Accelerating the estimation of collisionless energetic particle confinement statistics in stellarators using multifidelity Monte Carlo

2021 ◽  
Author(s):  
Frederick Law ◽  
Antoine J Cerfon ◽  
Benjamin Peherstorfer
Keyword(s):  
Monte Carlo ◽  
Surrogate Model ◽  
Energetic Particle ◽  
Small Time ◽  
Point Of View ◽  
High Fidelity ◽  
Monte Carlo Studies ◽  
Long Time ◽  
Particle Confinement ◽  
Fidelity Model

Abstract In the design of stellarators, energetic particle confinement is a critical point of concern which remains challenging to study from a numerical point of view. Standard Monte Carlo analyses are highly expensive because a large number of particle trajectories need to be integrated over long time scales, and small time steps must be taken to accurately capture the features of the wide variety of trajectories. Even when they are based on guiding center trajectories, as opposed to full-orbit trajectories, these standard Monte Carlo studies are too expensive to be included in most stellarator optimization codes. We present the first multifidelity Monte Carlo scheme for accelerating the estimation of energetic particle confinement in stellarators. Our approach relies on a two-level hierarchy, in which a guiding center model serves as the high-fidelity model, and a data-driven linear interpolant is leveraged as the low-fidelity surrogate model. We apply multifidelity Monte Carlo to the study of energetic particle confinement in a 4-period quasi-helically symmetric stellarator, assessing various metrics of confinement. Stemming from the very high computational efficiency of our surrogate model as well as its sufficient correlation to the high-fidelity model, we obtain speedups of up to 10 with multifidelity Monte Carlo compared to standard Monte Carlo.

scholarly journals THE VALUATION OF SELF-FUNDING INSTALMENT WARRANTS

2017 ◽  
Vol 20 (04) ◽  
pp. 1750025
Author(s):  
J. N. DEWYNNE ◽  
N. EL-HASSAN
Keyword(s):  
Monte Carlo ◽  
Finite Difference ◽  
Multiple Scales ◽  
Correction Term ◽  
Approximate Solutions ◽  
Fair Value ◽  
Small Time ◽  
Point Of View ◽  
First Order Correction ◽  
Short Time

We present two models for the fair value of a self-funding instalment warrant. In both models we assume the underlying stock process follows a geometric Brownian motion. In the first model, we assume that the underlying stock pays a continuous dividend yield and in the second we assume that it pays a series of discrete dividend yields. We show that both models admit similarity reductions and use these to obtain simple finite-difference and Monte Carlo solutions. We use the method of multiple scales to connect these two models and establish the first-order correction term to be applied to the first model in order to obtain the second, thereby establishing that the former model is justified when many dividends are paid during the life of the warrant. Further, we show that the functional form of this correction may be expressed in terms of the hedging parameters for the first model and is, from this point of view, independent of the particular payoff in the first model. In two appendices we present approximate solutions for the first model which are valid in the small volatility and the short time-to-expiry limits, respectively, by using singular perturbation techniques. The small volatility solutions are used to check our finite-difference solutions and the small time-to-expiry solutions are used as a means of systematically smoothing the payoffs so we may use pathwise sensitivities for our Monte Carlo methods.

Enhanced multi-fidelity model for flight simulation using global exploration and the Kriging method

2016 ◽  
Vol 231 (4) ◽  
pp. 606-620 ◽  
Author(s):  
Daeyeon Lee ◽  
Nhu Van Nguyen ◽  
Maxim Tyan ◽  
Hyung-Geun Chun ◽  
Sangho Kim ◽  
...  
Keyword(s):  
Surrogate Model ◽  
Cross Validation ◽  
Vortex Lattice ◽  
Flight Simulation ◽  
High Fidelity ◽  
Analysis Tool ◽  
Kriging Method ◽  
Flight Vehicles ◽  
Aerodynamic Database ◽  
Fidelity Model

Using the global exploration and Kriging-based multi-fidelity analysis methods, this study developed a multi-fidelity aerodynamic database for use in the performance analysis of flight vehicles and for use in flight simulations. Athena vortex lattice, a program based on vortex lattice method, was used as the low-fidelity analysis tool in the multi-fidelity analysis method. The in-house high-fidelity AADL-3D code was based on the Navier–Stokes equations. The AADL-3D code was validated by comparing the data and the analysis results of the Onera M-6 wing and NACA TN 3649. The design of experiment method and the Kriging method were applied to integrate low- and high-fidelity analysis results. General data tendencies were established from the low-fidelity analysis results. The high-fidelity analysis results and the Kriging method were used to generate a surrogate model, from which the low-fidelity analysis results were interpolated. To reduce repeated calculations, three design points were simultaneously added for each calculation. The convergence of three design points was avoided by considering only the peak points as additional design points. The reliability of the final surrogate model was determined by applying the leave-one-out cross-validation method and by obtaining the cross-validation root mean square error. Using the multi-fidelity model developed in this study, a multi-fidelity aerodynamic database was constructed for use in the three degrees of freedom flight simulation of flight vehicles.

scholarly journals Strong coupling methods in QCD thermodynamics

2021 ◽  
Author(s):  
Owe Philipsen
Keyword(s):  
Monte Carlo ◽  
Strong Coupling ◽  
Chemical Potential ◽  
Yang Mills ◽  
Coupling Methods ◽  
Sign Problem ◽  
Monte Carlo Studies ◽  
Long Time ◽  
Scaling Region ◽  
Strong Coupling Expansions

AbstractFor a long time, strong coupling expansions have not been applied systematically in lattice QCD thermodynamics, in view of the success of numerical Monte Carlo studies. The persistent sign problem at finite baryo-chemical potential, however, has motivated investigations using these methods, either by themselves or combined with numerical evaluations, as a route to finite density physics. This article reviews the strategies, by which a number of qualitative insights have been attained, notably the emergence of the hadron resonance gas or the identification of the onset transition to baryon matter in specific regions of the QCD parameter space. For the simpler case of Yang–Mills theory, the deconfinement transition can be determined quantitatively even in the scaling region, showing possible prospects for continuum physics.

A Multiobjective Adaptive Surrogate Modeling-Based Optimization (MO-ASMO) Framework Using Efficient Sampling Strategies

2017 ◽  
Author(s):  
Yong Hoon Lee ◽  
R. E. Corman ◽  
Randy H. Ewoldt ◽  
James T. Allison
Keyword(s):  
Surrogate Model ◽  
Design Space ◽  
Surrogate Modeling ◽  
Pareto Set ◽  
Test Problems ◽  
High Fidelity ◽  
Sampling Strategies ◽  
Nsga Ii ◽  
Sample Points ◽  
Fidelity Model

A novel multiobjective adaptive surrogate modeling-based optimization (MO-ASMO) framework is proposed to utilize a minimal number of training samples efficiently for sequential model updates. All the sample points are enforced to be feasible, and to provide coverage of sparsely explored sparse design regions using a new optimization subproblem. The MO-ASMO method only evaluates high-fidelity functions at feasible sample points. During an exploitation sample phase, samples are selected to enhance solution accuracy rather than the global exploration. Sampling tasks are especially challenging for multiobjective optimization; for an n-dimensional design space, a strategy is required for generating model update sample points near an (n − 1)-dimensional hypersurface corresponding to the Pareto set in the design space. This is addressed here using a force-directed layout algorithm, adapted from graph visualization strategies, to distribute feasible sample points evenly near the estimated Pareto set. Model validation samples are chosen uniformly on the Pareto set hypersurface, and surrogate model estimates at these points are compared to high-fidelity model responses. All high-fidelity model evaluations are stored for later use to train an updated surrogate model. The MO-ASMO algorithm, along with the set of new sampling strategies, are tested using two mathematical and one realistic engineering problems. The second mathematical test problems is specifically designed to test the limits of this algorithm to cope with very narrow, non-convex feasible domains. It involves oscillatory objective functions, giving rise to a discontinuous set of Pareto-optimal solutions. Also, the third test problem demonstrates that the MO-ASMO algorithm can handle a practical engineering problem with more than 10 design variables and black-box simulations. The efficiency of the MO-ASMO algorithm is demonstrated by comparing the result of two mathematical problems to the results of the NSGA-II algorithm in terms of the number of high fidelity function evaluations, and is shown to reduce total function evaluations by several orders of magnitude when converging to the same Pareto sets.

scholarly journals Selection of Existing Sail Designs for Multi-Fidelity Surrogate Models

2022 ◽  
Vol 7 (01) ◽  
pp. 31-51
Author(s):  
Tanya Peart ◽  
Nicolas Aubin ◽  
Stefano Nava ◽  
John Cater ◽  
Stuart Norris
Keyword(s):  
Surrogate Model ◽  
Lift Coefficient ◽  
Simulation Method ◽  
Surrogate Models ◽  
High Fidelity ◽  
Data Points ◽  
Velocity Prediction ◽  
The Difference ◽  
Fidelity Model ◽  
Selection Of

Velocity Prediction Programs (VPPs) are commonly used to help predict and compare the performance of different sail designs. A VPP requires an aerodynamic input force matrix which can be computationally expensive to calculate, limiting its application in industrial sail design projects. The use of multi-fidelity kriging surrogate models has previously been presented by the authors to reduce this cost, with high-fidelity data for a new sail being modelled and the low-fidelity data provided by data from existing, but different, sail designs. The difference in fidelity is not due to the simulation method used to obtain the data, but instead how similar the sail’s geometry is to the new sail design. An important consideration for the construction of these models is the choice of low-fidelity data points, which provide information about the trend of the model curve between the high-fidelity data. A method is required to select the best existing sail design to use for the low-fidelity data when constructing a multi-fidelity model. The suitability of an existing sail design as a low fidelity model could be evaluated based on the similarity of its geometric parameters with the new sail. It is shown here that for upwind jib sails, the similarity of the broadseam between the two sails best indicates the ability of a design to be used as low-fidelity data for a lift coefficient surrogate model. The lift coefficient surrogate model error predicted by the regression is shown to be close to 1% of the lift coefficient surrogate error for most points. Larger discrepancies are observed for a drag coefficient surrogate error regression.

Transient Operation in Pipeline Compressor Stations

2014 ◽  
Author(s):  
Rainer Kurz ◽  
Robert C. White ◽  
Klaus Brun
Keyword(s):  
Time Horizon ◽  
Control Strategies ◽  
Control Algorithms ◽  
High Fidelity ◽  
Driver Performance ◽  
Long Time ◽  
Compressor Installation ◽  
Demand Changes ◽  
Pipeline Model ◽  
Fidelity Model

Many pipelines are not operated under steady state conditions. This is in particular true for pipelines that are highly integrated with other pipelines, or have many different feed or gas take-off points. In many cases, the demand changes frequently, and cannot always be planned with a long time horizon. In this study, a simplified transient pipeline model, together with a high fidelity model of a compressor installation and its control system are used to evaluate control strategies that can optimize the fuel consumption and reaction time in these transient situations. The model for the compressor installation contains an accurate representation of the compressor and driver performance, together with the capability to simulate different, but realistic control strategies. This allows specific and general recommendations on the use of control algorithms.

Adjustable wetting of Liquid Flame Spray (LFS) TiO2-nanoparticle coated board: Batch-type versus roll-to-roll stimulation methods

2014 ◽  
Vol 29 (2) ◽  
pp. 271-279 ◽  
Author(s):  
Mikko Tuominen ◽  
Hannu Teisala ◽  
Janne Haapanen ◽  
Mikko Aromaa ◽  
Jyrki M. Mäkelä ◽  
...  
Keyword(s):  
Argon Plasma ◽  
Ultra Violet ◽  
High Volume ◽  
Point Of View ◽  
Flame Spray ◽  
Ambient Conditions ◽  
Batch Type ◽  
Roll To Roll ◽  
Long Time ◽  
Liquid Flame Spray

Abstract Superhydrophobic nanoparticle coating was created on the surface of board using liquid flame spray (LFS). The LFS coating was carried out continuously in ambient conditions without any additional hydrophobization steps. The contact angle of water (CAW) of ZrO2, Al2O3 and TiO2 coating was adjusted reversibly from >150° down to ~10−20° using different stimulation methods. From industrial point of view, the controlled surface wetting has been in focus for a long time because it defines the liquid-solid contact area, and furthermore can enhance the mechanical and chemical bonding on the interface between the liquid and the solid. The used stimulation methods included batch-type methods: artificial daylight illumination and heat treatment and roll-to-roll methods: corona, argon plasma, IR (infra red)- and UV (ultra violet)-treatments. On the contrary to batch-type methods, the adjustment and switching of wetting was done only in seconds or fraction of seconds using roll-to-roll stimulation methods. This is significant in the converting processes of board since they are usually continuous, high volume operations. In addition, the creation of microfluidic patterns on the surface of TiO2 coated board using simple photomasking and surface stimulation was demonstrated. This provides new advantages and possibilities, especially in the field of intelligent printing. Limited durability and poor repellency against low surface tension liquids are presently the main limitations of LFS coatings.

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