Pre-computed Solutions Research Articles

An accelerated computational platform for optimal field developments with reduced footprint

Reducing the environmental footprint and increasing efficiency of hydrocarbon production as well as geological sequestration of carbon dioxide (CO2) through optimally selected and operated fewer wells is crucial for cleaner and more sustainable energy transition. We describe a parallel subsurface field-development optimization (SFDO) platform with novel components. SFDO enables the optimization of well-locations/-trajectories (WLO), controls (WCO), and both jointly (WLO–WCO). All objective function computations are performed in parallel at a given iteration in SFDO.The novel distributed quasi-Newton (DQN) optimizer is an important new element in accelerating SFDO. DQN is developed using a multi-threaded optimization paradigm that utilizes high-performance computing (HPC) to distribute an ensemble of optimization threads. By operating its threads in parallel within a single optimization run, DQN efficiently identifies multiple distinct local optima of the objective function. DQN tracks and updates a common input-output (training) data set by recording the responses from successful simulation runs. The support-vector regression (SVR) method is used to approximate the Hessian matrix while objective function gradients are estimated analytically using SVR-computed sensitivities.The DQN implementation inside SFDO is extensively tested and validated in this work. We first validate DQN using a synthetic test case with a pre-computed solution. DQN incurs fewest number of simulations, and thus, the shortest run time while successfully finding the global optimum. For the first time in the literature, we show that DQN is more effective than alternative methods in problems involving WCO and WLO–WCO. Then, we report on DQN's performance against alternative techniques in four realistic applications, namely on a WLO problem for environmental footprint reduction and a novel WLO–WCO application for the geological sequestration of CO2 involving a novel take on WLO with deforming well trajectories. Finally, we describe two realistic WLO problems in which the well count is also optimized in addition to the well locations. One of these applications is for heater-well pattern optimization for an innovative unconventional thermal recovery method. DQN finds local optima by incurring a significantly lower computational cost in comparison to alternative methods. Results of the field tests support the advantageous qualities of DQN previously observed in synthetic tests. We conclude that SFDO accelerated with DQN helps increase the efficiency and reduce the footprint of realistic field-scale developments.

Numerical simulation of microwave-enhanced methane-air flames I: Modeling and one-dimensional premixed laminar flames

This study considers the numerical modeling of sub-breakdown microwave-enhanced combustion in one-dimensional laminar methane-air flames over a range of stoichiometries at standard temperature and pressure. The effect of uniform microwave fields on the laminar flame speed, post-flame temperature and composition is of primary interest here.A model for the non-thermal plasma generated by the microwave field in such flames is constructed based on fitting of electron properties and electron impact reaction rates to pre-computed solutions of the Boltzmann equation, combined with ambipolar diffusion transport for charged species. This model is used with a selection of existing and novel methane-air kinetics schemes to compute laminar flame profiles at a range of microwave field strengths and varying stoichiometry. The trends for laminar flame strength and temperature, peak- and outlet species fractions are compared over this parameter space. While all schemes demonstrate increasing flame speed and temperature with higher field strength and richer flames, significant variations in the form and magnitude of this increase are observed for the various kinetics schemes considered.The laminar flame-speed increase at sub-breakdown electric field strengths is found to be due primarily to electron heating of the gases in both the pre-heat region and across the flame. Analysis of the electron energy transfer shows that the majority of the energy at moderate field strengths is transferred via excitement of vibrational states of nitrogen, followed by water and carbon monoxide. In the pre-heat regime, vibrational excitement of methane is also seen to play an important role for fuel-rich flames. Particular attention is paid to the modification of the flame speed due to the relaxation time of the vibrational N2 states, which is demonstrated to result in a moderate reduction of the flame speed for lean and stoichiometric flames.A driving concern here is the development of models suitable for use within large-scale three-dimensional numerical simulations and the knowledge gained in comparing the existing schemes is used to derive a range of simplified mechanisms more suited for this purpose. The ability of these reduced models to capture the flame enhancement is demonstrated over a range of flame stoichiometries and sub-breakdown field strengths.

Multiparametric modeling of composite materials based on non-intrusive PGD informed by multiscale analyses: Application for real-time stiffness prediction of woven composites

In this paper, a multiparametric solution of the stiffness properties of woven composites involving several microstructure parameters is performed. For this purpose, non-intrusive PGD-based methods are employed. From offline pre-computed solutions generated through a full-field multiscale modeling, the proposed method approximates the multidimensional solution as a sum of products of one-dimensional functions each depending on a single variable. The present work aims at providing an accurate approximation of this multiparametric solution with lower computational cost for dataset generation. Thus, a comparative analysis of three non-intrusive PGD formulations (SSL, s-PGD and ANOVA-PGD) is carried out. The obtained results reveal and demonstrate that the ANOVA-PGD model works well for approximating the stiffness properties over the entire parameter space, i.e., along its boundary as well as inside it, by using only few pre-computed high-fidelity solutions. Finally, a GUI application is developed to exploit this multiparametric solution by incorporating other composite weave architectures. This application could be easily used by engineers and composite designers, to deduce, in real-time, the macroscopic properties of woven composite for a given set of microstructural parameters by simply varying the cursors and without any microstructure generation and meshing nor FE computations using periodic homogenization.

OPTIMAL POSITION AND PATH PLANNING FOR STOP-AND-GO LASERSCANNING FOR THE ACQUISITION OF 3D BUILDING MODELS

Abstract. Terrestrial laser scanning has become more and more popular in recent years. The according planning of the standpoint network is a crucial issue influencing the overhead and the resulting point cloud. Fully static approaches are both cost and time extensive, whereas fully kinematic approaches cannot produce the same data quality. Stop-and-go scanning, which combines the strengths of both strategies, represents a good alternative solution. In the scanning process, the standpoint planning is by now mostly a manual process based on expert knowledge and relying on the surveyor’s experience. This paper provides a method based on Mixed Integer Linear Programming (MILP) ensuring an optimal placement of scanner standpoints considering all scanner-related constraints (e.g. incidence angle), a full coverage of the scenery, a sufficient overlap for the subsequent registration and an optimal route planning solving a Traveling Salesperson Problem (TSP). This enables the fully automatic application of autonomous systems for providing a complete model while performing a stop-and-go laser scanning, e.g. with the Spot robot from Boston Dynamics. Our pre-computed solution, i.e. standpoints and trajectory, has been evaluated surveying a real-world environment using a 360° panoramic laser scanner and successfully compared with a precise LoD2 building model of the underlying scene. The performed ICP-based registration issued from our fully automatic pipeline turns out to be a very good and safe alternative of the otherwise laborious target-based registration.

Selection and Optimization of Hyperparameters in Warm-Started Quantum Optimization for the MaxCut Problem

Today’s quantum computers are limited in their capabilities, e.g., the size of executable quantum circuits. The Quantum Approximate Optimization Algorithm (QAOA) addresses these limitations and is, therefore, a promising candidate for achieving a near-term quantum advantage. Warm-starting can further improve QAOA by utilizing classically pre-computed approximations to achieve better solutions at a small circuit depth. However, warm-starting requirements often depend on the quantum algorithm and problem at hand. Warm-started QAOA (WS-QAOA) requires developers to understand how to select approach-specific hyperparameter values that tune the embedding of classically pre-computed approximations. In this paper, we address the problem of hyperparameter selection in WS-QAOA for the maximum cut problem using the classical Goemans–Williamson algorithm for pre-computations. The contributions of this work are as follows: We implement and run a set of experiments to determine how different hyperparameter settings influence the solution quality. In particular, we (i) analyze how the regularization parameter that tunes the bias of the warm-started quantum algorithm towards the pre-computed solution can be selected and optimized, (ii) compare three distinct optimization strategies, and (iii) evaluate five objective functions for the classical optimization, two of which we introduce specifically for our scenario. The experimental results provide insights on efficient selection of the regularization parameter, optimization strategy, and objective function and, thus, support developers in setting up one of the central algorithms of contemporary and near-term quantum computing.

Efficient aerodynamic shape optimization through reduced order CFD modeling

Although computational power is increasingly available, high-fidelity simulation based aerodynamic shape optimization is still challenging for industrial applications. To make the simulation based optimization acceptable in the practice of engineering design, a technique combining mesh morphing and reduced order modeling is proposed for efficient aerodynamic optimization based on CFD simulations. The former technique avoids the time-consuming procedure of geometry discretization. And the latter speeds up the procedure of field solution by exploiting pre-computed solution snapshots. To test the efficiency of the proposed method, the windshield of a motorbike is analyzed and optimized. It is shown that even the total number of cells of the mesh is around 0.4 million, the CFD computation and the post-processing of the results can be completed in less than 10 s if the reduced order model is adopted. Running on a personal computer, the generic algorithm is applied to optimize the profile of the windshield. A 8% reduction of the drag coefficient is achieved after 800 queries of the reduced order CFD model and the total CPU time is only around 2 h.

Efficient aerodynamic shape optimization through free-form mesh morphing and reduced order CFD modeling

Although computational power is increasingly available, high-fidelity simulation based aerodynamic shape optimization is still challenging for industrial applications. To make the simulation based optimization acceptable in the practice of engineering design, a technique combining mesh morphing and reduced order modeling is proposed for efficient aerodynamic optimization based on CFD simulations. The former technique avoids the time-consuming procedure of geometry discretization. And the latter speeds up the procedure of field solution by combining pre-computed solution snapshots. To test the efficiency of the proposed method, the windshield of a motorbike is analyzed and optimized. It is shown that even the total number of cells of the mesh is around 0.4 million, the CFD computation and the post processing of the results can be completed in less than 10 seconds if the reduced order model is adopted. Running on a personal computer, the generic algorithm is applied to optimize the profile of the windshield. A 8% reduction of the drag coefficient is achieved after 800 queries of the reduced order CFD model and the total CPU time is only around 2 hours.

Impact of geometric uncertainty on hemodynamic simulations using machine learning

Abstract In the cardiovascular system, blood flow rates, blood velocities and blood pressures can be modeled using the Navier–Stokes equations. Inputs to the system are typically uncertain, such as (a) the geometry of the arterial tree, (b) clinically measured blood pressure and viscosity, (c) boundary resistances, among others. Due to a large number of such parameters, efficient quantification of uncertainty in solution fields in this multi-parameter space is challenging. We use an adaptive stochastic collocation method to quantify the impact of uncertainty in geometry in patient-specific models. We develop a novel subdivision method to define the stochastic space of geometries. To accelerate convergence and make the problem tractable, we use a machine learning approach to approximate the simulation-based solution. Towards this, a reduced order model of the Navier–Stokes equations is developed using a segmental resistance analog boundary conditions (ratio of pressure to flow). Using an offline database of pre-computed solutions, we compute a map (rule) from the features to solution fields. We achieve significant speed-up (of a few orders of magnitude) by approximating the simulation-based solution using a machine learning predictor. A bootstrap aggregated decision tree was found to be the best predictor among many candidate regressors (correlation coefficient of training set was 0.94). We demonstrate stochastic space convergence using the adaptive stochastic collocation method, and also show robustness to the choice of geometry parameterization. The sensitivities to geometry obtained using machine learning had a correlation coefficient of 0.92 with the values obtained using finite element simulations. Segments with significant disease in the larger arteries had the highest sensitivities. Terminal segments are more sensitive to dilation and proximal healthy segments are more sensitive to erosion. Sensitivity to geometry is highest when geometric resistance is comparable to net downstream resistance.

Computational vademecums for the real-time simulation of haptic collision between nonlinear solids

In this paper a novel strategy is presented for the real-time simulation of contact between non-linear deformable solids at haptic feedback rates. The proposed method is somehow related to the Voxmap Pointshell method for two deformable solids. Its novelty and crucial advantages over existing implementations of this algorithm come from the intensive use of computational vademecums. These are in essence a pre-computed solution of a parametric model in which every possible situation during the on-line phase of the method has been considered through the introduction of the appropriate parameters. Such a high-dimensional parametric model is efficiently solved by using Proper Generalized Decompositions (PGD) and stored in memory as a set of vectors. The paper presents a thorough description of the developed algorithm together with some examples of its performance.

Extraction of process zones and low-dimensional attractive subspaces in stochastic fracture mechanics.

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional deterministic space. Such a low-dimensional space is obtained by a spectral analysis performed on pre-computed solution samples. A greedy algorithm is proposed to identify both process zone and low-dimensional representative subspace for the solution in the complementary region. In addition to the novelty of the tools proposed in this paper for the analysis of localised phenomena, we show that the reduced space generated by the method is a valid basis for the construction of a reduced order model.

Efficient simulation of an ammonia oxidation reactor using a solution mapping approach

A highly efficient single channel monolith reactor model for the oxidation of ammonia is implemented. A mechanistic model for ammonia oxidation on platinum is used, and all internal and external mass transfer effects are included. The model efficiency is derived from the use of pre-computed solutions of the mass balance equations. Spline interpolation functions are constructed from pre-computed solutions of the mass balances of one volume element of the reactor model. It is shown that these spline functions reproduce the exact outlet concentrations of the volume element with a relative error of less than 3%. This solution mapping approach allows computation of concentration profiles in the reactor by simple successive calls of the interpolation function without any numerical solution. Outlet concentrations of the complete reactor computed in this way show a relative error of less than 2%. Application of the solution mapping approach speeds up the solution of the concentration profiles by a factor of more than 3200, compared to the numerical solution of the mass balances. In this way one steady state concentration profile in an ammonia oxidation catalyst can be computed in less than 0.003 s, despite the fact that the model uses mechanistic surface kinetics and includes the radial diffusion in the washcoat.

Generalizations and Applications of the Lagrange Implicit Function Theorem

The implicit function theorem due to Lagrange is generalized to enable high order implicit rate calculations of general implicit functions about pre-computed solutions of interest. The sensitivities thus calculated are subsequently used in determining neighboring solutions about an existing root (for algebraic systems) or trajectory (in case of dynamical systems). The generalization to dynamical systems, as a special case, enables the calculation of high order time varying sensitivities of the solutions of boundary value problems with respect to the parameters of the system model and/or functions describing the boundary condition. The generalizations thus realized are applied to various problems arising in trajectory optimization. It was found that useful information relating the neighboring extremal paths can be deduced from these implicit rates characterizing the behavior in the neighborhood of the existing solutions. The accuracy of solutions obtained is subsequently enhanced using an averaging scheme based on the Global Local Orthogonal Polynomial (GLO-MAP) weight functions developed by the first author to blend many local approximations in a continuous fashion. Example problems illustrate the wide applicability of the presented generalizations of Lagrange’s classical results to static and dynamic optimization problems.

REDUCING THE TIME COMPLEXITY OF THE N-QUEENS PROBLEM

This paper presents a fast algorithm for solving the n-queens problem. The basic idea of this algorithm is to use pre-computed solutions in 75% of the cases, while the remaining cases are solved by calling the Sosic's algorithm. The novelty of this algorithm is in the observation that these pre-computable cases exhibit a modular nature. In addition, the pre-computed solutions run 100 times faster than Sosic's algorithm in most cases.

Quantifying Uncertainty in CFD

Quantifying Uncertainty in CFD