Calculation Algorithm Research Articles

Prediction of Helicopter Rotor Loads and Fatigue Damage Evaluation with Neural Networks

AbstractIn recent years, machine learning algorithms have experienced rapid advancement, driven by the exponential growth of data availability and computational capabilities. Among these algorithms, artificial neural networks stand out as one of the most renowned and effective classes, possessing the ability to discern relationships within data. In this study, we harness neural networks to deduce the relationship between flight mechanics parameters and resulting loads in an articulated rotor configuration. The accuracy of these algorithms hinges closely on the quality of the dataset used for training. Given that rotor loads manifest as time-periodic signals with precise harmonic content, we train dedicated neural networks to predict each harmonic individually. Subsequently, the load time history is reconstructed post hoc by amalgamating predictions from each individual network. Various network architectures are explored, and a sensitivity analysis is conducted on hyper-parameters to determine the optimal configuration for this specific application. Moreover, these predictions serve as input for a fatigue damage calculation algorithm.

A Segmentation-based Automated Calculation of Patient Size and Size-specific Dose Estimates in Pediatric Computed Tomography Scans.

Size-specific dose estimates (SSDE) have been introduced into computed tomography (CT) dosimetry to tailor patients' unique sizes to facilitate accurate CT radiation dose quantification and optimization. The purpose of this study was to develop and validate an automated algorithm for the determination of patient size (effective diameter) and SSDE. A MATLAB platform was used to develop software of algorithms based on image segmentation techniques to automate the calculation of patient size and SSDE. The algorithm was used to automatically estimate the individual size and SSDE of four CT dose index phantoms and 80 CT images of pediatric patients comprising head, thorax, and abdomen scans. For validation, the American Association of Physicists in Medicine (AAPM) manual methods were used to determine the patient's size and SSDE for the same subjects. The accuracy of the proposed algorithm in size and SSDE calculation was evaluated for agreement with the AAPM's estimations (manual) using Bland-Altman's agreement and Pearson's correlation coefficient. The normalized error, system bias, and limits of agreement (LOA) between methods were derived. The results demonstrated good agreement and accuracy between the automated and AAPM's patient size estimations with an error rate of 1.9% and 0.27% on the patient and phantoms study, respectively. A 1% percentage difference was found between the automated and manual (AAPM) SSDE estimates. A strong degree of correlation was seen with a narrow LOA between methods for clinical study (r > 0.9771) and phantom study (r > 0.9999). The proposed automated algorithm provides an accurate estimation of patient size and SSDE with negligible error after validation.

MATHEMATICAL MODEL AND ALGORITHM FOR THE DETERMINATION OF THE ORIGIN OF ELECTRICITY FROM RENEWABLE ENERGY SOURCES IN THE ELECTRIC POWER SYSTEM

The article deals with the development of a method and algorithm for calculation of individual compo-nents of electricity flows in the branches of an electric power grid circuit caused by generation and con-sumption in its nodes. In particular, it is about estimating the share of renewable energy sources (RES) in the electricity consumption of a given consumer. The method is based on methods and algorithms for the calculation of steady-state modes of power grids, integrating a mathematical model for determining the components of current flows in the branches of the power system circuit. The model employs distribution coefficients of currents in the circuit branches from RES nodes and node voltages to form a matrix of cur-rent distribution coefficients for RES across the power grid branches. Since RES in electric power systems (EPS) use general power grids to transmit the electricity they generate, accurate determination of their power share within overall flows enables the impact of RES on the EPS mode parameters to be considered. The peculiarity of the algorithm for estimating the share of RES in the electricity consumption of a given consumer is its consideration of physical processes in the power system. The input data for the calculation are the power system parameters, the node loads (specified by capacity or schedules), as well as arrays of RES generation and centralized power supply nodes and consumers with a controlled value of the Guar-anteed Origin of electricity from RES. The voltages during the formation of the matrix of power distribu-tion coefficients at nodes along the branches of the power grid are determined by the calculation results of the power grid steady-state modes or by experimental measurement data. The method's efficacy and the accuracy of estimating the RES share in the power consumption of a given consumer are verified and demonstrated through a practical example. Determination of the share of the consumer's electricity con-sumption, which origin from renewable sources can be guaranteed, creates an enabling environment that would foster producers and consumers to increase the use of renewable energy sources and promotes the development of the green energy market. Ref. 18. Fig.3.

A constrained differential evolution algorithm for calculation of two-phase equilibria at given volume, temperature and moles

A variety of strategies including two types of direct solution methods based on Newton's method and indirect solution methods based on thermodynamic principles have been developed, which can find satisfactory solutions for the phase equilibrium calculation problem at given volume, temperature and moles (NVT-flash). However, these methods are sensitive to the initial values and depend on the objective function's derivative during calculation. To resolve these deficiencies, a constrained differential evolution algorithm (abbreviated as CDE) for calculating two-phase equilibria at given volume, temperature, and moles is presented in this paper. The total Helmholtz free energy is regarded as the objective function, and the moles vector and volume of a certain phase are taken as the decision variables. This paper deals with the constraints of the NVT-flash problem by using direct search method and exterior point method. The results of the investigations on pure substance, binary and ternary mixtures are in agreement with the published data, which proves the effectiveness in solving the NVT-flash problem and the energy attenuation characteristic of the algorithm. The proposed algorithm represents the first successful attempt to apply the meta-heuristic optimization algorithm to solve the phase equilibrium computation under NVT-flash, and it shows the promising application prospect of meta-heuristic optimization algorithms for solving the phase equilibrium calculation problems.

Определение индивидуального риска травматизма горнорабочих в результате динамического проявления

The article analyses the effect of gas-dynamic manifestations on occupational injuries. It has been established that the most hazardous gas-dynamic manifestation for underground deep mines is a rock burst. As the rock burst is identified by the authors as the most hazardous effect by its manifestations, the authors offer their methodology of identification of occupational injury risk caused by a rock burst for a wider discussion. The main characteristics and causes of rock bursts and their signs and forecasting methods have been described. The statistics of accidents caused by rock bursts have been provided. The article contains statistical information on mild, severe, and lethal injuries caused by rock bursts in coal mines of the Kuznetsk coal basin. Multifunctional safety systems able to obtain information on the condition of rock mass have been analyzed. Special attention has been paid to the system of current control and forecast of rock mass conditions based on the «Mikon-GEO» system. In the majority of cases, based on the problems to solve, such a system is a part of multifunctional safety systems. The authors suggest that the forecast methodology is to be based on the data obtained by such systems operating based on the seismoacoustics principles. The mathematical model using the source data obtained from the «Mikon-GEO» system has been considered. The calculation algorithm enabling the assessment of the rock burst probability has been provided. The algorithm and the results of measurements of rock mass basic parameters are used to determine the individual risk value that is advisable to compare with the average value of occupational risk at production. The results obtained by the authors have been tested in one of the Kuznetsk Basin coal mines. The preliminary results of the forecast methodology use have shown the relevance of the studies and identified certain issues requiring specification and further research.

Dosimetric Impact of Prescription Point Placement in Heterogeneous Medium for Conformal Radiotherapy Dose Calculation with Various Algorithms.

The aim of the study is to compare the accuracy of dose calculation for different dose calculation algorithms with different prescription points (air, tissue, air-tissue interface in carcinoma lung patients and bone, tissue, and bone-tissue interface in carcinoma buccal Mucosa tumors). Forty-one patients with carcinoma lung and buccal mucosa were retrospectively selected for this study. A three-dimensional conformal radiotherapy reference plan was created using the prescription point in the tissue with Monte Carlo (MC) algorithms for both the groups of patients. The reference plan was modified by changing the prescription point and algorithms in the tissue, air, air-tissue interface for lung patients and tissue, bone, and bone-tissue interface for buccal mucosa patients. The dose received by the target volume and other organs at risk (OAR) structures was compared. To find out the statistical difference between different prescription points and algorithms, the statistical tests were performed with repeated measures ANOVA. The target volume receiving 95% dose coverage in lung patients decreased to -3.08%, -5.75%, and -1.87% in the dose prescription point at the air-tissue interface with the dose calculation algorithms like MC, collapsed cone (CC), and pencil beam (PB), respectively, compared to that of the MC tissue. Spinal cord dose was increased in the CC and PB algorithms in all prescription points in patients with lung and buccal mucosa. OAR dose calculated by PB in all prescription points showed a significant deviation compared to MC tissue prescription point. This study will help demonstrate the accuracy of dose calculation for the different dose prescription points with the different treatment algorithms in radiotherapy treatment planning.

THE ROLE OF SURROGATE MODELS AND MACHINE LEARNING IN MODERN ULTRASONIC FLOW MEASUREMENT

Recent developments in the field of machine learning have found their application in a wide range of design processes. They have particular use where numerical simulations are involved and fast, more accurate predictions and optimized models are very much needed. In order to speed up experiments on a device or system model, it is necessary to speed up its execution (simulation). Instead of detailed models, you can create a surrogate. Its main task is fast execution, small amount of occupied memory and preservation of the specified error threshold in relation to the detailed model. This article demonstrates the integration of machine learning into the flow measurement process using ultrasonic flowmeters. The main source of errors in the application of the modern ultrasonic principle of flow measurement arises from the difficulty of taking into account the actual velocity profile of the measuring flow. In practice, the distribution of velocities in the cross-section of the pipeline differs from the theoretical one introduced in the calculation algorithm. However, if the velocity profile is known, an appropriate correction can be estimated and taken into account during calibration. This will increase the accuracy of measurements. In this study, an intelligent compensation of errors caused by profile distortion was presented to improve the accuracy of using multipath meters in such ultrasonic conditions. The purpose of such an intelligent correction arises in the search for the optimal layout and the minimum sufficient number of chords in the measuring transducer for various installation conditions. The adoption of a new approach based on a surrogate model with a neural network made it possible to take an approximate flow profile that has a certain distortion. So, for the chosen topology of the acoustic flow sensing channels, programmatically, by changing the location angle of the measuring system, instead of the local resistance, add such a position of the chords for which it is possible to set maximum admissible measurement accuracy. This means using a neural network for the required input correction model, especially in an environment characterized by a change in the velocity profile under the influence of different flow distortions.

SINGLE-DEGREE-OF-FREEDOM VIBRATION ISOLATION SYSTEM WITH ONE ADDITIONAL SUPPORT

Vibration isolation is one of the most effective methods for reducing vibration levels of supporting structures when installing vibroactive equipment (active vibration isolation) or vibration levels of vibro-sensitive objects relative to foundation vibration levels (passive vibration isolation). Damping devices utilizing high-speed fluid flow through apertures have found wide applications in shock vibration isolation and vibration isolation systems in aerospace and defense sectors. Recent research has led to the development of viscous fluid dampers (VFDs) for use in civil engineering, particularly in earthquake-prone areas. Scientists conducted experiments aimed at determining the ability of viscous fluid dampers to reduce damages and displacements of structures without increasing stresses. Mathematical models have been developed and are applied in vibration isolation systems. When vibroactive equipment is installed on building and structure support systems, vibrations with sufficiently high vibration parameters may occur, potentially leading to loss of load-bearing capacity. In such cases, vibration isolation is considered one of the most effective methods for reducing these vibration levels. In this study, a calculation method has been developed, and calculation dependencies and algorithms for calculating vibration protection systems with nonlinear characteristics (additional support connections, viscous fluid damper) have been derived for both single-degree-of-freedom and two-degree-of-freedom systems. The research involved an analysis of normative and scientific-technical literature on the subject: types, structural solutions, calculation, and analysis of vibration protection systems. The main method selected was based on the use of transfer functions of linear systems (the non-traditional "normal form" method). Calculations were performed using computer mathematics systems- Matlab.

A PREDICTIVE APPROACH TO THE TAXONOMIC ANALYSIS OF A COMPANY'S FINANCIAL AND ECONOMIC HEALTH

Objective. The purpose of the article is to identify and evaluate alternatives to the application of the predictive approach to the taxonomic analysis of the financial and economic state of the enterprise.. Methods. During the research, the following methods are applied: the method taxonomy of (for taxonomic analysis based on the data of the enterprise «Kyivstar» PJSC); the method of analysis (for comparing integral and complex taxonomic indicators for different periods; the comparison method (for comparing the accuracy of the obtained forecast models); the autoregression forecasting method (for forecasting the input indicators for taxonomic analysis of «Kyivstar» PJSC and the taxonomic indicators themselves). Results. The expediency of applying the predictive approach to the taxonomic analysis of the financial and economic state of the enterprise on the example of PJSC "Kyivstar" is substantiated. It was determined that the application of the predictive approach allows not only to assess the current state of the enterprise, but also to identify trends and predict the future development of enterprises, contributes to more justified management decisions, increasing the effectiveness of strategic planning. Two directions of application of the predictive approach to the taxonomic analysis of the financial and economic state of the enterprise are proposed: forecasting of taxonomic indicators, forecasting of input data and calculation of taxonomic indicators based on actual and model data. It was established that the accuracy of forecasting according to the first approach (forecasting of taxonomic indicators) for integral indicators characterizing the company's income (I1), company's expenses (I2), the efficiency of the company's non-current assets (I3), the efficiency of the use of the company's own capital (I4), profitability and financial stability of the enterprise (I5), and the complex taxonomic indicator was 73%-86%, according to the second approach (forecasting input data and calculating taxonomic indicators based on actual and model data) - 78-91%. It was determined that the advantage of the first approach (forecasting taxonomic indicators) is a simple calculation algorithm, while forecasting is applied to only six resulting taxonomic indicators; the second (prediction of input data and calculation of taxonomic indicators based on actual and model data) – a more reasonable conclusion regarding the accuracy of the predicted values ​​of taxonomic integral and complex indicators.

공작기계 이송축의 운동 물성치 분석 툴 개발

In this study, a tool is developed to analyze the motion properties of feed axes to minimize machining time and improve productivity in manufacturing fields such as aircraft component machining. The motion properties of jerk, acceleration, and velocity are used to calculate the feeding time under a certain distance for the axis of a CNC machine tool. This analysis tool categorizes feed distances based on acceleration and speed and implements a feed-time calculation algorithm based on each distance type. A user-friendly graphical user interface is developed for interaction with users. The use of this tool is expected to minimize the machining time and improve productivity in manufacturing processes such as aircraft component machining. Furthermore, applying this analytical tool to the identification of appropriate motion properties can increase the efficiency of manufacturing processes and improve product quality.

Radiomics and Quantitative MDA Criteria in Breast Cancer with Bone Metastases by MRI: Examples of Calculation Algorithms and Their Practical Use

Radiomics and Quantitative MDA Criteria in Breast Cancer with Bone Metastases by MRI: Examples of Calculation Algorithms and Their Practical Use

Measurement Uncertainty and Risk of False Compliance Assessment Applied to Carbon Isotopic Analyses in Natural Gas Exploratory Evaluation.

The concept of uncertainty in an isotopic analysis is not uniform in the scientific community worldwide and can compromise the risk of false compliance assessment applied to carbon isotopic analyses in natural gas exploratory evaluation. In this work, we demonstrated a way to calculate one of the main sources of this uncertainty, which is underestimated in most studies focusing on gas analysis: the δ13C calculation itself is primarily based on the raw analytical data. The carbon isotopic composition of methane, ethane, propane, and CO2 was measured. After a detailed mathematical treatment, the corresponding expanded uncertainties for each analyte were calculated. Next, for the systematic isotopic characterization of the two gas standards, we calculated the standard uncertainty, intermediary precision, combined standard uncertainty, and finally, the expanded uncertainty for methane, ethane, propane, and CO2. We have found an expanded uncertainty value of 1.8‰ for all compounds, except for propane, where a value of 1.6‰ was obtained. The expanded uncertainty values calculated with the approach shown in this study reveal that the error arising from the application of delta calculation algorithms cannot be neglected, and the obtained values are higher than 0.5‰, usually considered as the accepted uncertainty associated with the GC-IRMS analyses. Finally, based on the use of uncertainty information to evaluate the risk of false compliance, the lower and upper acceptance limits for the carbon isotopic analysis of methane in natural gas are calculated, considering the exploratory limits between -55‰ and -50‰: (i) for the underestimated current uncertainty of 0.5‰, the lower and upper acceptance limits, respectively, are -54.6‰ and -50.4‰; and (ii) for the proposed realistic uncertainty of 1.8‰, the lower and upper acceptance limits would be more restrictive; i.e., -53.5‰ and -51.5‰, respectively.

Measuring homoplasy I: comprehensive measures of maximum and minimum cost under parsimony across discrete cost matrix character types.

Here, we propose, prove mathematically and discuss maximum and minimum measures of maximum parsimony evolution across 12 discrete phylogenetic character types, classified across 4467 morphological and molecular datasets. Covered character types are: constant, binary symmetric, multistate unordered (non-additive) symmetric, multistate linear ordered symmetric, multistate non-linear ordered symmetric, binary irreversible, multistate irreversible, binary Dollo, multistate Dollo, multistate custom symmetric, binary custom asymmetric and multistate custom asymmetric characters. We summarize published solutions and provide and prove a range of new formulae for the algebraic calculation of minimum (m), maximum (g) and maximum possible (gmax) character cost for applicable character types. Algorithms for exhaustive calculation of m, g and gmax applicable to all classified character types (within computational limits on the numbers of taxa and states) are also provided. The general algorithmic solution for minimum steps (m) is identical to a minimum spanning tree on the state graph or minimum weight spanning arborescence on the state digraph. Algorithmic solutions for character g and gmax are based on matrix mathematics equivalent to optimization on the star tree, respectively for given state frequencies and all possible state frequencies meeting specified numbers of taxa and states. We show that maximizing possible cost (gmax) with given transition costs can be equivalent to maximizing, across all possible state frequency combinations, the lowest implied cost of state transitions if any one state is ancestral on the star tree, via the solution of systems of linear equations. The methods we present, implemented in the Claddis R package, extend to a comprehensive range, the fundamental character types for which homoplasy may be measured under parsimony using m, g and gmax, including extra cost (h), consistency index (ci), retention index (ri) or indices based thereon.

Fast forward modeling of grounded electrical-source transient electromagnetic based on inverse Laplace transform adaptive hybrid algorithm

Frequency–time conversion is a crucial step in grounded electrical-source transient electromagnetic response calculation, and the performance of the algorithm is directly related to the overall accuracy and speed of forward modeling. In mainstream algorithms, algorithms with high accuracy often have slow computation speed while algorithms with high efficiency have unsatisfactory accuracy, especially when facing inversion problems that are difficult to meet requirements. This paper introduces three inverse Laplace transform algorithms for this problem: the Gaver–Stehfest algorithm, the Euler algorithm, and the Talbot algorithm. The performance of each algorithm in forward modeling was analyzed using half-space and layered models, and the optimal selection schemes for algorithm weight coefficients were provided. The numerical calculation results show that the Gaver–Stehfest algorithm has a unique advantage in computational efficiency, while the Talbot algorithm and Euler algorithm meet the accuracy requirements. After considering both accuracy and efficiency, the Talbot algorithm is selected to replace conventional algorithms for calculation of grounded electrical-source transient electromagnetic forward modeling. In addition, this paper combines the characteristics of the Gaver–Stehfest algorithm and the Talbot algorithm to implement an adaptive hybrid algorithm. This algorithm uses the Gaver–Stehfest algorithm for forward modeling in the early times and the Talbot algorithm to compensate for the decrease in accuracy in the later times. Through the comparison of forward modeling calculations, it can be seen that the hybrid algorithm proposed in this paper fully utilizes the advantages of both algorithms. The hybrid algorithm greatly improves computational speed while meeting accuracy requirements, and has significant advantages over conventional algorithms.

Calculating a conductor’s temperature-related sag as the limiting value for a Dynamic Line Rating

The ampacity — a term that refers to the maximum current in amperes — of existing overhead lines can be increased using Dynamic Line Rating (DLR) systems. Based on ambient online conditions and electrical power flow measurements, together with a forecast of future ambient conditions, the ampacity of overhead lines can be dynamically adjusted. In essence, the ampacity of an overhead line is determined by the operating temperature of the conductor that still guarantees the required safe distances to the objects under the overhead line. This paper presents a calculation algorithm for the sag of a conductor that addresses an unequal temperature of the conductor along the line as a response to an expected problem in the future, when increasing numbers of DLR sensors will be installed on or even near overhead lines. A novel approach to the sag-temperature calculation useful for a DLR is developed based on the linearization of cable equations. As a result, the computational costs are greatly reduced, which is an important factor when the DLR system includes a large number of overhead lines and processes them simultaneously. The presented methods are open and can be adapted for an arbitrary DLR system.

An ethically guided preclinical device for phenotyping H2 production in laboratory rodents.

Dihydrogen (H2) is produced endogenously by the intestinal microbiota through the fermentation of diet carbohydrates. Over the past few years, numerous studies have demonstrated the significant therapeutic potential of H2 in various pathophysiological contexts, making the characterization of its production in laboratory species of major preclinical importance. This study proposes an innovative solution to accurately monitor H2 production in free-moving rodents while respecting animal welfare standards. The developed device consisted of a wire rodent cage placed inside an airtight chamber in which the air quality was maintained, and the H2 concentration was continuously analyzed. After the airtightness and efficiency of the systems used to control and maintain air quality in the chamber were checked, tests were carried out on rats and mice with different metabolic phenotypes, over 12 min to 1-h experiments and repeatedly. H2 production rates (HPR) were obtained using an easy calculation algorithm based on a first-order moving average. HPR in hyperphagic Zucker rats was found to be twice as high as in control Wistar rats, respectively, 2.64 and 1.27 nmol.s-1 per animal. In addition, the ingestion of inulin, a dietary fiber, stimulated H2 production in mice. HPRs were 0.46 nmol.s-1 for animals under control diet and 1.99 nmol.s-1 for animals under inulin diet. The proposed device coupled with our algorithm enables fine analysis of the metabolic phenotype of laboratory rats or mice with regard to their endogenous H2 production.

Метод расчета ставок роялти на основе Big Data и Fuzzy Logic

The article by an expert from the Intellectual Property Valuation School and the Experimental Economics Laboratory of CEMI RAS is devoted to the development and application of the "LABRATE ROYALTY PRO" method for calculating royalty rates, based on Big Data analysis and Fuzzy Logic. Using the serial case of "Rikor Electronics" as an example, the problem of determining a fair (market) royalty rate, dependent on three key indi-cators — Licensor's Share (LS), Return on Sales (ROS), and EBIT Margin (EM) — has been addressed. Tradi-tional methods based on production or cost profitability do not correlate with sales revenue indicators, necessitat-ing adaptation to Russian realities and international practices. The article provides a detailed algorithm for calcula-tion, based on the analysis of companies' financial indicators, industry statistics, and the use of Big Data and Fuzzy Logic technologies. Examples from judicial practice confirm the effectiveness of the proposed approach in ensuring objective and fair decisions on determining royalty rates, the value of trademark usage rights, and com-pensation calculations. Special attention is given to the importance of precise and clear descriptions of the re-search objects and source data.

Algorithms for Computer-Based Calculation of Individual Strand Tensioning in the Stay Cables of Cable-Stayed Bridges

This paper introduces algorithms for computer-aided calculation, based on a proposed computational model for stay cables, decomposed from a bridge’s structural system. These algorithms determine the necessary tension forces and corresponding deformations in the cables for individual strand tensioning using lightweight hydraulic jacks. Two tensioning methods are discussed: the first involves single-cycle tensioning with varying force intensities, while the second employs multiple cycles by applying forces of constant intensity until achieving an equalization of forces in all strands of the cable. The efficiency of the proposed procedures is demonstrated through a numerical example.

Effective algorithms for calculation of quasi-probability distributions of bright “banana” states

Non-Gaussian quantum states, described by negative-valued Wigner functions, are important for both fundamental tests of quantum physics and for emerging quantum information technologies. One of the promising ways of generating a non-Gaussian state from a coherent one is the use of cubic (Kerr) optical nonlinearity, which produces the characteristic banana-like shape of the resulting quantum states. However, the Kerr effect is weak in highly transparent optical materials (dimensionless nonlinearity parameter Γ≲10−6). Therefore, a big number of the photons in the optical mode (n≳106) is necessary to generate an observable non-Gaussianity. In this case, the direct approach to calculation of the Wigner function becomes extremely computationally expensive. In this work, we develop quick algorithms for computing the Husimi and Wigner quasi-probability functions of these non-Gaussian states by means of the Kerr nonlinearity. This algorithm can be used for any realistic values of the photon numbers and the nonlinearity.

Deep-learning-based acceleration of critical point calculations

Computation of the critical point of complex fluid mixtures is an important part of understanding their thermodynamic phase behaviour. While algorithms for these calculations are well established, they are often slow when the number of constituting components is large. In this work, we propose a new procedure to significantly accelerate critical point calculations by leveraging deep neural network (DNN) models. A DNN model for critical point predictions of a given mixture is first trained based on the critical points of such a mixture with various compositions. The predictions of the DNN model are then used to initialize both of the commonly used algorithms for mixture critical point calculations: root finding and global minimization. We demonstrate that when using the DNN-based predictions to initialize the root-finding-based and optimization-based algorithms, we can achieve 50-90% and 80-90% reductions in the number of required iterations, respectively.