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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Multilevel Monte Carlo Estimators For Derivative-Free Optimization Under Uncertainty

Optimization is a key tool for scientific and engineering applications; however, in the presence of models affected by uncertainty, the optimization formulation needs to be extended to consider statistics of the quantity of interest. Optimization under uncertainty (OUU) deals with this endeavor and requires uncertainty quantification analyses at several design locations; i.e., its overall computational cost is proportional to the cost of performing a forward uncertainty analysis at each design location. An OUU workflow has two main components: an inner loop strategy for the computation of statistics of the quantity of interest, and an outer loop optimization strategy tasked with finding the optimal design, given a merit function based on the inner loop statistics. Here, in this work, we propose to alleviate the cost of the inner loop uncertainty analysis by leveraging the so-called multilevel Monte Carlo (MLMC) method, which is able to allocate resources over multiple models with varying accuracy and cost. The resource allocation problem in MLMC is formulated by minimizing the computational cost given a target variance for the estimator. We consider MLMC estimators for statistics usually employed in OUU workflows and solve the corresponding allocation problem. For the outer loop, we consider a derivative-free optimization strategy implemented in the SNOWPAC library; our novel strategy is implemented and released in the Dakota software toolkit. We discuss several numerical test cases to showcase the features and performance of our approach with respect to its Monte Carlo single fidelity counterpart.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

mpi-sppy: Optimization Under Uncertainty for Pyomo

We introduce a new Pyomo extension for optimization under uncertainty, mpi-sppy. This extension allows for the mixing of, and sharing of information between, various algorithmic approaches for optimization under uncertainty. We will discuss the underlying architecture and assess the performance and scalability of mpi-sppy on various systems, including HPC clusters.

27 ARPA - Advanced Research Projects Agency-Energy↗
DOE OSTI2026

Gradient-informed Hamiltonian Monte Carlo for multicomponent CALPHAD model optimization and uncertainty quantification

CALPHAD model parameter optimization is inherently challenging due to non-smooth objective functions, high-dimensional parameter spaces, and the need for uncertainty quantification (UQ). Traditional weighted nonlinear least squares approaches are computationally efficient but local, whereas black-box global optimizers and ensemble Markov Chain Monte Carlo (MCMC) methods provide broader exploration at substantial computational cost. The objective of this work is to combine the global exploration capability of gradient-informed Hamiltonian Monte Carlo – specifically the No-U-Turn Sampler (NUTS) – with local deterministic refinement using BFGS to efficiently optimize multicomponent CALPHAD models with minimal manual intervention. Analytic gradients are computed via the Jansson derivative framework. The methodology is demonstrated on the Cr—Fe binary system and extended to the Cr—Fe—Ni ternary system with 32 degrees of freedom. For Cr—Fe, NUTS achieves comparable or superior optimality relative to ensemble MCMC while requiring over an order-of-magnitude fewer likelihood evaluations. Parameter uncertainties are quantified through NUTS sampling and propagated to thermodynamic observables using local expansion, demonstrating a novel modular approach that combines binary and ternary parameter subsets without requiring global relaxation. These results establish gradient-informed exploration as a scalable strategy for multicomponent CALPHAD optimization and provide a practical route towards efficient higher-order database development with quantified uncertainty.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Surrogate-assisted optimization under uncertainty for design for remanufacturing considering material price volatility

Remanufacturing is a well-established end-of-life (EOL) strategy that promises significant savings in energy and carbon emissions. However, the current design practices are not remanufacturing-inclusive, i.e., the majority of products are designed for a single life cycle. As a result, potential products that can sustain multiple life cycles are deprived of additional benefits of being designed for remanufacturing, such as reduced material usage, lower cost, and improved environmental impact. Moreover, the uncertainty in design, material selection, and economics are not considered to produce remanufacturable designs. Accordingly, this research proposes a design for remanufacturing (DfRem) framework that accounts for design uncertainty and material price volatility. The framework systematically explores the design space, performs design optimization under uncertainty, followed by topology optimization to provide additional mass savings, and finally, a price volatility analysis for plausible design material choices. The candidate designs are evaluated based on their design mass, material price volatility, failure mode characteristics, carbon footprint, and embodied energy impacts. The proposed framework's utility is demonstrated via the use of an engine cylinder head case study subjected to thermo-mechanical loads along with fatigue and wear failure. Considering grey cast iron and aluminum alloy as the design material choices, it was found that the cast iron design reduced the initial design mass by 6% as opposed to a 5% decrease for aluminum. On the other hand, about 8% area of the cast iron design failed due to fatigue, compared to 3% for aluminum. Here, we further observed that although the aluminum design provided better mechanical performance than the cast iron design, this material was more expensive and volatile in price.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Pareto solutions in multicriteria optimization under uncertainty

We present and analyze several definitions of Pareto optimality for multicriteria optimization or decision problems with uncertainty primarily in their objective function values. In comparison to related notions of Pareto robustness, we first provide a full characterization of an alternative efficient set hierarchy that is based on six different ordering relations both with respect to the multiple objectives and a possibly finite, countably infinite or uncountable number of scenarios. We then establish several scalarization results for the generation of the corresponding efficient points using generalized weighted-sum and epsilon-constraint techniques. Finally, we leverage these scalarization results to also derive more general conditions for the existence of efficient points in each of the corresponding optimality classes, under suitable assumptions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Wake steering optimization under uncertainty

Turbines in wind power plants experience significant power losses when wakes from upstream turbines affect the energy production of downstream turbines. A promising plant-level control strategy to reduce these losses is wake steering, where upstream turbines are yawed to direct wakes away from downstream turbines. However, there are significant uncertainties in many aspects of the wake steering problem. For example, infield sensors do not give perfect information, and inflow to the plant is complex and difficult to forecast with available information, even over short time periods. Here, we formulate and solve an optimization under uncertainty (OUU) problem for determining optimal plant-level wake steering strategies in the presence of independent uncertainties in the direction, speed, turbulence intensity, and shear of the incoming wind, as well as in turbine yaw positions. The OUU wake steering strategy is first examined for a two-turbine test case to explore the impacts of different types of inflow uncertainties, and it is then demonstrated for a more realistic 11-turbine wind power plant. Of the sources of uncertainty considered, we find that wake steering strategies are most sensitive to uncertainties in the wind speed and direction. When maximizing expected power production, the OUU strategy also tends to favor smaller yaw angles, which have been shown in previous work to reduce turbine loading. Ultimately, the plant-level wake steering strategy formulated using an OUU approach yields 0.48?% more expected annual energy production for the 11-turbine wind plant than a strategy that neglects uncertainty when considering stochastic inputs. Thus, not only does the present OUU strategy produce more power in realistic conditions, but it also reduces risk by prescribing strategies that call for less extreme yaw angles.

17 WIND ENERGY↗
DOE OSTI2022

Equation of State Optimization and Uncertainty Quantization: Implementation in the LANL EOS Production Code OpenSesame

We detail the approaches of particle swarm optimization and Bayesian inference through Markov chain Monte Carlo for equation of state development. This work includes formulation of the modeling for the equation of state, numeric optimization of the parametric models via particle swarm optimization, and generation of probability distributions of equations of state from Markov chain Monte Carlo.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Optimization under uncertainty of a hybrid waste tire and natural gas feedstock flexible polygeneration system using a decomposition algorithm

Market uncertainties motivate the development of flexible polygeneration systems that are able to adjust operating conditions to favor production of the most profitable product portfolio. However, this operational flexibility comes at the cost of higher capital expenditure. A scenario-based two-stage stochastic nonconvex Mixed-Integer Nonlinear Programming (MINLP) approach lends itself naturally to optimizing these trade-offs. This work studies the optimal design and operation under uncertainty of a hybrid feedstock flexible polygeneration system producing electricity, methanol, dimethyl ether, olefins or liquefied (synthetic) natural gas. A recently developed C++ based software framework (named GOSSIP) is used for modeling the optimization problem as well as its efficient solution using the Nonconvex Generalized Benders Decomposition (NGBD) algorithm. Two different cases are studied: The first uses estimates of the means and variances of the uncertain parameters from historical data, whereas the second assesses the impact of increased uncertain parameter volatility. The value of implementing flexible designs characterized by the value of the stochastic solution (VSS) is in the range of 260–405 M$ for a scale of approximately 893 MW of thermal input. Increased price volatility around the same mean results in higher expected net present value and VSS as operational flexibility allows for asymmetric exploitation of price peaks.

42 ENGINEERING↗
DOE OSTI2025

Surrogate-driven design optimization with uncertainty constraints in Monte Carlo simulations

In multi-objective design tasks, the computational cost increases rapidly when high-fidelity simulations are used to evaluate objective functions. Surrogate models help mitigate this cost by approximating the simulation output, simplifying the design process. However, under high uncertainty, surrogate models trained on noisy data can produce inaccurate predictions, as their performance depends heavily on the quality of training data. This study investigates the impact of data uncertainty on two multi-objective design problems modelled using Monte Carlo transport simulations: a neutron moderator and an ion-to-neutron converter. For each, a grid search was performed using five different tally uncertainty levels to generate training data for neural network surrogate models. These models were then optimized using NSGA-III. The recovered Pareto-fronts were analyzed across uncertainty levels: in the moderator problem, normalized hypervolume dropped from 0.886 at 1.0% uncertainty to 0.748 at 10% uncertainty, while in the converter problem it remained near 0.50 for all cases. Average simulation times were also compared to evaluate the trade-off between accuracy and computational cost. Results show that the influence of simulation uncertainty is strongly problem-dependent. In the neutron moderator case, higher uncertainties led to exaggerated objective sensitivities and distorted Pareto-fronts, reducing normalized hypervolume. In contrast, the ion-to-neutron converter task was less affected—low-fidelity simulations produced results similar to those from high-fidelity data. These findings suggest that a fixed-fidelity approach is not optimal. Surrogate models can recover the Pareto-front under noisy conditions, and multi-fidelity studies help identify suitable uncertainty levels for each problem to balance efficiency and accuracy.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2020

Koopman-Based Approach to Nonintrusive Reduced Order Modeling: Application to Aerodynamic Shape Optimization and Uncertainty Propagation

A methodology for nonintrusive projection-based nonlinear model reduction originally presented by Renganathan et al. is further extended here toward parametric systems with a focus on application to aerospace design. Specifically, the method is extended to address static systems with parametric geometry (that deforms the mesh) in addition to parametric freestream boundary conditions. The main idea is to first perform a transformation on the governing equations such that it is lifted to a higher-dimensional but linear underdetermined system. This enables one to extract the system matrices easily as compared to that of the original nonlinear system. The underdetermined system is closed with a set of model-dependent nonlinear constraints upon which the model reduction is finally performed. The methodology is validated on the subsonic and transonic inviscid flows past the NACA0012 and the RAE2822 airfoils with parametrized shapes. The utility of the approach is further demonstrated by applying it to two common problems in aerospace design, namely, derivative-free global optimization and parametric uncertainty quantification with Monte Carlo sampling. Overall, the methodology is shown to achieve accuracy up to 5% and computational speedup of two to three orders of magnitude relative to the full order model. Comparison against another nonintrusive model reduction method revealed that the proposed approach is more robust, accurate, and retains the consistency between the state variables.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Selection of a Pair of Experiments to Optimally Reduce Uncertainty in Targeted Nuclear Data

We propose a novel process to select a pair of differential and integral experiments that best reduce uncertainties in targeted 239 ⁢Pu nuclear data while compressing the current nuclear data pipeline from 20 to 3 years. 239⁢ Pu nuclear data are poorly understood for neutrons in the intermediate energy range due to sparsity and uncertainty in historical experiments. New experiments targeting this range will enable better understanding of these nuclear data, but choosing the ideal experiments to conduct is challenging. Beginning with a prior distribution represented by samples of nuclear data generated from theory, generalized least squares adjustments are made to incorporate data from historical experiments. To quantify potential uncertainty reduction obtainable from a pair of candidate experiments, we compute the D-optimality criterion of the posterior covariance of intermediate energy range nuclear data compared to the equivalent covariance after additional adjustment to the pair of candidate experiments. Repeating the process for each of many candidate pairs facilitates the final selection. Results support 63⁢ Cu total cross section measurements for differential experiments and alumina and alumina/graphite configurations for integral experiments. This analysis enables choosing differential and integral experiments to be executed concurrently while shortening decision times relative to the current nuclear data pipeline.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Stochastic Optimization and Uncertainty Quantification of Natrium-based Nuclear-Renewable Energy Systems for Flexible Power Applications in Deregulated Markets

Rapid integration of variable renewable energy sources (VRES) has made modeling and stochastic optimization of hybrid energy systems crucial for studying their long-term performance and viability. However, most studies have focused on just historical data, which may be unreliable for capturing short-term fluctuations, rare events, and long-term patterns of energy demand, price, and the variability of renewable energy sources. For this study, optimal synthetic time series models were developed using Wasserstein distance. The models were validated by comparing the key statistical measures against those of the historical data. They were then used to optimize the integrated Natrium-style advanced energy systems and their long-term (30 years) economics. The stochastic model performs bi-level optimization to find the optimal sizes for the balance of plant and thermal energy storage, while also optimizing energy dispatch to achieve the maximum net present value. In studies of two deregulated markets (California ISO and the Electric Reliability Council of Texas), the integrated Natrium-style system performed better in CAISO than in ERCOT, given higher and more consistent electricity prices during peak-demand periods. The potentially enlarged cost associated with the variable operation and maintenance of the TES system also plays a significant role in driving the system sizing, thus its impacts on the system are investigated in detail through comparison against a baseline case. The study also finds that the bi-level optimization results based on stochastic gradient descent closely match the grid search results. The uncertainty quantification of the stochastic signals provides further NPV-related insights and probability distributions for the case studies. The normal standard error of the mean of NPV for the case with and without TES VOM for CAISO were found to be 7.73M (plus-minus sign) 1.09M USD and 104.99M (plus-minus sign) 1.25M USD, respectively based on a 95% confidence. Given the relatively small NPV variance based on 150 samples, the analysis affords the most robust possible prediction of the techno-economic performance of the integrated Natrium-style energy systems.

25 ENERGY STORAGE↗
DOE OSTI2024

Bayes_Opt-SWMM: A Gaussian process-based Bayesian optimization tool for real-time flood modeling with SWMM

Real-time flood model plays a pivotal role in averting urban flood damage, particularly when there is minimal lead time for preparatory measures. However, urban flood modeling in real-time often contends with inherent uncertainties arising from input data uncertainty and parameter ambiguities. Here this study introduces a real-time calibration (RTC) tool called Bayes_Opt-SWMM, specifically tailored for real-time urban flood modeling and uncertainty optimization. This tool leverages the Gaussian process-based Bayesian optimization algorithm and interfaces seamlessly with the Stormwater Management Model (SWMM). It integrates real-time model forcing data and flood monitoring collected through sensors and gauges which are strategically placed within critical locations of urban drainage systems. Our approach hinges on the Surrogate Model based Uncertainty Optimization (SMUO) concept, providing an avenue for enhancing real-time flood modeling. Bayes_Opt-SWMM runs the optimization process using a surrogate model called Gaussian Process emulator with two inference methods: (1) the Gaussian Process (GP) model and (2) Markov Chain Monte Carlo (MCMC) algorithm in GP model (GP_MCMC). Furthermore, three acquisition functions, namely Expected Improvement (EI), Maximum Probability of Improvement (MPI), and Lower Confidence Bound (LCB), facilitate optimal parameter fitting within the surrogate models. The efficiency of GP-based surrogate models in learning SWMM model parameters, leads to an improved uncertainty quantification and accelerated real-time flood modeling in urban areas. Overall, Bayes_Opt-SWMM emerges as a cost-effective and valuable tool for real-time flood modeling and monitoring, with significant potential for managing intelligent storm water systems in urban environments.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A parallel hub-and-spoke system for large-scale scenario-based optimization under uncertainty

Practical solution of stochastic programming problems generally requires the use of parallel computing resources. Here, we describe the open source package mpi-sppy, in which efficient and scalable parallelization is a central feature. We report computational experiments that demonstrate the ability to solve very large stochastic programming problems - including mixed-integer variants - in minutes of wall clock time, efficiently leveraging significant parallel computing resources. We report results for the largest publicly available instances of stochastic mixed-integer unit commitment problems, solving to provably tight optimality gaps. In addition, we introduce a novel software architecture that facilitates combinations of methods for accelerating convergence that can be combined in plug-and-play manner. Finally, the mpi-sppy package is written in Python, leverages the widely used Pyomo (http://www.pyomo.org) library for modeling mathematical programs, builds on existing MPI implementations to ensure efficiency and scalability, and is available via http://github.com/Pyomo/mpi-sppy.

97 MATHEMATICS AND COMPUTING↗