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Results for “Optimization Under Uncertainty”

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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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Multistage economic MPC for systems with a cyclic steady state: A gas network case study

Multistage model predictive control (MPC) provides a robust control strategy for dynamic systems with uncertainties and a setpoint tracking objective. Moreover, extending MPC to minimize an economic cost instead of tracking a pre-calculated optimal setpoint improves controller performance. This paper presents a novel multistage economic nonlinear model predictive control (E-NMPC) framework for dynamic systems operating under uncertainty, with specific application to natural gas transmission networks. A key innovation lies in the integration of cyclic steady-state (CSS) constraints within the multistage MPC formulation, enabling the controller to manage periodic operating conditions commonly observed in energy systems. A Lyapunov-based descent condition is enforced to ensure robust stability of the controller. The multistage economic MPC framework is validated on two gas pipeline case studies, where it successfully minimizes net energy consumption, respects operational constraints under uncertain demand profiles, and guides the network to optimal cyclic operation. The Lyapunov function remains bounded in both case studies, validating the robust stability of multistage E-NMPC.

03 NATURAL GAS↗
NASA NTRSDate not supplied

Copernicus-LinCov (COPCOV) Software Integration in Support of Robust Trajectory Optimization

Robust trajectory optimization is the process of optimizing a trajectory while accounting for system uncertainty due to a variety of potential error sources. This work highlights the development and features of a novel tool known as CopCov to support robust trajectory optimization efforts. CopCov acts as an interface between Copernicus, a generalized trajectory design and optimization tool, and LinCov, a linear covariance analysis tool. By having a direct interface between these two software packages, Copernicus can receive covariance information from LinCov through a direct feedback loop, thus enabling optimization of a trajectory that is robust to trajectory dispersions and navigation errors. This paper details the architecture of CopCov and its flexibility to operate under varying configurations, including with both tools running locally or alternatively with the tools communicating via a remote connection. Additionally, the CopCov tool is demonstrated on a simple Hohmann transfer reference trajectory with varying numbers of Trajectory Correction Maneuvers (TCMs) and varying problem formulations. This example scenario is used to highlight how the inclusion of the CopCov interface affects burn placement of both major burns and minor burns (i.e., TCMs) in the optimized solution. Results are compared against analytical solutions and against a Genetic Algorithm (GA) optimizer for independent verification and validation.

Copernicus↗
DOE OSTI2026

Uncertainty quantification for inverse problems with application to ptychographic reconstruction

Inverse problems in imaging are commonly solved by optimization or learned surrogates that return a single reconstruction, while uncertainty information is often unavailable. In many experimental settings, however, uncertainty is required to assess reliability, guide downstream analysis, and prioritize additional measurements. In this note, we present a compact uncertainty-quantification framework based on local objective curvature, and then specialize it to ptychographic reconstruction. We further show how repeated reconstructions can be aggregated in a statistically principled way, including a practical implementation path for PtychoNN.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Uncertainty Estimation for SMAP Level-1 Brightness Temperature Assimilation at Different Timescales

In this study, we assimilate Soil Moisture Active Passive (SMAP) mission brightness temperature (Tb) observations into NASA’s Catchment Land Surface Model using an Ensemble Kalman filter to update surface and root-zone soil moisture simulations. Different time series components of the Tb observations are assimilated including anomalies, inter-annual variations, and high-frequency variations. To optimize the weights that the data assimilation (DA) puts on the observations, the ratio between the un-certainties of modeled and observed Tb is approximated using modeled and observed soil moisture uncertainties estimated using triple collocation analysis. Results are compared to a benchmark experiment that mimics the operational SMAP Level-4 algorithm, which assimilates Tb observations using a spatially-constant 4 Kelvin (K) observation uncertainty. All DA experiments exhibit notable skill improvements in most regions. Improvements are greatest for the inter-annual variations in the simulations of both surface and root-zone soil moisture (mean improvements in terms of Pearson correlation (-) are 0.08 and 0.06, respectively). Anomaly simulations improve similarly (0.07), and improvements in the high-frequency variations are only observed for sur-face soil moisture simulations (0.06). Strikingly, however, no notable difference in skill—neither improvement nor deterioration—is observed between the experiments that use optimized observation uncertainty parameters and the 4 K benchmark experiment. We show, analytically, that this may be explained by the presence of large observation operator errors, which have the potential to render post-update uncertainty insensitive to inaccuracies in the Kalman gain.

Alexander Gruber↗
DOE OSTI2024

Shortest path network interdiction with asymmetric uncertainty

Abstract This paper considers an extension of the shortest path network interdiction problem that incorporates robustness to account for parameter uncertainty. The shortest path interdiction problem is a game of two players with conflicting agendas and capabilities: an evader, who traverses the arcs of a network from a source node to a sink node using a path of shortest length, and an interdictor, who maximizes the length of the evader's shortest path by interdicting arcs on the network. It is usually assumed that the parameters defining the network are known exactly by both players. We consider the situation where the evader assumes the nominal parameter values while the interdictor uses robust optimization techniques to account for parameter uncertainty or sensor degradation. We formulate this problem as a nonlinear mixed‐integer semi‐infinite bilevel program and show that it can be converted into a mixed‐integer linear program with a second order cone constraint. We use random geometric networks and transportation networks to perform computational studies and demonstrate the unique decision strategies that our variant produces. Solving the shortest path interdiction problem with asymmetric uncertainty protects the interdictor from investing in a strategy that hinges on key interdictions performing as promised. It also provides an alternate strategy that mitigates the risk of these worst‐case possibilities.

Punla‐Green, She'ifa Z.↗
DOE OSTI2023

Pragmatic Uncertainty Quantification and Propagation in Inverse Estimation of Structural Dynamics Parameters given Material Property Uncertainties and Limited Sensor Data

In this report we demonstrate some relatively simple and inexpensive methods to effectively account for various sources of epistemic lack-of-knowledge type uncertainty in inverse problems. The demonstration problem involves inverse estimation of six parameters of a bolted joint that attaches a kettlebell shaped object to a thick plate. The parameters are efficiently inverted in a modal-based model calibration using gradient-based optimization. Two material properties of the kettlebell are treated as uncertain to within given epistemic uncertainty bounds. We apply and test interval and sparse-sample probabilistic approaches to account for uncertainty in the estimated parameters (and various scalar functionals of the parameters as generic quantities of interest, QOIs) due to uncertainties in the material properties. We also investigate the error effects of limited numbers of vibration sensors (accelerometers) on the kettlebell and plate, and therefore abbreviated excitation/response information in the parameter inversions. We propose and demonstrate a Leave-K-Sensors-Out “cross-prediction” UQ approach to estimate related uncertainties on the parameters and QOI functionals. We indicate how uncertainties from material properties and limited sensors are treated in a combined manner. The economical combined UQ approach involves just three to five samples (i.e. three to five inverse simulations), with no added complication or error/uncertainty from use of surrogate models for affordability. Finally, we describe a related economical UQ approach for handling potential parameter solution non-uniqueness and numerical optimization related precision uncertainties in the estimated parameter values. Indicated further research is identified.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Optimization Through Multi-Fidelity Modeling

We present a novel method for optimizing parameter selection for simulations with an evaluation budget. We start with an existing method for building a multi-fidelity model out of many low-fidelity simulations and few high-fidelity simulations. We propose a novel method to simplify parameter selection without sacrificing performance. We verify these results and compare with existing literature. Next, we propose a novel algorithm which uses this difference model to suggest new points in the parameter design space to simulate. We add each point we simulate to the model to improve its quality for the next iteration. The algorithm trades off reducing the uncertainty of the existing model with optimization of the objective. The first is more useful when a large fraction of the computation budget remains. The second is more useful when a small fraction of the computation budget remains. Our method converges to the optimum by using a high-fidelity evaluation for just 16 of the 427 points. Our method is general enough to work if there is no low-fidelity model. Furthermore, it is agnostic to the underlying physics of the problem. Therefore, both the low-fidelity and high-fidelity models can be generated by any arbitrary function, including simulations and physical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Measurement of the muon neutrino charged-current mesonless cross section in the NOvA near detector

NOvA is a long-baseline accelerator neutrino experiment at Fermilab. Its physics goals include precision neutrino oscillation measurements, neutrino interaction cross-section measurements and beyond Standard Model explorations. We present a measurement of muon neutrino charged-current cross section with zero mesons in the final state at the NOvA near detector. This measurement is performed as a function of the kinematics of the final state muon. Our chosen interaction channel is especially sensitive to quasielastic and meson exchange current interactions and it provides handles for constraining the cross section systematic uncertainties in oscillation analyses in present and future experiments. For particle identification, we use a convolutional neural network (CNN) trained on individual particles simulated in the NOvA Near detector. This allows us to select the desired signal while reducing the potential bias from neutrino interaction modeling. We study strategies for constraining the remaining charged-pion background via Michel electron information in a template fitting approach. The main experimental result is a two-dimensional differential cross section as a function of final-state muon kinetic energy and polar angle. The parameters of this measurement, including binning and unfolding, were optimized to reduce the expected systematic uncertainty in the total cross section. The final result shows good agreement with the main GENIE-based simulation framework that was independently fine-tuned in NOvA. We finally propose improvements and subsequent steps that build on this analysis and further dissect the final states of neutrino interactions. This work has been supported by US DOE grant DE-SC0015684.

Sánchez Falero, Sebastián Jesús [Iowa State U.]↗
NASA NTRS2004

Investigation of Navier-Stokes Code Verification and Design Optimization

With rapid progress made in employing computational techniques for various complex Navier-Stokes fluid flow problems, design optimization problems traditionally based on empirical formulations and experiments are now being addressed with the aid of computational fluid dynamics (CFD). To be able to carry out an effective CFD-based optimization study, it is essential that the uncertainty and appropriate confidence limits of the CFD solutions be quantified over the chosen design space. The present dissertation investigates the issues related to code verification, surrogate model-based optimization and sensitivity evaluation. For Navier-Stokes (NS) CFD code verification a least square extrapolation (LSE) method is assessed. This method projects numerically computed NS solutions from multiple, coarser base grids onto a freer grid and improves solution accuracy by minimizing the residual of the discretized NS equations over the projected grid. In this dissertation, the finite volume (FV) formulation is focused on. The interplay between the xi concepts and the outcome of LSE, and the effects of solution gradients and singularities, nonlinear physics, and coupling of flow variables on the effectiveness of LSE are investigated. A CFD-based design optimization of a single element liquid rocket injector is conducted with surrogate models developed using response surface methodology (RSM) based on CFD solutions. The computational model consists of the NS equations, finite rate chemistry, and the k-6 turbulence closure. With the aid of these surrogate models, sensitivity and trade-off analyses are carried out for the injector design whose geometry (hydrogen flow angle, hydrogen and oxygen flow areas and oxygen post tip thickness) is optimized to attain desirable goals in performance (combustion length) and life/survivability (the maximum temperatures on the oxidizer post tip and injector face and a combustion chamber wall temperature). A preliminary multi-objective optimization study is carried out using a geometric mean approach. Following this, sensitivity analyses with the aid of variance-based non-parametric approach and partial correlation coefficients are conducted using data available from surrogate models of the objectives and the multi-objective optima to identify the contribution of the design variables to the objective variability and to analyze the variability of the design variables and the objectives. In summary the present dissertation offers insight into an improved coarse to fine grid extrapolation technique for Navier-Stokes computations and also suggests tools for a designer to conduct design optimization study and related sensitivity analyses for a given design problem.

Vaidyanathan, Rajkumar↗
NASA NTRS2006

Strict Constraint Feasibility in Analysis and Design of Uncertain Systems

This paper proposes a methodology for the analysis and design optimization of models subject to parametric uncertainty, where hard inequality constraints are present. Hard constraints are those that must be satisfied for all parameter realizations prescribed by the uncertainty model. Emphasis is given to uncertainty models prescribed by norm-bounded perturbations from a nominal parameter value, i.e., hyper-spheres, and by sets of independently bounded uncertain variables, i.e., hyper-rectangles. These models make it possible to consider sets of parameters having comparable as well as dissimilar levels of uncertainty. Two alternative formulations for hyper-rectangular sets are proposed, one based on a transformation of variables and another based on an infinity norm approach. The suite of tools developed enable us to determine if the satisfaction of hard constraints is feasible by identifying critical combinations of uncertain parameters. Since this practice is performed without sampling or partitioning the parameter space, the resulting assessments of robustness are analytically verifiable. Strategies that enable the comparison of the robustness of competing design alternatives, the approximation of the robust design space, and the systematic search for designs with improved robustness characteristics are also proposed. Since the problem formulation is generic and the solution methods only require standard optimization algorithms for their implementation, the tools developed are applicable to a broad range of problems in several disciplines.

Crespo, Luis G.↗
DOE OSTI2023

GPU-resident sparse direct linear solvers for alternating current optimal power flow analysis

Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This motivates the investigation of more efficient computational methods, especially those for solving the underlying linear systems, which typically take more than half of the overall computation time. In this paper, we present our work on sparse linear solvers that take advantage of hardware accelerators, such as graphical processing units (GPUs), and improve the overall performance when used within economic dispatch computations. We treat the problems as sparse, which allows for faster execution but also makes the implementation of numerical methods more challenging. We present the first GPU-native sparse direct solver that can execute on both AMD and NVIDIA GPUs. We demonstrate significant performance improvements when using high-performance linear solvers within alternating current optimal power flow (ACOPF) analysis. Furthermore, we demonstrate the feasibility of getting significant performance improvements by executing the entire computation on GPU-based hardware. Finally, we identify outstanding research issues and opportunities for even better utilization of heterogeneous systems, including those equipped with GPUs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Sizing battery energy storage and PV system in an extreme fast charging station considering uncertainties and battery degradation

In this paper, we present mixed integer linear programming (MILP) formulations to obtain optimal sizing for a battery energy storage system (BESS) and solar generation system in an extreme fast charging station (XFCS) to reduce the annualized total cost. The proposed model characterizes a typical year with eight representative scenarios and obtains the optimal energy management for the station and BESS operation to exploit the energy arbitrage for each scenario. Contrasting extant literature, this paper proposes a constant power constant voltage (CPCV) based improved probabilistic approach to model the XFCS charging demand for weekdays and weekends. This paper also accounts for the monthly and annual demand charges based on realistic utility tariffs. Furthermore, BESS life degradation is considered in the model to ensure no replacement is needed during the considered planning horizon. Different from the literature, this paper offers pragmatic MILP formulations to tally BESS charge/discharge cycles using the cumulative charge/discharge energy concept. McCormick relaxations and the Big-M method are utilized to relax the bi-linear terms in the BESS operational constraints. Finally, a robust optimization-based MILP model is proposed and leveraged to account for uncertainties in electricity price, solar generation, and XFCS demand. Case studies were performed to signify the efficacy of the proposed formulations.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Benders Decomposition Using Graph Modeling and Multi-Parametric Programming

Benders decomposition is a widely used method for solving large and structured optimization problems, but its performance is affected by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating Benders decomposition. Specifically, we express the problem structure by using a graph-theoretic modeling abstraction in which nodes represent optimization subproblems and edges represent connectivity between subproblems. A key innovation of our approach is that we embed multiparametric programming (mp) surrogates for node subproblems, which maps the exact analytical map of the subproblem solution space. The use of mp surrogates allows us to replace subproblem solves with fast look-ups and function evaluations for primal and dual variables during the iterative Benders process. We formally show the equivalence between classical Benders cuts and those derived from the mp solution. We implement our framework in the open-source PlasmoBenders.jl software package. To demonstrate the capabilities of the proposed framework, we apply it to a two-stage stochastic programming problem, which aims to make optimal capacity expansion decisions under market uncertainty. We evaluate both single-cut and multicut variants of Benders decomposition and show that the use of mp surrogates achieves substantial speedups in subproblem solve time, while preserving the convergence guarantees of Benders decomposition. We highlight advantages in solution analysis and interpretability that is enabled by mp critical region tracking; specifically, we show that these reveal how decisions evolve geometrically across the Benders search. Our results aim to demonstrate that combining surrogate modeling with graph modeling offers a promising and extensible foundation for structure-exploiting decomposition. In addition, by decomposing the problem into more tractable subproblems, the proposed approach also aims to overcome scalability issues of mp. Finally, the use of mp surrogates provides a unifying and modular optimization framework that enables the representation of heterogeneous node subproblems as modeling objects with a homogeneous structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Uncertainties Induced by Processing Parameter Variation in Selective Laser Melting of Ti6Al4V Revealed by In-Situ X-ray Imaging

Selective laser melting (SLM) additive manufacturing (AM) exhibits uncertainties, where variations in build quality are present despite utilizing the same optimized processing parameters. In this work, we identify the sources of uncertainty in SLM process by in-situ characterization of SLM dynamics induced by small variations in processing parameters. We show that variations in the laser beam size, laser power, laser scan speed, and powder layer thickness result in significant variations in the depression zone, melt pool, and spatter behavior. On average, a small deviation of only ~5% from the optimized/reference laser processing parameter resulted in a ~10% or greater change in the depression zone and melt pool geometries. For spatter dynamics, small variation (10 μm, 11%) of the laser beam size could lead to over 40% change in the overall volume of the spatter generated. The responses of the SLM dynamics to small variations of processing parameters revealed in this work are useful for understanding the process uncertainties in the SLM process.

36 MATERIALS SCIENCE↗
NASA NTRS2004

Uncertainty-Based Approach for Dynamic Aerodynamic Data Acquisition and Analysis

Development of improved modeling methods to provide increased fidelity of flight predictions for aircraft motions during flight in flow regimes with large nonlinearities requires improvements in test techniques for measuring and characterizing wind tunnel data. This paper presents a method for providing a measure of data integrity for static and forced oscillation test techniques. Data integrity is particularly important when attempting to accurately model and predict flight of today s high performance aircraft which are operating in expanded flight envelopes, often maneuvering at high angular rates at high angles-of-attack, even above maximum lift. Current aerodynamic models are inadequate in predicting flight characteristics in the expanded envelope, such as rapid aircraft departures and other unusual motions. Present wind tunnel test methods do not factor changes of flow physics into data acquisition schemes, so in many cases data are obtained over more iterations than required, or insufficient data may be obtained to determine a valid estimate with statistical significance. Additionally, forced oscillation test techniques, one of the primary tools used to develop dynamic models, do not currently provide estimates of the uncertainty of the results during an oscillation cycle. A method to optimize the required number of forced oscillation cycles based on decay of uncertainty gradients and balance tolerances is also presented.

Heim, Eugene H. D.↗
DOE OSTI2025

Genetic algorithm optimization of nuclear criticality experiment for reduction of intermediate-energy 239 Pu nuclear data uncertainties

Nuclear criticality experiments are conducted to investigate specific nuclear data important for safe handling and storage of fissile materials, reactor design and operation, and the validation of radiation transport codes. Incorrect or uncertain nuclear data can prohibitively impact operational safety limits, reactor licensing, and predictive simulation capability; therefore, integral measurements from criticality experiments are necessary and should be performed frequently. To maximize the impact of the integral measurements, it is important to consider experiment geometry, material selection, and component dimensions. When taking these considerations into account, the experiment design process becomes iterative and very time intensive. This work utilizes a genetic algorithm to efficiently explore potential nuclear criticality experiment designs for the Laboratory Directed Research & Development project PARADIGM (PARallel Approach of Differential and InteGral Measurements) at Los Alamos National Laboratory. In this paper, the building blocks of the genetic algorithm are discussed in detail, the genetic algorithm methodology is verified, and the genetic algorithm is used to produce three candidate experiment models for the final PARADIGM design. The three candidate models produced by the genetic algorithm consist of copper-reflected assemblies containing 14 repeating units of alumina, graphite, boron, and plutonium plates. Furthermore, in addition to the optimization results, final design considerations are also discussed for designs with a height and/or weight very close to or slightly above assembly machine operational limits.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Automated ICRF heating surrogate modeling via machine learning

This work introduces automated machine learning workflows that address critical bottlenecks in surrogate model development for Ion Cyclotron Range of Frequencies (ICRF) heating applications. The automated framework includes data analysis tools that transform raw datasets into actionable insights in seconds, replacing weeks of manual exploratory effort and ensuring consistent, reproducible dataset characterization. By integrating advanced hyperparameter optimization (HPO) methods including Bayesian optimization via BoTorch and Tree-structured Parzen Estimators (TPE), the framework significantly reduces model development time from weeks to hours, decreasing computational cost and required expertise, while enabling high-accuracy surrogate models. Compared to traditional hyperparameter scanning (HPS) techniques such as methodical, randomized, and grid searches, HPO methods achieve superior convergence and predictive performance, even when compared to already well-tuned reference models. On NSTX High Harmonic Fast Wave (HHFW) heating datasets, both Random Forest Regressor (RFR) and neural network surrogates demonstrate improved accuracy, achieving R 2 values beyond 0.97 and 0.98, respectively. The results show that while HPO gains are modest for robust architectures like RFR, they become essential for more sensitive models such as neural networks, highlighting the trade-offs across optimization strategies. Through automated workflows that eliminate manual hyperparameter tuning and require minimal ML expertise, this work enables widespread adoption of high-fidelity surrogate models across the fusion community for real-time plasma control, uncertainty quantification, rapid experimental scenario development, and integrated system optimization.

Sanchez-Villar, Alvaro [Princeton Plasma Physics L↗