Class Of Solvers Research Articles

Solving realistic large‐scale ill‐conditioned power flow cases based on combination of numerical solvers

With the increasing electricity consumption and difficulty in upgrading existing infrastructures, ill-conditioned power flow (PF) cases are becoming more frequent nowadays. In this context, classical robust solvers may be unsuitable for realistic networks, which typically encompass thousands of buses, because of their high computational burden or low convergence rate. This article tackles this issue by proposing a novel PF solver, which presents acceptable robustness and efficiency in solving large-scale ill-conditioned systems. The proposed algorithm collects the advantage of various numerical solvers, which by separate present different weaknesses, but actuating in coordination their strengths can be jointly exploited. More precisely, the robust Forward-Euler and Trapezoidal rules are combined with the efficient Darvishi cubic technique. Thereby, an original predictor-corrector algorithm is developed to effectively coordinate the different numerical algorithms involved, obtaining a robust but efficient yet solution procedure. Various large-scale ill-conditioned benchmark systems are studied under different stressing conditions. The results obtained with the developed technique are promising, outperforming other robust and standard PF solvers.

Large-eddy lattice-Boltzmann modeling of transonic flows

A D3Q19 hybrid recursive regularized pressure based lattice-Boltzmann method (HRR-P LBM) is assessed for the simulation of complex transonic flows. Mass and momentum conservation equations are resolved through a classical LBM solver coupled with a finite volume resolution of entropy equation for a complete compressible solver preserving stability, accuracy, and computational costs. An efficient treatment for wall and open boundaries is coupled with a grid refinement technique and extended to the HRR-P LBM in the scope of compressible aerodynamics. A Vreman subgrid turbulence model and an improved coupling of immersed boundary method with turbulence wall model on Cartesian grid accounts for unresolved scales by large-eddy simulation. The validity of the present method for transonic applications is investigated through various test cases with increasing complexity starting from an inviscid flow over a 10% bump and ending with a turbulent flow over a ONERA M6 three-dimensional wing.

Agile Earth Observation Satellite Scheduling With a Quantum Annealer

We present a comparison study of state-of-the-art classical optimization methods to a D-Wave 2000Q quantum annealer for the scheduling of agile Earth observation satellites. The problem is to acquire high-value images while obeying the attitude maneuvering constraint of the satellite. In order to investigate close to real-world problems, we created benchmark problems by simulating realistic scenarios. Our results show that a tuned quantum annealing approach can run faster when used to find the optimal solution than a classical exact solver for some of the problem instances. Moreover, we find that the solution quality of the quantum annealer is comparable to the heuristic method used operationally for small problem instances, but degrades rapidly due to the limited precision of the quantum annealer.

A non-local model to analyse 2D and 3D microbuckling of long carbon fibre epoxy material

Compression failure is a mechanism of non-local ruin that depends on the composite structure (layer thickness, load gradient) which makes it a peculiarity. The mechanism has been described and modelled in the literature with very specific numerical tools and experiments that accounted for this effect. A new finite element model purely based on classical elements of ABAQUS® is developed in this article to predict microbuckling in a 2D or 3D structure. More precisely, a theoretical formulation is proposed which defines the material and structural properties (BNL model) of a numerical model, coupling a continuum media and beams (2D or 3D). The elastic eigenvalues of instability are derived from classical solver of ABAQUS® (subspace). It permits to predict the elastic local instability of unidirectional plies inside a structure in case of complex loads. The ‘structural effect’ explained in the literature is confirmed and new results are obtained. To predict the failure in compression under complex load, a nonlinear behaviour is developed and implemented in the model with the user subroutine (USDFLD). The quantification of the different parameters (plasticity, initial defects, structural effects) is obtained with the BNL model which can be used to study the strength of compression in complex composite structures.

Intervention Planning in ITIL Context

In incident management and especially in after-sales services, customer interventions must be planned according to a priority order set by service level agreements as well as the availability of both technicians and clients. Despite the availability of incident management software solutions, intervention planning is still performed manually in most solutions because numerous constraints must be considered such as the synchronization of technician skills and customer requests, their availability, and the customer priorities. The intervention planning problem is considered as a difficult combinatorial optimization issue. Various approaches have been proposed in the literature including the transformation of this problem into a vehicle routing problem (VRP) or into a CSP in the context of ITIL framework. Yet, the resolution of this problem with a classical CSP solver is time consuming and must be optimized by proposing filtering rules or specific heuristics. This paper proposes the improved CSP and COP models for intervention planning problem with implementing filtering rules and techniques.

Warm-starting quantum optimization

There is an increasing interest in quantum algorithms for problems of integer programming and combinatorial optimization. Classical solvers for such problems employ relaxations, which replace binary variables with continuous ones, for instance in the form of higher-dimensional matrix-valued problems (semidefinite programming). Under the Unique Games Conjecture, these relaxations often provide the best performance ratios available classically in polynomial time. Here, we discuss how to warm-start quantum optimization with an initial state corresponding to the solution of a relaxation of a combinatorial optimization problem and how to analyze properties of the associated quantum algorithms. In particular, this allows the quantum algorithm to inherit the performance guarantees of the classical algorithm. We illustrate this in the context of portfolio optimization, where our results indicate that warm-starting the Quantum Approximate Optimization Algorithm (QAOA) is particularly beneficial at low depth. Likewise, Recursive QAOA for MAXCUT problems shows a systematic increase in the size of the obtained cut for fully connected graphs with random weights, when Goemans-Williamson randomized rounding is utilized in a warm start. It is straightforward to apply the same ideas to other randomized-rounding schemes and optimization problems.

The Riemann problem for van der Waals fluids with nonclassical phase transitions

We consider the Riemann problem for fluids of van der Waals type with phase transitions involving nonclassical shocks. The model is elliptic-hyperbolic and the pressure function admits two inflection points. First, a unique classical Riemann solver is constructed, which is based on rarefaction waves, classical shocks and zero-speed shocks. Second, we investigate nonclassical Riemann solvers, which involve nonclassical shocks. Nonclassical shocks are shock waves which violate the Liu entropy condition and satisfy a kinetic relation. It can be shown that then two wave curves always intersect either once or twice at different phases. Consequently, the Riemann problem always admit one or two solutions in the class of classical and nonclassical shocks, zero-speed shocks, and rarefaction waves.

Robust implementation of generative modeling with parametrized quantum circuits

Although the performance of hybrid quantum-classical algorithms is highly dependent on the selection of the classical optimizer and the circuit ansätze (Benedetti et al, npj Quantum Inf 5:45, 2019; Hamilton et al, 2018; Zhu et al, 2018), a robust and thorough assessment on-hardware of such features has been missing to date. From the optimizer perspective, the primary challenge lies in the solver’s stochastic nature, and their significant variance over the random initialization. Therefore, a robust comparison requires one to perform several training curves for each solver before one can reach conclusions about their typical performance. Since each of the training curves requires the execution of thousands of quantum circuits in the quantum computer, such a robust study remained a steep challenge for most hybrid platforms available today. Here, we leverage on Rigetti’s Quantum Cloud Services (QCS™) to overcome this implementation barrier, and we study the on-hardware performance of the data-driven quantum circuit learning (DDQCL) for three different state-of-the-art classical solvers, and on two-different circuit ansätze associated to different entangling connectivity graphs for the same task. Additionally, we assess the gains in performance from varying circuit depths. To evaluate the typical performance associated with each of these settings in this benchmark study, we use at least five independent runs of DDQCL towards the generation of quantum generative models capable of capturing the patterns of the canonical Bars and Stripes dataset. In this experimental benchmarking, the gradient-free optimization algorithms show an outstanding performance compared to the gradient-based solver. In particular, one of them had better performance when handling the unavoidable noisy objective function to be minimized under experimental conditions.

Ring oscillators yield analysis: Improving Monte Carlo models with optimized clustering methods

SummaryThe aim of this article is to demonstrate the interest of the optimized clustering method (OCM) when dealing with the yield analysis of ring oscillators, given uncertain assumptions over inputs. Indeed, the complementary metal–oxide semiconductor (CMOS) integrated circuit domain is facing a major challenge since these devices are subjected to noticeable fluctuations (mostly due to transistor constant scaling down at sub‐micron sizes), with utmost expectations regarding their performances (e.g., for digital circuits). Whether the classical approach requires use of Monte Carlo methods coupled with classical circuit solver (e.g., Spice and/or transistor model), the natural complexity of systems and varying inputs needs to provide alternative techniques, such as OCM. The foundations of the method and its efficiency will be presented and illustrated through ring oscillator applications.

Sparse Reconstruction for Near-Field MIMO Radar Imaging Using Fast Multipole Method

Radar imaging using multiple input multiple output systems are becoming popular recently. These applications typically contain a sparse scene and the imaging system is challenged by the requirement of high quality real-time image reconstruction from under-sampled measurements via compressive sensing. In this paper, we deal with obtaining sparse solution to near- field radar imaging problems by developing efficient sparse reconstruction, which avoid storing and using large-scale sensing matrices. We demonstrate that the “fast multipole method” can be employed within sparse reconstruction algorithms to efficiently compute the sensing operator and its adjoint (backward) operator, hence improving the computation speed and memory usage, especially for large-scale 3-D imaging problems. For several near-field imaging scenarios including point scatterers and 2-D/3-D extended targets, the performances of sparse reconstruction algorithms are numerically tested in comparison with a classical solver. Furthermore, effectiveness of the fast multipole method and efficient reconstruction are illustrated in terms of memory requirement and processing time.

A nonlinear solver based on an adaptive neural network, introduction and application to porous media flow

Sensitivity to derivatives and a need for proper initial guesses are the main disadvantages of classic nonlinear solvers like Newton's method. To overcome the obstacles, a numerical solver for second-order nonlinear Partial Differential Equations (PDEs) based on an Adaptive Neural Network (AdNN) is introduced. While using Newton's method needs to form the Jacobian matrix and its inversion, which both of them are time-consuming and dependent on the nature of the problem, the proposed solver tries to find the roots of the algebraic equations by changing the weights of AdNN by the help adaptive laws. The proposed approach has been applied to solve the governing PDEs of the gas flow in shale resources and the immiscible two-phase flow of water and oil in hydrocarbon reservoirs as two highly nonlinear phenomena. The generated profiles of pressures and saturations show a satisfying match with the outputs of Newton's method. However, using the presented algorithm not only removes the former necessities but also helps the community to solve the relevant PDEs governing the critical elements of the energy market in the future with a higher level of confidence.

Computationally Efficient Practical Method for Solving the Dynamics of Fluid Power Circuits in the Presence of Singularities

In this article, a practical method is proposed for the efficient solution of fluid power systems with singularities originating (in particular) from the presence in the system of small volumes. The method is based on the use of an enhanced version of the pseudodynamic solver (the advanced pseudodynamic solver), which seeks the steady-state solution of pressure building up in the small volume. This solver can be attributed to the class of explicit solvers. There are two main advantages of the proposed solver. The first is the higher accuracy and numerical stability of the solution compared with the classical pseudo-dynamic solver, owing to the enhanced solver structure and the use of an adaptive convergence criterion. The second is the faster calculation time compared with conventional integration methods such as the fourth-order Runge–Kutta method, owing to the obtained possibility of larger integration time step usage. Thus, the advanced pseudodynamic solver can become a preferred method in the simulation of complex fluid power circuits. Simulation results of the C code implementation confirm that the advanced pseudodynamic solver is better than conventional solvers for the solution of the real-time systems that include fluid power components with small volumes.

Achieving large and distant ancestral genome inference by using an improved discrete quantum-behaved particle swarm optimization algorithm

BackgroundReconstructing ancestral genomes is one of the central problems presented in genome rearrangement analysis since finding the most likely true ancestor is of significant importance in phylogenetic reconstruction. Large scale genome rearrangements can provide essential insights into evolutionary processes. However, when the genomes are large and distant, classical median solvers have failed to adequately address these challenges due to the exponential increase of the search space. Consequently, solving ancestral genome inference problems constitutes a task of paramount importance that continues to challenge the current methods used in this area, whose difficulty is further increased by the ongoing rapid accumulation of whole-genome data.ResultsIn response to these challenges, we provide two contributions for ancestral genome inference. First, an improved discrete quantum-behaved particle swarm optimization algorithm (IDQPSO) by averaging two of the fitness values is proposed to address the discrete search space. Second, we incorporate DCJ sorting into the IDQPSO (IDQPSO-Median). In comparison with the other methods, when the genomes are large and distant, IDQPSO-Median has the lowest median score, the highest adjacency accuracy, and the closest distance to the true ancestor. In addition, we have integrated our IDQPSO-Median approach with the GRAPPA framework. Our experiments show that this new phylogenetic method is very accurate and effective by using IDQPSO-Median.ConclusionsOur experimental results demonstrate the advantages of IDQPSO-Median approach over the other methods when the genomes are large and distant. When our experimental results are evaluated in a comprehensive manner, it is clear that the IDQPSO-Median approach we propose achieves better scalability compared to existing algorithms. Moreover, our experimental results by using simulated and real datasets confirm that the IDQPSO-Median, when integrated with the GRAPPA framework, outperforms other heuristics in terms of accuracy, while also continuing to infer phylogenies that were equivalent or close to the true trees within 5 days of computation, which is far beyond the difficulty level that can be handled by GRAPPA.

On speeding up factoring with quantum SAT solvers

There have been several efforts to apply quantum SAT solving methods to factor large integers. While these methods may provide insight into quantum SAT solving, to date they have not led to a convincing path to integer factorization that is competitive with the best known classical method, the Number Field Sieve. Many of the techniques tried involved directly encoding multiplication to SAT or an equivalent NP-hard problem and looking for satisfying assignments of the variables representing the prime factors. The main challenge in these cases is that, to compete with the Number Field Sieve, the quantum SAT solver would need to be superpolynomially faster than classical SAT solvers. In this paper the use of SAT solvers is restricted to a smaller task related to factoring: finding smooth numbers, which is an essential step of the Number Field Sieve. We present a SAT circuit that can be given to quantum SAT solvers such as annealers in order to perform this step of factoring. If quantum SAT solvers achieve any asymptotic speedup over classical brute-force search for smooth numbers, then our factoring algorithm is faster than the classical NFS.

Compressibility in lattice Boltzmann on standard stencils: effects of deviation from reference temperature.

With growing interest in the simulation of compressible flows using the lattice Boltzmann (LB) method, a number of different approaches have been developed. These methods can be classified as pertaining to one of two major categories: (i) solvers relying on high-order stencils recovering the Navier-Stokes-Fourier equations, and (ii) approaches relying on classical first-neighbour stencils for the compressible Navier-Stokes equations coupled to an additional (LB-based or classical) solver for the energy balance equation. In most cases, the latter relies on a thermal Hermite expansion of the continuous equilibrium distribution function (EDF) to allow for compressibility. Even though recovering the correct equation of state at the Euler level, it has been observed that deviations of local flow temperature from the reference can result in instabilities and/or over-dissipation. The aim of the present study is to evaluate the stability domain of different EDFs, different collision models, with and without the correction terms for the third-order moments. The study is first based on a linear von Neumann analysis. The correction term for the space- and time-discretized equations is derived via a Chapman-Enskog analysis and further corroborated through spectral dispersion-dissipation curves. Finally, a number of numerical simulations are performed to illustrate the proposed theoretical study. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

Adaptive Gaussian radial basis function methods for initial value problems: Construction and comparison with adaptive multiquadric radial basis function methods

Adaptive radial basis function (RBF) methods have been developed recently in Gu and Jung (2020) based on the multiquadric (MQ) RBFs for solving initial value problems (IVPs). The proposed adaptive RBF methods utilize the free parameter in order to adaptively enhance the local convergence of the numerical solution. Methods pertaining to the polynomial interpolation yield only fixed rate of convergence regardless of the solution smoothness while the proposed methods use the smoothness of the solution, given in derivatives of the solution, to control the rate of convergence. In this paper, for the completion of the development of the adaptive RBF methods, we develop various adaptive Gaussian RBF methods for solving IVPs by modifying the classical solvers such as the Euler’s method, midpoint method, Adams–Bashforth method and Adams–Moulton method by replacing the polynomial basis with the Gaussian RBFs. For each development, we compare the performance with the adaptive MQ-RBF methods and explain when and why the adaptive Gaussian methods are better or not than the MQ-RBF ones. We provide the collection of modifications with the MQ and Gaussian RBFs. We also provide the stability regions for the adaptive Gaussian methods. Numerical results confirm that the adaptivity enhances accuracy and convergence and also show the differences and similarities between MQ and Gaussian RBFs in their performance — we found that the adaptive MQ-RBF method has larger stability region than the Gaussian RBF method. Both MQ and Gaussian RBF methods yield the desired order of convergence while the superiority of one method to the other depends on the method and the problem considered.

Row and column iteration methods to solve linear systems on a quantum computer

We consider the quantum implementations of the two classical iterative solvers for a system of linear equations, including the Kaczmarz method which uses a row of coefficient matrix in each iteration step, and the coordinate descent method which utilizes a column instead. These two methods are widely applied in big data science due to their very simple iteration schemes. In this paper we use the block-encoding technique and propose fast quantum implementations for these two approaches, under the assumption that the quantum states of each row or each column can be efficiently prepared. The quantum algorithms achieve exponential speed up at the problem size over the classical versions, meanwhile their complexity is nearly linear at the number of steps.

Kernel Regression for Vehicle Trajectory Reconstruction under Speed and Inter-vehicular Distance Constraints

This work tackles the problem of reconstructing vehicle trajectories with the side information of physical constraints, such as inter-vehicular distance and speed limits. It is notoriously difficult to perform a regression while enforcing these hard constraints on time intervals. Using reproducing kernel Hilbert spaces, we propose a convex reformulation which can be directly implemented in classical solvers such as CVXGEN. Numerical experiments on a simple dataset illustrate the efficiency of the method, especially with sparse and noisy data.

Multiblock ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers

Solving combinatorial optimization problems on current noisy quantum devices is currently being advocated for (and restricted to) binary polynomial optimization with equality constraints via quantum heuristic approaches. This is achieved using, e.g., the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). We present a decomposition-based approach to extend the applicability of current approaches to "quadratic plus convex" mixed binary optimization (MBO) problems, so as to solve a broad class of real-world optimization problems. In the MBO framework, we show that the alternating direction method of multipliers (ADMM) can split the MBO into a binary unconstrained problem (that can be solved with quantum algorithms), and continuous constrained convex subproblems (that can be solved cheaply with classical optimization solvers). The validity of the approach is then showcased by numerical results obtained on several optimization problems via simulations with VQE and QAOA on the quantum circuits implemented in Qiskit, an open-source quantum computing software development framework.

Архитектура программного средства с открытым исходным кодом для численного моделирования потоков на горных склонах

In this paper, we compare two approaches to describe the dynamics of flows on mountain slopes using the depth-averaged equations of continuum mechanics and using the complete, not depth-averaged, equations of continuum mechanics for three-dimensional modeling. Using these two approaches, a simulation of an experimental slush flow in the tank and the interaction of the flow with dam barrier protection was carried out. Numerical solutions are compared with experimental data. Also, both approaches are applied to the calculation of an avalanche in the 22nd avalanche cite of Mount Yukspor (Khibiny). Avalanche run-out distance and the shape of the avalanche deposits are compared with field data obtained from the measurement of a real avalanche. In the course of a numerical experiment, distributions of such quantities as flow velocity, depth, density, molecular and turbulent viscosity, values of the density of turbulent kinetic energy, dissipation of turbulent kinetic energy, and shear stress at the bottom of the flow were obtained. Using the obtained data a mathematical model is developed to describe the entrainment of the underlying material by the flow during slope erosion and the deposition of the flow material on the slope. To implement the obtained mathematical model, the architecture of the multiphaseEulerChangeFoam solver was developed, which implements a three-phase multi-velocity model with phase exchange between the material of the underlying surface and the material of the flow. The classic solver multiphaseEulerFoam from the OpenFOAM package is taken as a basis for the developed solver.