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The paper provides a method for selecting the composition of a refrigerant with a given isobaric cooling curve using an artificial neural network (ANN). This method is based on the use of 1D layers of a convolutional neural network. To train the neural network, we applied a technological model of a simple heat exchanger in the UniSim design program, using the Peng – Robinson equation of state.We created synthetic database on isobaric boiling curves of refrigerants of different compositions using the technological model. To record the database, an algorithm was developed in the Python programming language, and information on isobaric boiling curves for 1 049 500 compositions was uploaded using the COM interface. The compositions have generated by Monte Carlo method. Designed architecture of ANN allows select composition of a mixed refrigerant by 101 points of boiling curve. ANN gives mole flows of mixed refrigerant by composition (methane, ethane, propane, nitrogen) on the output layer. For training ANN, we used method of cyclical learning rate. For results demonstration we selected MR composition by natural gas cooling curve with a minimum temperature drop of 3 К and a maximum temperature drop of no more than 10 К, which turn better than we predicted via UniSim SQP optimizer and better than predicted by $k$-nearest neighbors algorithm. A significant value of this article is the fact that an artificial neural network can be used to select the optimal composition of the refrigerant when analyzing the cooling curve of natural gas. This method can help engineers select the composition of the mixed refrigerant in real time, which will help reduce the energy consumption of natural gas liquefaction.

The article is devoted to solving ill-posed problems of mathematical physics for elliptic and parabolic equations, such as the Cauchy problem for the Helmholtz equation and the retrospective Cauchy problem for the heat equation with constant coefficients. These problems are reduced to problems of convex optimization in Hilbert space. The gradients of the corresponding functionals are calculated approximately by solving two well-posed problems. A new method is proposed for solving the optimization problems under study, it is component-by-component descent in the basis of eigenfunctions of a self-adjoint operator associated with the problem. If it was possible to calculate the gradient exactly, this method would give an arbitrarily exact solution of the problem, depending on the number of considered elements of the basis. In real cases, the inaccuracy of calculations leads to a violation of monotonicity, which requires the use of restarts and limits the achievable quality. The paper presents the results of experiments confirming the effectiveness of the constructed method. It is determined that the new approach is superior to approaches based on the use of gradient optimization methods: it allows to achieve better quality of solution with significantly less computational resources. It is assumed that the constructed method can be generalized to other problems.

This work considers the problem of optimal control galvanic process in multianode bath. The nonstationary mathematical model of galvanic process, which considers change concentrations of electrolyte components, is developed. Demonstrated rationale for the choice of the form to extremal control on example chrome galvanic process in the standard electrolyte.

In this paper we consider the controlled motion of a helical body with three blades in an ideal fluid, which is executed by rotating three internal rotors. We set the problem of selecting control actions, which ensure the motion of the body near the predetermined trajectory. To determine controls that guarantee motion near the given curve, we propose methods based on the application of hybrid genetic algorithms (genetic algorithms with real encoding and with additional learning of the leader of the population by a gradient method) and artificial neural networks. The correctness of the operation of the proposed numerical methods is estimated using previously obtained differential equations, which define the law of changing the control actions for the predetermined trajectory.

In the approach based on hybrid genetic algorithms, the initial problem of minimizing the integral functional reduces to minimizing the function of many variables. The given time interval is broken up into small elements, on each of which the control actions are approximated by Lagrangian polynomials of order 2 and 3. When appropriately adjusted, the hybrid genetic algorithms reproduce a solution close to exact. However, the cost of calculation of 1 second of the physical process is about 300 seconds of processor time.

To increase the speed of calculation of control actions, we propose an algorithm based on artificial neural networks. As the input signal the neural network takes the components of the required displacement vector. The node values of the Lagrangian polynomials which approximately describe the control actions return as output signals . The neural network is taught by the well-known back-propagation method. The learning sample is generated using the approach based on hybrid genetic algorithms. The calculation of 1 second of the physical process by means of the neural network requires about 0.004 seconds of processor time, that is, 6 orders faster than the hybrid genetic algorithm. The control calculated by means of the artificial neural network differs from exact control. However, in spite of this difference, it ensures that the predetermined trajectory is followed exactly.

We consider one of the problems of transport modelling — searching the equilibrium distribution of traffic flows in the network. We use the classic Beckman’s model to describe time costs and flow distribution in the network represented by directed graph. Meanwhile agents’ behavior is not completely rational, what is described by the introduction of Markov logit dynamics: any driver selects a route randomly according to the Gibbs’ distribution taking into account current time costs on the edges of the graph. Thus, the problem is reduced to searching of the stationary distribution for this dynamics which is a stochastic Nash – Wardrope equilibrium in the corresponding population congestion game in the transport network. Since the game is potential, this problem is equivalent to the problem of minimization of some functional over flows distribution. The stochasticity is reflected in the appearance of the entropy regularization, in contrast to non-stochastic case. The dual problem is constructed to obtain a solution of the optimization problem. The universal primal-dual gradient method is applied. A major specificity of this method lies in an adaptive adjustment to the local smoothness of the problem, what is most important in case of the complex structure of the objective function and an inability to obtain a prior smoothness bound with acceptable accuracy. Such a situation occurs in the considered problem since the properties of the function strongly depend on the transport graph, on which we do not impose strong restrictions. The article describes the algorithm including the numerical differentiation for calculation of the objective function value and gradient. In addition, the paper represents a theoretical estimate of time complexity of the algorithm and the results of numerical experiments conducted on a small American town.

Ligand protected metal nanoclusters (NCs) have gained much attention due to their unique physicochemical properties and potential applications in material science. Noble metal NCs protected with thiolate ligands have been of interest because of their long-term stability. The detailed structures of most of the ligandstabilized metal NCs remain unknown due to the absence of crystal structure data for them. Theoretical calculations using quantum chemistry techniques appear as one of the most promising tools for determining the structure and electronic properties of NCs. That is why finding a cost-effective strategy for calculations is such an important and challenging task. In this work, we compare the performance of different theoretical methods of geometry optimization and absorption spectra calculation for silver-thiolate complexes. We show that second order Moller–Plesset perturbation theory reproduces nicely the geometries obtained at a higher level of theory, in particular, with RI-CC2 method. We compare the absorption spectra of silver-thiolate complexes simulated with different methods: EOM-CCSD, RI-CC2, ADC(2) and TDDFT. We show that the absorption spectra calculated with the ADC(2) method are consistent with the spectra obtained with the EOM-CCSD and RI-CC2 methods. CAM-B3LYP functional fails to reproduce the absorption spectra of the silver-thiolate complexes. However, M062X global hybrid meta-GGA functional seems to be a nice compromise regarding its low computational costs. In our previous study, we have already demonstrated that M062X functional shows good accuracy as compared to ADC(2) ab initio method predicting the excitation spectra of silver nanocluster complexes with nucleobases.

A new discrete ecological-evolutionary mathematical model is presented, in which the search mechanisms for evolutionarily stable migration routes of fish populations are implemented. The proposed adaptive designs have a small dimension, and therefore have high speed. This allows carrying out calculations on long-term perspective for an acceptable machine time. Both geometric approaches of nonlinear analysis and computer “asymptotic” methods were used in the study of stability. The migration dynamics of the fish population is described by a certain Markov matrix, which can change during evolution. The “basis” matrices are selected in the family of Markov matrices (of fixed dimension), which are used to generate migration routes of mutant. A promising direction of the evolution of the spatial behavior of fish is revealed for a given fishery and food supply, as a result of competition of the initial population with mutants. This model was applied to solve the problem of optimal catch for the long term, provided that the reservoir is divided into two parts, each of which has its own owner. Dynamic programming is used, based on the construction of the Bellman function, when solving optimization problems. A paradoxical strategy of “luring” was discovered, when one of the participants in the fishery temporarily reduces the catch in its water area. In this case, the migrating fish spends more time in this area (on condition of equal food supply). This route is evolutionarily fixes and does not change even after the resumption of fishing in the area. The second participant in the fishery can restore the status quo by applying “luring” to its part of the water area. Endless sequence of “luring” arises as a kind of game “giveaway”. A new effective concept has been introduced — the internal price of the fish population, depending on the zone of the reservoir. In fact, these prices are Bellman's private derivatives, and can be used as a tax on caught fish. In this case, the problem of long-term fishing is reduced to solving the problem of one-year optimization.

The mathematical model, finite-difference schemes and algorithms for computation of transient thermoand hydrodynamic processes involved in commissioning the unified system including the oil producing well, electrical submersible pump and fractured-porous reservoir with bottom water are developed. These models are implemented in the computer package to simulate transient processes with simultaneous visualization of their results along with computations. An important feature of the package Oil-RWP is its interaction with the special external program GCS which simulates the work of the surface electric control station and data exchange between these two programs. The package Oil-RWP sends telemetry data and current parameters of the operating submersible unit to the program module GCS (direct coupling). The station controller analyzes incoming data and generates the required control parameters for the submersible pump. These parameters are sent to Oil-RWP (feedback). Such an approach allows us to consider the developed software as the “Intellectual Well System”.

Some principal results of the simulations can be briefly presented as follows. The transient time between inaction and quasi-steady operation of the producing well depends on the well stream watering, filtration and capacitive parameters of oil reservoir, physical-chemical properties of phases and technical characteristics of the submersible unit. For the large time solution of the nonstationary equations governing the nonsteady processes is practically identical to the inverse quasi-stationary problem solution with the same initial data. The developed software package is an effective tool for analysis, forecast and optimization of the exploiting parameters of the unified oil-producing complex during its commissioning into the operating regime.

Image denoising is one of the fundamental problems in digital image processing. This problem usually refers to the reconstruction of an image from an observed image degraded by noise. There are many factors that cause this degradation such as transceiver equipment, or environmental influences, etc. In order to obtain higher quality images, many methods have been proposed for image denoising problem. Most image denoising method are based on total variation (TV) regularization to develop efficient algorithms for solving the related optimization problem. TV-based models have become a standard technique in image restoration with the ability to preserve image sharpness.

In this paper, we focus on Poisson noise usually appearing in photon-counting devices. We propose an effective regularization model based on combination of first-order and fractional-order total variation for image reconstruction corrupted by Poisson noise. The proposed model allows us to eliminate noise while edge preserving. An efficient alternating minimization algorithm is employed to solve the optimization problem. Finally, provided numerical results show that our proposed model can preserve more details and get higher image visual quality than recent state-of-the-art methods.

The equilibrium configurations of charged electrons, confined in the hard disk potential, are analysed by means of the hybrid numerical algorithm. The algorithm is based on the interpolation formulas, that are obtained from the analysis of the equilibrium configurations, provided by the variational principle developed in the circular model. The solution of the nonlinear equations of the circular model yields the formation of the shell structure which is composed of the series of rings. Each ring contains a certain number of particles, which decreases as one moves from the boundary ring to the central one. The number of rings depends on the total number of electrons. The interpolation formulas provide the initial configurations for the molecular dynamics calculations. This approach makes it possible to significantly increase the speed at which an equilibrium configuration is reached for an arbitrarily chosen number of particles compared to the Metropolis annealing simulation algorithm and other algorithms based on global optimization methods.