# Browsing by Subject "Variance reduction"

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Item Assessment of Monte Carlo N-Particle variance reduction techniques for small solid angle neutron transport(2022-05-03) Webb, Matthew David; Charlton, William S.; Landsberger, Sheldon; Haas, Derek; Graham, JosephShow more A benchmark experiment for a small solid angle neutron transport system was designed and measured at The University of Texas's Nuclear Engineering Teaching Laboratory. The benchmark problem consists of an MP320 14.1MeV DT Neutron Generator streaming fast neutrons through an opening in a graphite rod. The flux at the far end of the graphite was measured with a Holmium activation foil and used to calculate the absolute source strength of the DT Generator. The experimental measurements were then compared to an analog MCNP simulation of the experimental setup to verify the benchmark MCNP problem was accurate with real world phenomena. Once the analog benchmark was verified, variance reduction methods were included in the MCNP simulation both independently and together in order to evaluate their effectiveness for small solid angle neutron transport problems. Multiple variance reduction techniques were identified to be effective when implemented individually. However, significant performance gains were achieved by implementing multiple complimentary variance reduction techniques in combination.Show more Item Decomposition and variance reduction techniques for stochastic mixed integer programs(2018-08) Zolan, Alexander Joseph; Hasenbein, John J.; Morton, David P.; Bard, Jonathan F; Hanasusanto, Grani A; Newman, Alexandra MShow more Obtaining upper and lower bounds on the optimal value of a stochastic integer program can require solution of multiple-scenario problems, which are computationally expensive or intractable using off-the-shelf integer-programming software. Additionally, optimal solutions to a two-stage problem whose second stage spans long time horizons may be optimistic, due to the model's inappropriate ability to plan for future periods which are not known in practice. To that end, we present a framework for optimizing system design in the face of a restricted class of policies governing system operation, which aim to model realistic operation. This leads to a natural decomposition of the problem yielding upper and lower bounds which we can compute quickly. We illustrate these ideas using a model that seeks to design and operate a microgrid to support a forward operating base. Here, designing the microgrid includes specifying the number and type of diesel generators, PV systems, and batteries while operating the grid involves dispatching these assets to satisfy load at minimum cost. We extend our approach to solve the same problem under load and photovoltaic uncertainty, and propose a method to generate appropriately correlated scenarios by simulating building occupancy via a bottom-up approach, then using the occupancy levels to inform environmental control unit loads on the base. Finally, in a separate line of work, we optimize the design of the strata for a stratified sampling estimator to reduce variance. We extend this method to the multivariate setting by optimizing the strata for a nonuniform Latin hypercube estimator. We then present empirical results that show that our method reduces the variance of the estimator, compared to one using equal-probability strata.Show more Item A discrete velocity method for the Boltzmann equation with internal energy and stochastic variance reduction(2015-12) Clarke, Peter Barry; Varghese, Philip L.; Goldstein, David Benjamin; Raja, Laxminarayan; Gamba, Irene; Magin, ThierryShow more The goal of this work is to develop an accurate and efficient flow solver based upon a discrete velocity description of the Boltzmann equation. Standard particle based methods such as Direct Simulation Monte Carlo (DSMC) have a number of difficulties with complex and transient flows, stochastic noise, trace species, and high level internal energy states. To address these issues, a discrete velocity method (DVM) was developed which models the evolution of a flow through the collisions and motion of variable mass quasi-particles defined as delta functions on a truncated, discrete velocity domain. The work is an extension of a previous method developed for a single, monatomic species solved on a uniformly spaced velocity grid. The collision integral was computed using a variance reduced stochastic model where the deviation from equilibrium was calculated and operated upon. This method produces fast, smooth solutions of near-equilibrium flows. Improvements to the method include additional cross-section models, diffuse boundary conditions, simple realignment of velocity grid lines into non-uniform grids, the capability to handle multiple species (specifically trace species or species with large molecular mass ratios), and both a single valued rotational energy model and a quantized rotational and vibrational model. A variance reduced form is presented for multi-species gases and gases with internal energy in order to maintain the computational benefits of the method. Every advance in the method allows for more complex flow simulations either by extending the available physics or by increasing computational efficiency. Each addition is tested and verified for an accurate implementation through homogeneous simulations where analytic solutions exist, and the efficiency and stochastic noise are inspected for many of the cases. Further simulations are run using a variety of classical one-dimensional flow problems such as normal shock waves and channel flows.Show more