Results for “Optimization Under Uncertainty” — Page 4

DOE OSTI2021

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.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

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.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

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.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

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.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

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.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

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.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

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.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2010

Asymptotic Linearity of Optimal Control Modification Adaptive Law with Analytical Stability Margins

Optimal control modification has been developed to improve robustness to model-reference adaptive control. For systems with linear matched uncertainty, optimal control modification adaptive law can be shown by a singular perturbation argument to possess an outer solution that exhibits a linear asymptotic property. Analytical expressions of phase and time delay margins for the outer solution can be obtained. Using the gradient projection operator, a free design parameter of the adaptive law can be selected to satisfy stability margins.

Nguyen, Nhan T.↗

NASA NTRS2004

Towards Risk Based Design for NASA's Missions

This paper describes the concept of Risk Based Design in the context of NASA s low volume, high cost missions. The concept of accounting for risk in the design lifecycle has been discussed and proposed under several research topics, including reliability, risk analysis, optimization, uncertainty, decision-based design, and robust design. This work aims to identify and develop methods to enable and automate a means to characterize and optimize risk, and use risk as a tradeable resource to make robust and reliable decisions, in the context of the uncertain and ambiguous stage of early conceptual design. This paper first presents a survey of the related topics explored in the design research community as they relate to risk based design. Then, a summary of the topics from the NASA-led Risk Colloquium is presented, followed by current efforts within NASA to account for risk in early design. Finally, a list of "risk elements", identified for early-phase conceptual design at NASA, is presented. The purpose is to lay the foundation and develop a roadmap for future work and collaborations for research to eliminate and mitigate these risk elements in early phase design.

Tumer, Irem Y.↗

NASA NTRS2010

Robustness-Based Design Optimization Under Data Uncertainty

This paper proposes formulations and algorithms for design optimization under both aleatory (i.e., natural or physical variability) and epistemic uncertainty (i.e., imprecise probabilistic information), from the perspective of system robustness. The proposed formulations deal with epistemic uncertainty arising from both sparse and interval data without any assumption about the probability distributions of the random variables. A decoupled approach is proposed in this paper to un-nest the robustness-based design from the analysis of non-design epistemic variables to achieve computational efficiency. The proposed methods are illustrated for the upper stage design problem of a two-stage-to-orbit (TSTO) vehicle, where the information on the random design inputs are only available as sparse point and/or interval data. As collecting more data reduces uncertainty but increases cost, the effect of sample size on the optimality and robustness of the solution is also studied. A method is developed to determine the optimal sample size for sparse point data that leads to the solutions of the design problem that are least sensitive to variations in the input random variables.

Zaman, Kais↗

NASA NTRS2015

The Observed State of the Water Cycle in the Early Twenty-First Century

This study quantifies mean annual and monthly fluxes of Earth's water cycle over continents and ocean basins during the first decade of the millennium. To the extent possible, the flux estimates are based on satellite measurements first and data-integrating models second. A careful accounting of uncertainty in the estimates is included. It is applied within a routine that enforces multiple water and energy budget constraints simultaneously in a variational framework in order to produce objectively determined optimized flux estimates. In the majority of cases, the observed annual surface and atmospheric water budgets over the continents and oceans close with much less than 10% residual. Observed residuals and optimized uncertainty estimates are considerably larger for monthly surface and atmospheric water budget closure, often nearing or exceeding 20% in North America, Eurasia, Australia and neighboring islands, and the Arctic and South Atlantic Oceans. The residuals in South America and Africa tend to be smaller, possibly because cold land processes are negligible. Fluxes were poorly observed over the Arctic Ocean, certain seas, Antarctica, and the Australasian and Indonesian islands, leading to reliance on atmospheric analysis estimates. Many of the satellite systems that contributed data have been or will soon be lost or replaced. Models that integrate ground-based and remote observations will be critical for ameliorating gaps and discontinuities in the data records caused by these transitions. Continued development of such models is essential for maximizing the value of the observations. Next-generation observing systems are the best hope for significantly improving global water budget accounting.

Numerical analysis/modeling↗

DOE OSTI2020

Optimal Estimation Retrievals and Their Uncertainties: What Every Atmospheric Scientist Should Know

Remote sensing instruments are heavily used to provide observations for both the operational and research communities. These sensors do not provide direct observations of the desired atmospheric variables, but instead, retrieval algorithms are necessary to convert the indirect observations into the variable of interest. It is critical to be aware of the underlying assumptions made by many retrieval algorithms, including that the retrieval problem is often ill posed and that there are various sources of uncertainty that need to be treated properly. In short, the retrieval challenge is to invert a set of noisy observations to obtain estimates of atmospheric quantities. The problem is often complicated by imperfect forward models, by imperfect prior knowledge, and by the existence of nonunique solutions. Optimal estimation (OE) is a widely used physical retrieval method that combines measurements, prior information, and the corresponding uncertainties based on Bayes’s theorem to find an optimal solution for the atmospheric state. Furthermore, OE also allows the relative contributions of the different sources of error to the uncertainty in the final retrieved atmospheric state to be understood. Here, we provide a novel Python library to illustrate the use of OE for inverse problems in the atmospheric sciences. We introduce two example problems: how to retrieve drop size distribution parameters from radar observations and how to retrieve the temperature profile from ground-based microwave sensors. Using these examples, we discuss common pitfalls, how the various error sources impact the retrieval, and how the quality of the retrieval results can be quantified.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

A staged deep learning approach to spatial refinement in 3D temporal atmospheric transport

High-resolution spatiotemporal simulations effectively capture the complexities of atmospheric plume dispersion in complex terrain. However, their high computational cost makes them impractical for applications requiring rapid responses or iterative processes, such as optimization, uncertainty quantification, or inverse modeling. To address this challenge, this work introduces the Dual-Stage Temporal Three-dimensional UNet Super-resolution (DST3D-UNet-SR) model, a highly efficient deep learning model for plume dispersion predictions. DST3D-UNet-SR is composed of two sequential modules: the temporal module (TM), which predicts the transient evolution of a plume in complex terrain from low-resolution temporal data, and the spatial refinement module (SRM), which subsequently enhances the spatial resolution of the TM predictions. We train DST3D-UNet-SR using a comprehensive dataset derived from high-resolution large eddy simulations (LES) of plume transport. We propose the DST3D-UNet-SR model to significantly accelerate LES of three-dimensional (3D) plume dispersion by three orders of magnitude. Additionally, the model demonstrates the ability to dynamically adapt to evolving conditions through the incorporation of new observational data, substantially improving prediction accuracy in high-concentration regions near the source.

3D temporal sequences↗

DOE OSTI2022

LaSDI: Parametric Latent Space Dynamics Identification

Enabling fast and accurate physical simulations with data has become an important area of computational physics to aid in inverse problems, design-optimization, uncertainty quantification, and other various decision-making applications. This paper presents a data-driven framework for parametric latent space dynamics identification procedure that enables fast and accurate simulations. The parametric model is achieved by building a set of local latent space model and designing an interaction among them. An individual local latent space dynamics model achieves accurate solution in a trust region. By letting the set of trust region to cover the whole parameter space, our model shows an increase in accuracy with an increase in training data. Herein we introduce two different types of interaction mechanisms, i.e., point-wise and region-based approach. Both linear and nonlinear data compression techniques are used. We illustrate the framework of Latent Space Dynamics Identification (LaSDI) enable a fast and accurate solution process on various partial differential equations, i.e., Burgers’ equations, radial advection problem, and nonlinear heat conduction problem, achieving 0 (100)x speed-up and 0 (1)% relative error with respect to the corresponding full order models.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

JetGP: A derivative enhanced Gaussian process library

Derivative enhanced Gaussian Processes (DEGPs) can significantly improve surrogate model accuracy over standard Gaussian Process (GP) formulations by incorporating derivative information. However, standard implementations scale poorly with dimension, limiting their use in high dimensional engineering problems. JetGP is a Python framework that unifies existing derivative enhanced GP methodologies into a single library and extends them to support arbitrary order derivative information. The library implements four complementary formulations: standard derivative enhanced Gaussian Processes (DEGP), directional DEGP (DDEGP), generalized directional DEGP (GDDEGP), and weighted DEGP (WDEGP). By unifying these approaches in a consistent interface with robust numerical implementations, JetGP enables practitioners to balance predictive accuracy and computational efficiency for high dimensional optimization, uncertainty quantification, and sensitivity analysis in engineering design.

Derivative enhanced Gaussian process↗

DOE OSTI2022

Source-to-Source Automatic Differentiation of OpenMP Parallel Loops

This article presents our work toward correct and efficient automatic differentiation of OpenMP parallel worksharing loops in forward and reverse mode. Automatic differentiation is a method to obtain gradients of numerical programs, which are crucial in optimization, uncertainty quantification, and machine learning. The computational cost to compute gradients is a common bottleneck in practice. For applications that are parallelized for multicore CPUs or GPUs using OpenMP, one also wishes to compute the gradients in parallel. Here, we propose a framework to reason about the correctness of the generated derivative code, from which we justify our OpenMP extension to the differentiation model. We implement this model in the automatic differentiation tool Tapenade and present test cases that are differentiated following our extended differentiation procedure. Performance of the generated derivative programs in forward and reverse mode is better than sequential, although our reverse mode often scales worse than the input programs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Safeguards Technology Program FY2026 Mid-Year Report for Project WBS# 24.1.3.3: Development of Procedures for Th-U Radiochronometry of Uranium Particles by LG-SIMS

Implementing 230 Th- 234 U radiochronometry of environmental uranium particles by large geometry secondary ion mass spectrometry (LG-SIMS) requires assessment, validation, and technical support before safeguards conclusions can be drawn from the information. This project investigates the most challenging aspects of LG-SIMS particle radiochronometry 230 Th- 234 U measurements through a collaboration between LANL and NIST, to provide best practices and procedures for determining high quality ages with optimized uncertainties. This includes exploration of reducing detector backgrounds, investigating the best ways to report uncertainties, and establishing recommended instrument setups.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗