane constraint (MPC)-based parameter identification approach is introduced to the calibration task of the PEF to effectively reduce the difficulty of the pose information measurement in the current cost-effective constraint calibration method. Finally, the simulation and prototype experiments validate that the proposed calibration method (i.e., the combination of the POE-based error model and the MPC-based parameter identification approach) can accomplish the calibration tasks in clinical applications and meet the cost-effectiveness and efficiency requirements.

Computer-vision-based artificial intelligence for detection and recognition of instruments and organs during radical laparoscopic gastrectomy for gastric cancer: a multicenter study

Objective: To investigate the feasibility and accuracy of computer vision-based artificial intelligence technology in detecting and recognizing instruments and organs in the scenario of radical laparoscopic gastrectomy for gastric cancer. Methods: Eight complete laparoscopic distal radical gastrectomy surgery videos were collected from four large tertiary hospitals in China (First Medical Center of Chinese PLA General Hospital [three cases], Liaoning Cancer Hospital [two cases], Liyang Branch of Jiangsu Province People's Hospital [two cases], and Fudan University Shanghai Cancer Center [one case]). PR software was used to extract frames every 5-10 seconds and convert them into image frames. To ensure quality, deduplication was performed manually to remove obvious duplication and blurred image frames. After conversion and deduplication, there were 3369 frame images with a resolution of 1,920×1,080 PPI. LabelMe was used for instance segmentation of the images into the following 23 categories: veins, arteries, sutures, needle holders, ultrasonic knives, suction devices, bleeding, colon, forceps, gallbladder, small gauze, Hem-o-lok, Hem-o-lok appliers, electrocautery hooks, small intestine, hepatogastric ligaments, liver, omentum, pancreas, spleen, surgical staplers, stomach, and trocars. The frame images were randomly allocated to training and validation sets in a 9:1 ratio. The YOLOv8 deep learning framework was used for model training and validation. Precision, recall, average precision (AP), and mean average precision (mAP) were used to evaluate detection and recognition accuracy. Results: The training set contained 3032 frame images comprising 30 895 instance segmentation counts across 23 categories. The validation set contained 337 frame images comprising 3407 instance segmentation counts. The YOLOv8m model was used for training. The loss curve of the training set showed a smooth gradual decrease in loss value as the number of iteration calculations increased. In the training set, the AP values of all 23 categories were above 0.90, with a mAP of 0.99, whereas in the validation set, the mAP of the 23 categories was 0.82. As to individual categories, the AP values for ultrasonic knives, needle holders, forceps, gallbladders, small pieces of gauze, and surgical staplers were 0.96, 0.94, 0.91, 0.91, 0.91, and 0.91, respectively. The model successfully inferred and applied to a 5-minutes video segment of laparoscopic gastroenterostomy suturing. Conclusion: The primary finding of this multicenter study is that computer vision can efficiently, accurately, and in real-time detect organs and instruments in various scenarios of radical laparoscopic gastrectomy for gastric cancer.

A semi-analytic method for buoyancy-induced thermal stratification in hot water tanks during standby periods

Buoyancy-induced thermal stratification is a spontaneous phenomenon arising from standby periods of hot water tanks. Accurate estimation of temperature levels is crucial for energy-efficient operations of hot water tanks and associated water heating systems. However, temperature estimation by numerical schemes requires sophisticated algorithms and considerable computation resources. This study proposes a novel semi-analytic method to address buoyancy-induced thermal stratification conveniently without iterative calculations. An explicit water temperature function to tank height and time is analytically derived from the modified energy balance equation where the heat convection term is disregarded. The convection effect is compensated for by artificial enhancement of heat conduction, which is indicated by a synthetic parameter, amplification factor. A comprehensive numerical study is carried out to investigate static and transient characteristics of buoyant flows and temperature distribution in a hot water tank during standby periods. The findings imply a strong analogy between buoyancy-induced thermal stratification and a bottom-initiated heat conduction process, which reinforces the physical rationale for the semi-analytic method. The experimental verification of the semi-analytic method is conducted against published experiment data, the proposed method shows excellent estimation accuracy with the rooted mean square error of less than 0.42 °C. Furthermore, suitable case-specific amplification factors are determined with numerical simulations, and a ready-for-use correlation equation of the amplification factor is formulated for a wide range of tank volumes and aspect ratios. This novel semi-analytic method substantially reduces computation time compared with numerical solvers, and the simple form of the water temperature function can help in formulating more detailed hot water tank models in energy system studies.

Optimization of Sparse Matrix Computation for Algebraic Multigrid on GPUs

AMG is one of the most efficient and widely used methods for solving sparse linear systems. The computational process of AMG mainly consists of a series of iterative calculations of generalized sparse matrix-matrix multiplication (SpGEMM) and sparse matrix-vector multiplication (SpMV). Optimizing these sparse matrix calculations is crucial for accelerating solving linear systems. In this paper, we first focus on optimizing the SpGEMM algorithm in AmgX, a popular AMG library for GPUs. We propose a new algorithm called SpGEMM-upper, which achieves an average speedup of 2.02x on Tesla V100 and 1.96x on RTX 3090 against the original algorithm. Next, through experimental investigation, we conclude that no single SpGEMM library or algorithm performs optimally for most sparse matrices, and the same holds true for SpMV. Therefore, we build machine learning-based models to predict the optimal SpGEMM and SpMV used in the AMG calculation process. Finally, we integrate the prediction models, SpGEMM-upper, and other selected algorithms into a framework for adaptive sparse matrix computation in AMG. Our experimental results prove that the framework achieves promising performance improvements on the test set.

A Hybrid Continuation Framework for Analyzing Nonlinear Normal Modes of Systems With Contact Nonlinearity

Abstract The prediction of the modal properties of structural systems with contact clearances and prestress presents a computational challenge, as the nonlinearity induced by piecewise-linear stiffness eliminates the use of efficient linear modal analysis techniques. The most common approach to obtaining the nonlinear normal modes (NNMs) of these structural systems is a numerical framework that integrates numerical integration, the shooting method, and the pseudo-arc-length continuation scheme. This numerical continuation framework (NCF) computes NNMs through iterative numerical calculations; thus, the computational cost of the nonlinear modal analysis of complex nonlinear systems, particularly piecewise-linear systems, becomes prohibitively expensive as the model size increases. In this study, a hybrid continuation framework (HCF) combining analytic and numerical methods is proposed to enable efficient computations of NNMs for systems with contact boundaries. This new hybrid framework utilizes a semi-analytic method to conduct the iterative shooting procedure; thus, the computational burden of the numerical continuation can be significantly reduced. The proposed method is demonstrated on spring-mass oscillators with contact elements, and the NNMs obtained using the proposed method are validated by those computed using the traditional numerical continuation framework. The modal properties of the systems can be computed using the proposed framework with significant speed-up. Furthermore, the modal properties, including internal resonance and sharp turning in NNM curves, of the piecewise-linear systems are identified and discussed.

Key technologies of smart antenna in WLAN based on adaptive array

In order to improve the communication quality and transmission rate of WLAN, the key technologies of smart antenna in WLAN based on adaptive array are proposed. The adaptive array is used to suppress the WLAN interference signal, and the feedback from the output is used to adjust the weight loaded on the signal, and the optimal weight corresponding to the linear constraint minimum variance is obtained to achieve beamforming optimization. On this basis, the optimal antenna selection algorithm and the sub-optimal antenna selection algorithm are designed, and the sub-channel matrix with the maximum capacity can be obtained by repeated iterative calculation, so as to realize the smart antenna selection and further optimize the performance of WLAN. Experimental results show that the smart antenna signal has 100% coverage in WLAN compared with conventional methods. When the transmission rate is greater than 35 mb/s, the delay of the study method is not jitter compared to the contrast method. When the transmission rate is greater than 35 mb/s, the packet loss rate of the proposed method remains stable, while the packet loss rate of the two comparison methods begins to increase. When the transmission rate is greater than 12 mb/s, the throughput of the proposed method is more stable than the other methods. In conclusion, this method has the characteristics of large signal coverage, low delay, low packet loss rate and high throughput, and can be widely used in practice. The contribution of this study is that the weight of the antenna array can be dynamically adjusted through the adaptive algorithm, thus optimizing the quality of the received signal and improving the receiving sensitivity.

Combined nomograms for calculating the bearing capacity and reinforcement of high-strength and normal concrete RC columns

PurposeThis paper aims to obtain a calculation method by hand without iteration.Design/methodology/approachThis paper adopts strains as known quantities to solve the internal forces and deformations of the section, simplifies the deflection curve of the column and obtains nomograms that can calculate the bearing capacity and reinforcement of circular reinforced concrete (RC) columns by hand.FindingsNomograms include five variables: mechanical reinforcement ratio, relative normal force, dimensionless bending moment, slenderness ratio and ultimate dimensionless curvature. Nomograms corresponding to all classes of concrete have been drawn, and their dimensionless form makes them widely applicable. The calculation results of nomograms are compared and analysed with numerical calculation results, and the difference is within 5%, meeting the engineering requirements.Originality/valueCalculating the bearing capacity of compression bending components requires considering second-order effects. Therefore, the calculation of the bearing capacity of circular RC columns requires iterative calculation, as it includes dual nonlinearity of material and geometry, and the two are coupled with each other. To calculate the bearing capacity of the section adopting ordinary concrete, it is necessary to solve the transcendental equation iteratively. For high-strength concrete, it can only be solved by numerical integration. A fast calculation method by hand is proposed in this paper.

Analysis of the Mathematical Models for Identifying the Thickness of the Fouling Layer in Natural Gas Coolers

This article presents an analysis of three different approaches to the identification of the thickness of the fouling layer inside the pipes of natural gas (NG) coolers. At present, there is no existing simple analytical procedure for the identification of the fouling layer thickness. The authors of this article describe in detail the balance method, which required the use of a large number of physical parameters, changes in their sizes depending on the output temperature of the gas, the temperature of the cooling air, the air quantity, as well as the physical properties of both media. The computational model was robust, and its disadvantage was the iterative computation. The second analysed method was a dimensional analysis. It was applied using the Buckingham’s theorem to express the individual similarity criteria. In this method, 10 simplexes and two complexes were created. The fouling layer thickness, expressed using a derived criterial equation, exhibited real results. The third analysed method was based on analysing selected physical parameters with the use of a multiple regression analysis in MinitabX 18 software. The analysis showed that the fouling layer thickness depended on fewer parameters than the number of parameters assumed in the dimensional analysis or the balance method. The standard deviation that was identified in the multiple linear regression for a double crossflow cooler was 0.0667 and the value of reliability (the coefficient of determination of the multiple linear regression) R2 was 0.9985.

An integrated method for gravity gradient inversion and gravity gradient depth imaging

SUMMARY Gravity gradient data can show the structural features of geological bodies in the shallow lithosphere with higher sensitivity and resolution than conventional gravity data. Gravity gradient inversion can be applied to obtain the lithospheric density structures of geological bodies. However, as with gravity data, gravity gradient data have no inherent depth resolution. The methods of gravity gradient depth imaging and gravity gradient inversion are integrated in this study. The depth imaging method is effective for calculations without prior information and iterative computations. As the parameters in the depth weighting function should be chosen from a set of values used in inversion tests of synthetic data, which brings some uncertainties, the depth imaging results of gravity gradient are introduced into the depth weighting function. Several synthetic models are tested to demonstrate the advantages and features of the effective integrated method. Finally, the integrated method is applied to the interpretation of the GOCE satellite gravity gradient tensors over the northeastern margin of the Qinghai–Tibet Plateau. The results reveal that in the crust of the study area, the distribution of density anomalies is more in line with the mechanism of the crustal flow model, in the upper mantle of the study area, the density anomalies are mainly influenced by the high heat flow environment.

Analytical method for calculating internal forces and deformations in foundation pit support under asymmetric loading

Sheet pile walls are significant forms of foundation pit supports that are widely employed in foundation pit support projects in combination with inner bracing. The complex geological conditions, surrounding environments, and earthwork excavations associated with foundation pits generally lead to noticeable asymmetric loading on a support system, posing challenges for accurately calculating the internal forces and deformations. To study the calculation methods for the internal forces and deformations in foundation pit support structures and bracing systems under asymmetric loading, a new model was established for foundation pits subjected to asymmetric unbalanced force loading on opposite sides. This method provides an adjusting technique for bracing forces on both sides based on the principle of equalizing axial forces, thereby providing a calculation approach for the stress and deformation of the foundation pit support system. Additionally, the developed axial force iterative calculation method was compared with numerical analysis methods to analyze the stress and deformation patterns in the support structure, which validated its effectiveness and accuracy.

Analysis of the correction process for the initial field iteration calculation of the stability analysis program

As the heart of aircraft, the performance requirements of aviation engines are increasing, and analyzing the aerodynamic stability of engines has become an essential part. The methods for analyzing the stability boundary of engines at home and abroad are also gradually improving. When using a domestic engine stability analysis program, it was found that the turbine drop pressure ratio changed during the calculation process, which was inconsistent with the initial given. This article focuses on this issue and analyzes the process of parameter correction during the calculation process by analyzing the parameter changes discovered during its use. This program ensures power balance and duct and bypass outlet static pressure balance. The calculation accuracy is improved through these correction processes.

A new computationally efficient algorithm to generate global fractional vegetation cover from Sentinel-2 imagery at 10 m resolution

ABSTRACT The multi-angle method in the pixel dichotomy model (PDM) is used to produce fine spatial resolution (FSR) products of fractional vegetation cover (FVC), which involves numerous iterative computations. This phenomenon causes a low computational efficiency for global FVC. Here, we established the multi-angle equations, and simplified the two-stream approximation method to obtain multi-angle reflectance, which calculated the KDM parameters possible. Moreover, to accelerate the calculation of parameters in the multi-angle equations, land cover data were utilized as priority knowledge, which aims to decrease iterative computations to speed up the computational speed. Finally, we proposed an accelerated pixel dichotomy coupled linear kernel-driven model (PDKDM-A). By validating PDKDM-A using field measurements and FVC products, we found that the global FVC computed for various land covers exhibited strong agreement with the field measurements. The root mean square errors (RMSEs) were consistently below 0.150, except for grasslands, croplands, and cropland/natural vegetation mosaics. When comparing FVC products on the same scale, we discovered that the RMSE was less than 0.103, except for deciduous broadleaf forests. Our study demonstrates that PDKDM-A is an efficient algorithm, with the potential to quickly generate accurate global FVC products with fine spatial resolution.

Ultrasonic phased array imaging of multi-layered structures using full-matrix migration and normalized cross-correlation matching technique

Multi-layered structures play a critical role in aerospace, automotive and electrical industries, so the non-destructive evaluation and maintenance of such structures must be accurate and rapid. The application of conventional ultrasonic phased array imaging methods is limited due to computational complexity, image quality and image size. In this paper, we proposed a cost-effective, high-quality imaging method that uses full-matrix migration total focus method (FM-TFM) and produces large-area scanned image with the aid of normalized cross-correlation (NCC) template matching technique. The FM-TFM method eliminated the need for iterative refraction point calculations by using full matrix migration extrapolation, and the optimization of NCC was also investigated in the study. The verification was divided into two parts, fixed transducer experiment and manual scanned experiment, to demonstrate the advantages of FM-TFM with improved SNR (22 % or greater) and one order of magnitude reduction in computational time when compared to ray tracing total focus method (RT-TFM) and NCC matching accuracy of multilayer specimen, respectively. The proposed method can help eliminate the need for costly scanning equipment and shows great potential for extension to other TFM-based approaches.

Contribution To the Evaluation of Soot Deposit Thickness Evolution and Its Impact on Heat Transfer Within Heavy Diesel Engines: An Innovative Simplistic Procedure

This study deals with a numerical procedure designed and built to evaluate the evolution of soot deposits thickness and their impact on heat transfer for a high-pressure common rail 16V280 marine diesel engine piston. Using a combination of 3D numerical computations and an iterative calculation algorithm, this work reveals the complex relationship between soot deposit, temperature distribution, and piston thermal dynamics. Non-uniform soot deposit distribution is observed, concentrated at the piston bowl peripheral regions. This distribution aligns with theoretical expectations, indicating the influence of the swirl effect. The presence of soot deposits alters the temperature distribution, implying displacement of high-temperature zones towards the bowl region of the piston. The reduction in surface temperature of approximately 14%, is attributed to the lower heat transfer coefficient of deposited layers. This greatly influences the distribution of thermo-mechanical stresses of the piston. The proposed procedure offers an approach to assess the impact of soot deposit on heat transfer. In addition, this study contributes to a better understanding of realistic piston conditions and addresses the challenges introduced by soot deposits in heavy-duty diesel engines by combining the proposed procedure with investigations based on CFD software tools.

The mechanical properties of Al3Sc single crystal investigated by nanoindentation using Hertzian elasticity theory method and Oliver-Pharr method

The crystal structure, orientation, reduced modulus, and hardness of Al3Sc single crystal were studied using X-ray diffraction (XRD), electron backscatter diffraction (EBSD) and nanoindentation techniques, combined with Hertzian elastic theory method (Hertz) and Oliver-Pharr method (O&P). Millimeter-sized Al3Sc single crystals were prepared using quasi-equilibrium solidification of hypereutectic Al-15(wt %) Sc alloy. The XRD results showed that the samples were composed of L12-Al3Sc and Al phases. The EBSD and nanoindentation results showed that for five Al3Sc single crystals with different orientations, the reduced moduli measured by Hertz method were 146.6 ± 0.4–148.3 ± 0.2 GPa; while measured by O&P method they were 147 ± 2–150 ± 3 GPa. The corresponding hardnesses were varied between 3.8 ± 0.1 and 3.9 ± 0.1 GPa. The Poisson's ratio and elastic constants were determined through iterative calculation based on the relationship between the reduced modulus and Young’s modulus at various orientations. The polycrystal elastic properties, bulk modulus, shear modulus and Young's modulus, were determined. The elastic constants c11, c12, and c44 were 179.2 ± 0.4, 44.1 ± 0.1, and 68.3 ± 0.3 GPa, respectively; the Poisson's ratio was 0.196 ± 0.001. The Young's modulus of five Al3Sc single crystals oriented in different directions was in the narrow range 161–164 GPa. The anisotropy factor of Al3Sc crystal was 1.011 ± 0.002, confirming that it is elastically isotropic. These results provide fundamental information for the research and development of the Al3Sc intermetallic compound and related alloys in future.

A dynamic one-dimensional model for simulating unsteady air-water stratified flow in sewer pipes.

Ventilation is paramount in sanitary and stormwater sewer systems to mitigate odor problems and avert pressure surges. Existing numerical models have constraints in practical applications in actual sewer systems due to insufficient airflow modeling or suitability only for steady-state conditions. This research endeavors to formulate a mathematical model capable of accurately simulating various operational conditions of sewer systems under the natural ventilation condition. The dynamic water flow is modeled using a shock-capturing MacCormack scheme. The dynamic airflow model amalgamates energy and momentum equations, circumventing laborious pressure iteration computations. This model utilizes friction coefficients at interfaces to enhance the description of the momentum exchange in the airflow and provide a logical explanation for air pressure. A systematic analysis indicates that this model can be easily adapted to include complex boundary conditions, facilitating its use for modeling airflow in real sewer networks. Furthermore, this research uncovers a direct correlation between the air-to-water flow rate ratio and the filling ratio under natural ventilation conditions, and an empirical formula encapsulating this relationship is derived. This finding offers insights for practical engineering applications.

Study on cluster centers optimization of max-min distance k-means clustering algorithm based on inter-cluster separation measure

Clustering is an essential unsupervised technique when category information is not available. Although K-means and Max-min distance K-means clustering algorithms are widely used, they have some disadvantages such as dependence on the initial centers, sensitivity to outliers caused by using only distance as the clustering criterion. To overcome the problems, this paper proposes SMM-K-means algorithm which overcomes the dependence on the initial cluster centers and the initial number of clusters and the sensitivity to the outliers. First, the initial value K of the optimal cluster number is determined by the elbow method, and K-means is used for initial clustering. A new inter-cluster separation measure is then constructed based on the idea of q-nearest neighbors, which is constructed by comprehensive considering the separation between clusters and the distribution compactness of clusters themselves. Finally, the two sample points with highest degree of separation are brought into Max-min distance K-means algorithm as new initial centers for clustering. The definite determining method of cluster centers eliminates the complicated iterative calculation, and the construction of inter-cluster separation measure overcomes the sensitivity of clustering results to noise points and isolated points, and has good applicability and generalization. In addition, this algorithm is not limited by the shape and size of the clusters and has better flexibility. The experimental results show that the SMM-K-means algorithm has higher CH values, resulting in a better clustering effect and stability.

Application graph theory to evaluate the stability of landslide slopes

Evaluation of the stability of slopes is a complex and important engineering task, the solution of which requires the analysis of a significant number of factors. Many different methods of slope stability calculation have been developed to solve this type of problem. However, two groups of methods - limit equilibrium methods and the finite element method (FEM) - have become the most widely used. However, these methods have certain disadvantages. Limit equilibrium methods are limited by the assumptions used during the calculation, including the hypothesis of a solid compartment, which does not allow analyzing the stress-strain state. The FEM of the elements does not make it possible to unambiguously localize the sliding surface of the slope, and the determination of the stability coefficient using the method of reducing the strength of the soil requires a large number of complex iterative calculations. The methods and approaches of graph theory can be used precisely to combat the shortcomings of FEM. The paper examines the basics of graph theory. The main methods of specifying graphs, as well as certain types of graphs with an indication of their key features, are presented. The concept of isomorphism of graphs and some features of their graphical representation are revealed. The article presents the basic idea of using graph theory to calculate the stability of slopes. The main questions that must be solved when applying graph theory to the given type of problem are outlined. Two methods of converting a mesh of finite elements into a graph are considered in detail. The advantages and disadvantages of the proposed methods are analyzed. The transformation of the calculation scheme of an imaginary slope with a given geometry, which was simulated in the LIRA-SAPR software complex, into graphs using the above methods is demonstrated. An overview of the approaches that can be used to create a graph weight function is given.