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The effect of model uncertainty on some optimal routing problems
The effect of model uncertainties on optimal routing in a system of parallel queues is examined. The uncertainty arises in modeling the service time distribution for the customers (jobs, packets) to be served. For a Poisson arrival process and Bernoulli routing, the optimal mean system delay generally depends on the variance of this distribution. However, as the input traffic load approaches the system capacity the optimal routing assignment and corresponding mean system delay are shown to converge to a variance-invariant point. The implications of these results are examined in the context of gradient-based routing algorithms. An example of a model-independent algorithm using online gradient estimation is also included.
Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach
This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.
Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis version 6.0 theory manual
The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quanti cation, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.
Machine learning based rate optimization under geologic uncertainty
We propose a novel approach for rate optimization during a waterflood under geologic uncertainty in reservoir properties such as permeability and porosity. The traditional approach typically involves several runs of the forward simulator. This may not scale well when the optimization is to be performed at the full field-level and over multiple geologic realizations. A machine-learning (ML) based approach which is quick and scalable for rate optimization over multiple geologic realizations is proposed instead. The training data for the model is generated by running the forward simulator with randomly assigned well rates using multiple geologic realizations. A reduced order representation of the permeability heterogeneity in each of the realizations is derived using a grid connectivity transformation (GCT). This step involves finding basis functions corresponding to the different modal frequencies of the grid connectivity represented by the grid Laplacian. The projection of the heterogeneous property field along these basis functions gives the basis coefficients that form the reduced order representation. Subsequently, for each training datapoint, streamlines are traced and the minimum time of flight (TOF) representing the tracer breakthrough time at each producer is recorded. The basis coefficients and well rates are fed to a machine learning model as input and the minimum TOF at the producers forms the output of the model. This trained model can then be used along with an optimizer for computing the optimal injection rates to maximize the injection sweep efficiency. This corresponds to minimizing the variance in the minimum TOF within each well group. Different architectures of neural network are tested using 5-fold cross validation to decide the best ML model to compute the streamline time of flight. The trained model is used to perform well rate optimization over multiple realizations of geology by using a risk tolerance penalty. The optimal well rates thus obtained are compared with two cases: a) equal well rates assigned to all injectors and producers and b) well rates obtained by optimizing over a single realization without considering the uncertainty in geology. The optimal well rates are seen to offer better oil recovery and sweep efficiency than both cases.
Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis (V.6.14) (Theory Manual)
The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.
Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Theory Manual (V.6.15)
The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.
Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis: Version 6.12 Theory Manual
The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.
Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.13 Theory Manual
The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.
Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.16 Theory Manual
The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota’s iterative analysis capabilities.
Expert‐in‐the‐loop design of integral nuclear data experiments
Abstract Nuclear data are fundamental inputs to radiation transport codes used for reactor design and criticality safety. The design of experiments to reduce nuclear data uncertainty has been a challenge for many years, but advances in the sensitivity calculations of radiation transport codes within the last two decades have made optimal experimental design possible. The design of integral nuclear experiments poses numerous challenges not emphasized in classical optimal design, in particular, constrained design spaces (in both a statistical and engineering sense), severely under‐determined systems, and optimality uncertainty. We present a design pipeline to optimize critical experiments that uses constrained Bayesian optimization within an iterative expert‐in‐the‐loop framework. We show a successfully completed experiment campaign designed with this framework that involved two critical configurations and multiple measurements that targeted compensating errors in 239 Pu nuclear data.
Advancing Inverse Sensitivity/Uncertainty Methods for Nuclear Fuel Cycle Applications
The inverse sensitivity/uncertainty quantification (IS/UQ) method has recently been implemented in the Inverse Sensitivity/UnceRtainty Estimator (INSURE) module of the AMPX cross section processing system [M.E. Dunn and N.M. Greene, “AMPX-2000: A Cross-Section Processing System for Generating Nuclear Data for Criticality Safety Applications,” Trans. Am. Nucl. Soc. 86, 118–119 (2002)]. The IS/UQ method aims to quantify and prioritize the cross section measurements along with uncertainties needed to yield a given nuclear application(s) target response uncertainty, and doing this at a minimum cost. Since in some cases the extant uncertainties of the differential cross section data are already near the limits of the present-day state-of-the-art measurements, requiring significantly smaller uncertainties may be unrealistic. Therefore, we have incorporated integral benchmark experiments (IBEs) data into the IS/UQ method using the generalized linear least-squares method, and have implemented it in the INSURE module. We show how the IS/UQ method could be applied to systematic and statistical uncertainties in a self-consistent way and how it could be used to optimize uncertainties of IBEs and differential cross section data simultaneously. We itemize contributions to the cost of differential data measurements needed to define a realistic cost function.
Status on the Development of a Modeling and Simulation Framework for the Economic Assessment of Nuclear Hybrid Energy Systems
An effort to design and build a modeling and simulation framework to assess the economic viability of Nuclear Hybrid Energy Systems (NHES) was undertaken in fiscal year 2015 (FY15). The purpose of this report is to document the various tasks associated with the development of such a framework and to provide a status on its progress. Several tasks have been accomplished. First, starting from a simulation strategy, a rigorous mathematical formulation has been achieved in which the economic optimization of a Nuclear Hybrid Energy System is presented as a constrained robust (under uncertainty) optimization problem. Some possible algorithms for the solution of the optimization problem are presented. A variation of the Simultaneous Perturbation Stochastic Approximation algorithm has been implemented in RAVEN and preliminary tests have been performed. The development of the software infrastructure to support the simulation of the whole NHES has also moved forward. The coupling between RAVEN and an implementation of the Modelica language (OpenModelica) has been implemented, migrated under several operating systems and tested using an adapted model of a desalination plant. In particular, this exercise was focused on testing the coupling of the different code systems; testing parallel, computationally expensive simulations on the INL cluster; and providing a proof of concept for the possibility of using surrogate models to represent the different NHES subsystems. Another important step was the porting of the RAVEN code under the Windows™ operating system. This accomplishment makes RAVEN compatible with the development environment that is being used for dynamic simulation of NHES components. A very simplified model of a NHES on the electric market has been built in RAVEN to confirm expectations on the analysis capability of RAVEN to provide insight into system economics and to test the capability of RAVEN to identify limit surfaces even for stochastic constraints. This capability will be needed in the future to enforce the stochastic constraints on the electric demand coverage from the NHES. The development team gained experience with many of the tools that are currently envisioned for use in the economic analysis of NHES and completed several important steps. Given the complexity of the project, preference has been given to a structural approach in which several independent efforts have been used to build the cornerstone of the simulation framework. While this is good approach in establishing such a complex framework, it may delay reaching more complete results on the performance of analyzed system configurations. The integration of the previously reported exergy analysis approach was initially proposed as part of this milestone. However, in reality, the exergy-based apportioning of cost will take place only in a second stage of the implementation since it will be used to properly allocate cost among the different NHES subsystems. Therefore, exergy does not appear at the level of the main drivers in the analysis framework; the latter development of the base framework is the focus of this report.
Intrusive Uncertainty Quantification and Optimal Experiment Design in the Open-Source Pyomo Ecosystem
This contribution describes ParmEst and Pyomo.DoE, two pillars of the open-source Python-based Pyomo ecosystem for computational optimization with (partial differential) algebraic equation mathematical models. Specifically, ParmEst facilitates intrusive frequentist parameter estimation (PE) and uncertainty quantification (UQ) through built-in features, such as covariance matrix estimation, bootstrapping, and likelihood ratio tests. Complementary, Pyomo.DoE enables optimal experiment design by maximizing various metrics of the Fisher information matrix, such as A-optimality (trace), D-optimality (determinant), E-optimality (minimum eigenvalue), and ME-optimality (condition number). ParmEst and Pyomo.DoE can solve high-dimensional optimization problems by leveraging the model structure and exact derivative information. Finally, we will discuss future opportunities to integrate PE and UQ capabilities with optimization under uncertainty, including robust optimization with non-convex models via PyROS.
Neural message-passing for objective-based uncertainty quantification and optimal experimental design
Various real-world scientific applications involve the mathematical modeling of complex uncertain systems with numerous unknown parameters. Accurate parameter estimation is often practically infeasible in such systems, as the available training data may be insufficient and the cost of acquiring additional data may be high. In such cases, based on a Bayesian paradigm, we can design robust operators retaining the best overall performance across all possible models and design optimal experiments that can effectively reduce uncertainty to enhance the performance of such operators maximally. While objective-based uncertainty quantification (objective-UQ) based on MOCU (mean objective cost of uncertainty) provides an effective means for quantifying uncertainty in complex systems, the high computational cost of estimating MOCU has been a challenge in applying it to real-world scientific/engineering problems. In this work, we propose a novel scheme to reduce the computational cost for objective-UQ via MOCU based on a data-driven approach. We adopt a neural message-passing model for surrogate modeling, incorporating a novel axiomatic constraint loss that penalizes an increase in the estimated system uncertainty. As an illustrative example, we consider the optimal experimental design (OED) problem for uncertain Kuramoto models, where the goal is to predict the experiments that can most effectively enhance robust synchronization performance through uncertainty reduction. We show that our proposed approach can accelerate MOCU-based OED by four to five orders of magnitude, without any visible performance loss compared to the state-of-the-art. The proposed approach applies to general OED tasks, beyond the Kuramoto model.
IER 489: Critical Unresolved Region Integral Experiment (CURIE) CEDT Phase-2 Final Design
The final design for the CURIE integral benchmark experiment is presented in this report. Measurements will be performed on the Comet vertical assembly machine and include various critical configurations consisting of High Enriched Uranium (HEU) metal plates and Teflon moderator plates surrounded by a thick copper reflector. The various configurations with different Teflon plate thickness planned allow for complimentary measurements with differing nuclear data sensitivity in the Unresolved Resonance Region (URR). Similar to previously performed Zeus experiments, the proposed work will serve to validate vital nuclear data quantities and uncertainties and identify deficiencies in current radiation transport codes. Additionally, it will assess the applicability of optimization approaches to nuclear critical experiment design. The final experiment design is detailed in this report and includes design, optimization, uncertainty and continuous-energy nuclear data sensitivity analysis for the final experimental configurations that will provide the basis for a future benchmark evaluation intended for submission to the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook [1]. This document discusses the method, approach, considerations and final design chosen with conclusions. It also includes cost and schedule. The basis and principles of this document come from the preliminary design report [2]. Section 2 discusses the content and potential impact; section 3 gives an overview of the nuclear data and unresolved resonance region; section 4 gives a summary of the work done during the preliminary design; section 5 discusses the machine learning method and principles used for final design; section 6 summaries the results from final design; section 7 provides conclusions and the range of configurations chosen to carry forward to experiment execution; and section 8 includes a summary of costs.
Advancing Inverse Sensitivity/Uncertainty Methods for Nuclear Fuel Cycle Applications
The inverse sensitivity/uncertainty quantification (IS/UQ) method has recently been implemented in the Inverse Sensitivity/UnceRtainty Estimiator (INSURE) module of the AMPX system [1]. The IS/UQ method aims to quantify and prioritize the cross section measurements along with uncertainties needed to yield a given nuclear application(s) target response uncertainty, and doing this at a minimum cost. Since in some cases the extant uncertainties of the differential cross section data are already near the limits of the present-day state-of-the-art measurements, requiring significantly smaller uncertainties may be unrealistic. Therefore we have incorporated integral benchmark experiments (IBEs) data into the IS/UQ method using the generalized linear least-squares method, and have implemented it in the INSURE module. We show how the IS/UQ method could be applied to systematic and statistical uncertainties in a self-consistent way. We show how the IS/UQ method could be used to optimize uncertainties of IBEs and differential cross section data simultaneously.
Optimal Wind Power Uncertainty Intervals for Electricity Market Operation
It is important to select an appropriate uncertainty level of the wind power forecast for power system scheduling and electricity market operation. Traditional methods hedge against a predefined level of wind power uncertainty, such as a specific confidence interval or uncertainty set, which leaves the questions of how to best select the appropriate uncertainty levels. To bridge this gap, this paper proposes a model to optimize the forecast uncertainty intervals of wind power for power system scheduling problems, with the aim of achieving the best trade-off between economics and reliability. Then we reformulate and linearize the models into a mixed integer linear programming (MILP) without strong assumptions on the shape of the probability distribution. In order to invest the impacts on cost, reliability, and prices in a electricity market, we apply the proposed model on a twosettlement electricity market based on a six-bus test system and on a power system representing the U.S. state of Illinois. The results show that the proposed method can not only help to balance the economics and reliability of the power system scheduling, but also help to stabilize the energy prices in electricity market operation.