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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Taylor approximation variance reduction for approximation errors in PDE-constrained Bayesian inverse problems

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors, i.e. the errors between the accurate parameter-to-observable mapping and the surrogate. The statistics of these errors are, however, in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline, i.e. before considering the data, the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to directly and efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.

Bayesian approximation error↗
DOE OSTI2020

Physics and technology considerations for the deuterium–tritium fuel cycle and conditions for tritium fuel self sufficiency

The tritium aspects of the DT fuel cycle embody some of the most challenging feasibility and attractiveness issues in the development of fusion systems. The review and analyses in this paper provide important information to understand and quantify these challenges and to define the phase space of plasma physics and fusion technology parameters and features that must guide a serious R&D in the world fusion program. We focus in particular on components, issues and R&D necessary to satisfy three 'principal requirements': (1) achieving tritium self-sufficiency within the fusion system, (2) providing a tritium inventory for the initial start-up of a fusion facility, and (3) managing the safety and biological hazards of tritium. A primary conclusion is that the physics and technology state-of-the-art will not enable DEMO and future power plants to satisfy these principal requirements. We quantify goals and define specific areas and ideas for physics and technology R&D to meet these requirements. A powerful fuel cycle dynamics model was developed to calculate time-dependent tritium inventories and flow rates in all parts and components of the fuel cycle for different ranges of parameters and physics and technology conditions. Dynamics modeling analyses show that the key parameters affecting tritium inventories, tritium start-up inventory, and tritium self-sufficiency are the tritium burn fraction in the plasma (f b ), fueling efficiency (η f ), processing time of plasma exhaust in the inner fuel cycle (t p ), reactor availability factor (AF), reserve time (tr) which determines the reserve tritium inventory needed in the storage system in order to keep the plant operational for time t r in case of any malfunction of any part of the tritium processing system, and the doubling time (t d ). Results show that η f f b > 2% and processing time of 1–4 h are required to achieve tritium self-sufficiency with reasonable confidence. For η f f b = 2% and processing time of 4 h, the tritium start-up inventory required for a 3 GW fusion reactor is ~11 kg, while it is <5 kg if η f f b = 5% and the processing time is 1 h. To achieve these stringent requirements, a serious R&D program in physics and technology is necessary. The EU-DEMO direct internal recycling concept that carries fuel directly from the plasma exhaust gas to the fueling systems without going through the isotope separation system reduces the overall processing time and tritium inventories and has positive effects on the required tritium breeding ratio (TBR R ). A significant finding is the strong dependence of tritium self-sufficiency on the reactor availability factor. Simulations show that tritium self-sufficiency is: impossible if AF < 10% for any η f f b , possible if AF > 30% and 1% ≤ η f f b ≤ 2%, and achievable with reasonable confidence if AF > 50% and η f f b > 2%. These results are of particular concern in light of the low availability factor predicted for the near-term plasma-based experimental facilities (e.g. FNSF, VNS, CTF), and can have repercussions on tritium economy in DEMO reactors as well, unless significant advancements in RAMI are made. There is a linear dependency between the tritium start-up inventory and the fusion power. The required tritium start-up inventory for a fusion facility of 100 MW fusion power is as small as 1 kg. Since fusion power plants will have large powers for better economics, it is important to maintain a 'reserve' tritium inventory in the tritium storage system to continue to fuel the plasma and avoid plant shutdown in case of malfunctions of some parts of the tritium processing lines. But our results show that a reserve time as short as 24 h leads to unacceptable reserve and start-up inventory requirements. Therefore, high reliability and fast maintainability of all components in the fuel cycle are necessary in order to avoid the need for storing reserve tritium inventory sufficient for continued fusion facility operation for more than a few hours. The physics aspects of plasma fueling, tritium burn fraction, and particle and power exhaust are highly interrelated and complex, and predictions for DEMO and power reactors are highly uncertain because of lack of experiments with burning plasma. Fueling by pellet injection on the high field side of tokamak has evolved to be the preferred method to fuel a burning plasma. Extrapolation from the DIII-D penetration scaling shows fueling efficiency expected in DEMO to be <25%, but such extrapolations are highly uncertain. The fueling efficiency of gas in a reactor relevant regime is expected to be extremely poor and not very useful for getting tritium into the core plasma efficiently. Gas fueling will nonetheless be useful for feedback control of the divertor operating parameters. Extensive modeling has been carried out to predict burn fraction, fueling requirements, and fueling efficiency for ITER, DEMO, and beyond. The fueling rate required to operate Q = 10 ITER plasmas in order to provide the required core fueling, helium exhaust and radiative divertor plasma conditions for acceptable divertor power loads was calculated. If this fueling is performed with a 50–50 DT mix, the tritium burn fraction in ITER would be ~0.36%, which is too low to satisfy the self-sufficiency conditions derived from the dynamics modeling for fusion reactors. Extrapolation to DEMO using this approach would also yield similarly low burn fraction. Extensive analysis presented shows that specific features of edge neutral dynamics in ITER and fusion reactors, which are different from present experiments, open possibilities for optimization of tritium fueling and thus to improve the burn fraction. Using only tritium in pellet fueling of the plasma core, and only deuterium for edge density, divertor power load and ELM control results in significant increase of the burn fraction to 1.8–3.6%. These estimates are performed with physics models whose results cannot be fully validated for ITER and DEMO plasma conditions since these cannot be achieved in present tokamak experiments. Thus, several uncertainties remain regarding particle transport and scenario requirements in ITER and DEMO. The safety standard requirements for protection of the public and release guidelines for tritium have been reviewed. General safety approaches including minimizing tritium inventories, reducing tritium permeation through materials, and decontaminating material for waste disposal have been suggested.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Calibration of the 2-Phase Bubble Tracking Model for Liquid Mercury Target Simulation with Machine Learning Surrogate Models

The Spallation Neutron Source (SNS) at Oak Ridge National Laboratory is one of the most powerful accelerator-driven neutron sources in the world. The intense protons strike on SNS's mercury target to provide bright neutron beams, which also leads to severe fluid-structure interactions inside the target. Prediction of resultant loading on the target is difficult particularly when helium gas is injected into mercury to reduce the loading and mitigate the pitting damage on vessel walls. A 2-phase material model that incorporates the Rayleigh-Plesset (R-P) model is expected to address this multi-physics problem. However, several uncertain parameters in the R-P model require intensive simulations to determine their optimal values. With the help of machine learning and the measured target strain, we have studied the major uncertain parameters in this R-P model and developed a framework to identify optimal parameters that significantly reduce the discrepancy between simulations and experimental strains. The preliminary results show the possibility of using this mercury/helium mixture and surrogate models to predict a better match of target strain response when the helium gas is injected.

Lin, Lianshan↗
DOE OSTI2025

Information divergences to parametrize astrophysical uncertainties in dark matter direct detection

Astrophysical uncertainties in dark matter direct detection experiments are typically addressed by parametrizing the velocity distribution in terms of a few uncertain parameters that vary around some central values. Here we propose a method to optimize over all velocity distributions lying within a given distance measure from a central distribution. We discretize the dark matter velocity distribution as a superposition of streams and use a variety of information divergences to parametrize its uncertainties. With this, we bracket the limits on the dark matter–nucleon and dark matter–electron scattering cross sections, when the true dark matter velocity distribution deviates from the commonly assumed Maxwell-Boltzmann form. The methodology pursued is general and could be applied to other physics scenarios where a given physical observable depends on a function that is uncertain.

particle astrophysics↗
DOE OSTI2021

Quantifying the Multi-Objective Cost of Uncertainty

Various real-world applications involve modeling complex systems with immense uncertainty and optimizing multiple objectives based on the uncertain model. Quantifying the impact of the model uncertainty on the given operational objectives is critical for designing optimal experiments that can most effectively reduce the uncertainty that affect the objectives pertinent to the application at hand. In this paper, we propose the concept of mean multi-objective cost of uncertainty (multi-objective MOCU) that can be used for objective-based quantification of uncertainty for complex uncertain systems considering multiple operational objectives. We provide several illustrative examples that demonstrate the concept and strengths of the proposed multi-objective MOCU. Furthermore, we present a real-world example based on the mammalian cell cycle network to demonstrate how the multi-objective MOCU can be used for quantifying the operational impact of model uncertainty when there are multiple, possibly competing, objectives.

42 ENGINEERING↗
DOE OSTI2026

Bayesian Physics Informed Spatio-Temporal Network for Streamflow Data Imputation

Reliable reconstruction of incomplete streamflow records is critical for improving hydrological forecasting, flood preparedness, and water resource management. However, large observational gaps and uncertainties in governing physical parameters limit the accuracy of traditional statistical and machinelearning imputation frameworks. To address these challenges, we develop a Bayesian Physics-Informed Spatio-Temporal Network (BPI-STNet) that jointly captures spatial and temporal dependencies while enforcing hydrologic consistency through embedded physical constraints. The framework integrates a GraphSAGE-LSTM architecture to model spatial connectivity across gauges and temporal flow dynamics, coupled with a Bayesian update mechanism to estimate uncertain parameters in a simplified water-balance framework. Unlike conventional physics-informed networks that rely on sampling-based posterior estimation, BPI-STNet derives an analytic solution to the inverse problem, allowing closed-form Bayesian updates of uncertain parameters Λ={α,β,k} using Gaussian priors and likelihoods. Applied to daily observations from the Susquehanna River Basin (1980-2022), BPI-STNet achieves substantial improvements over a purely data-driven RGNN baseline, which reduced RMSE by 23 % and MAE by 9 %, and achieving an average NSE values up to 0.96. The results demonstrate that coupling Bayesian inference with physics-informed learning yields physically consistent, uncertainty-aware reconstructions that preserve the temporal persistence and statistical distribution of observed flows. The proposed framework establishes a generalizable paradigm for data-sparse hydrologic systems where both data fidelity and physical interpretability are essential.

Krishnan Kutty Ambika, Anukesh [ORNL] (ORCID:00000↗
DOE OSTI2025

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

adaptation models↗
DOE OSTI2020

Optimal Eco-Driving Control of Connected and Autonomous Vehicles Through Signalized Intersections

This article focuses on the speed planning problem for connected and automated vehicles (CAVs) communicating to traffic lights. The uncertainty of traffic signal timing for signalized intersections on the road is considered. The eco-driving problem is formulated as a data-driven chance-constrained robust optimization problem. Effective red-light duration (ERD) is defined as a random variable, and describes the feasible passing time through the signalized intersections. Usually, the true probability distribution for ERD is unknown. Consequently, a data-driven approach is adopted to formulate chance constraints based on empirical sample data. This incorporates robustness into the eco-driving control problem with respect to uncertain signal timing. Dynamic programming (DP) is employed to solve the optimization problem. The simulation results demonstrate that the proposed method can generate optimal speed reference trajectories with 40% less vehicle fuel consumption, while maintaining the arrival time at a similar level compared to a modified intelligent driver model (IDM). The proposed control approach significantly improves the controller's robustness in the face of uncertain signal timing, without requiring to know the distribution of the random variable a priori.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Numerical and Visual Representations of Uncertainty Lead to Different Patterns of Decision Making

Although visualizations are a useful tool for helping people to understand information, they can also have unintended effects on human cognition. This is especially true for uncertain information, which is difficult for people to understand. Prior work has found that different methods of visualizing uncertain information can produce different patterns of decision making from users. However, uncertainty can also be represented via text or numerical information, and few studies have systematically compared these types of representations to visualizations of uncertainty. We present two experiments that compared visual representations of risk (icon arrays) to numerical representations (natural frequencies) in a wildfire evacuation task. Like prior studies, we found that different types of visual cues led to different patterns of decision making. In addition, our comparison of visual and numerical representations of risk found that people were more likely to evacuate when they saw visualizations than when they saw numerical representations. These experiments reinforce the idea that design choices are not neutral: seemingly minor differences in how information is represented can have important impacts on human risk perception and decision making.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Generalized Copula-Polynomial Chaos Expansion for Probabilistic Power Flow Considering Nonlinear Correlations of PV Injections

This paper develops a generalized Copula-polynomial chaos expansion (PCE) framework for power system probabilistic power flow that can handle both linear and nonlinear correlations of uncertain power injections, such as wind and PVs. A data-driven Copula statistical model is used to capture the correlations of uncertain power injections. This allows us to resort to the Rosenblatt transformation to transform correlated variables into independent ones while preserving the dependence structure. This paves the way of leveraging the PCE for surrogate modeling and uncertainty quantification of power flow results, i.e., achieving the probabilistic distributions of power flows. Simulations carried out on the IEEE 57-bus system show that the proposed framework can get much more accurate results than other alternatives with different linear and nonlinear power injection correlations.

copula↗
DOE OSTI2023

Evaluation of Distributed Power Apportioning with Net Load Management Engine in Microgrids Using Power Hardware-in-the-Loop Simulation

This article presents the performance evaluation of ratio consensus-based distributed power apportioning engine along with centralized net load management (NLM) engine that ensures viable and stable operation of an islanded microgrid. Managing net load variability in a microgrid with high penetrations of uncertain renewable generation and ever-changing load demands is a crucial need in order to ensure viable and stable operation of the microgrid. Centralized “dispatch-rule”-based and/or multi-agent-based distributed control of distributed energy resources (DERs) in microgrid are well accepted for microgrid by adapting ANSI/ISA-95-based hierarchical control architecture. In the application where microgrid network has large geographical span with multiple DERs dispersed in the network, high penetration of uncertain renewable energy resources, and ever-changing load demands, a judicious selection of techniques/solutions for managing net-load resources for maintaining viability and stability is required. With this motivation, this article proposes a novel solution to mitigate the challenges by incorporating a mixed centralized NLM engine and distributed power apportioning control of DERs and loads. A power-hardware-in-the-loop (PHIL) -based experiment is conducted with the centralized NLM engine and the distributed power apportioning engine along with two commercial inverters. The experimental results validates the efficacy of the proposed method in ensuring viability and stability of a microgrid.

hardware-in-the-loop simulation↗
DOE OSTI2021

Integration of Storage in the DC Link of a Full Converter-Based Distributed Wind Turbine

Energy storage is known to support the dispatchability of variable renewable resources. In this paper, we model a battery energy storage system (BESS) integrated with the DC link of a Type IV full converter-based wind turbine and the necessary controls to achieve efficient dispatch. To support the validation of control methodologies, we build a detailed model of a Type IV research wind turbine at the National Renewable Energy Laboratory (NREL), the Controls Advanced Research Turbine (CART 3), and we integrated a lithium-ion BESS model in grid-following mode into the model. The simulation results illustrate the sizing and control of the DC link-integrated BESS for a given variable wind resource and varying dispatch strategies (i.e., under constant, uncertain, and ramping wind scenarios). The integrated storage can smooth variabilities in distributed wind output, hedge against uncertainties, provide the ramping capability, as well as support stability under voltage and frequency transients. All of these have been illustrated in MATLAB/Simulink.

DC-link voltage↗
DOE OSTI2022

Signal-Compensation-Based Adaptive PID Control for Fused Magnesia Smelting Processes

For fused magnesia smelting processes, the proportional-integral-derivative (PID) controller is difficult to regulate the smelting currents within desired ranges due to unexpected variations of the dynamics caused by material feeding operations. To solve this problem, we first proposed its dynamic model composed of a linear model and an uncertain nonlinear dynamic system that describes the unknown time-varying dynamics of nonlinearity and strong couplings among controlled variables. Then, using the accurately calculated value of the uncertain part at the previous sampling time instant and the tracking error that reflects the influence of its change rate, we developed a feedforward and a one-step optimal control to obtain two signal compensators to eliminate the impact of frequent variations of the uncertainties. For the compensators, we proposed a weight selection method to minimize the sum of the squared tracking error with ensured closed-loop stability. Based on the abovementioned modeling and control structure, we finally developed a novel adaptive PID controller augmented with signal compensators to control the whole process. Industrial applications have shown that the proposed method can always keep the tracking error and the control input within their targeted ranges, leading to a significantly reduced energy consumption per ton and increased fused magnesia production.

Wang, Weizhou↗
DOE OSTI2020

A Comprehensive Scheduling Framework using SP-ADMM for Residential Demand Response with Weather and Consumer Uncertainties

This paper presents a comprehensive scheduling framework for residential demand response (DR) programs considering both the day-ahead and real-time electricity markets. In the first stage, residential customers determine the operating status of their responsive devices such as heating, ventilation, and air conditioning (HVAC) systems and electric water heaters (EWHs), while the distribution system operator (DSO) computes the amount of electricity to be purchased in the day-ahead electricity market. In the second stage, the DSO purchases insufficient (or sells surplus) electricity in the real-time electricity market to maintain the supply-demand balance. Due to its computational complexity and data privacy issues, the proposed model cannot be directly solved in a centralized manner, especially with a large number of uncertain scenarios. Therefore, this paper proposes a combination of stochastic programming (SP) and the alternating direction method of multipliers (ADMM) algorithm, called SP-ADMM, to decompose the original model and then solve each sub-problem in a distributed manner while considering multiple uncertain scenarios. The simulation study is performed on the IEEE 33-bus system including 121 residential houses. Here, the results demonstrate the effectiveness of the proposed approach for large-scale residential DR applications under weather and consumer uncertainties.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

A Machine Learning-based Reliability Evaluation Model for Integrated Power-Gas Systems

This article proposes a hybrid machine learning method for the reliability evaluation of integrated power-gas systems (IPGS) under the uncertain component failure probability distributions. The Random Forest (RF) method is designed to select important features to solve the insufficient quantity of data and the curse of dimensionality problems. The Extreme Gradient Boosting (XGBoost) regression algorithm is developed to quantify the relationship between the uncertain parameters and reliability metrics. Moreover, a ten-fold cross-validation method is employed to further improve the accuracy of the regression model. Simulation results on three test systems show that the proposed method can achieve high accuracy for the reliability evaluation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

A Predictive Prescription Framework for Stochastic Unit Commitment Using Boosting Ensemble Learning Algorithms

To take unit commitment (UC) decisions under uncertain load, most existing stochastic optimization (SO) frameworks adopt a generic representation of uncertainty. While load levels that materialize on a particular day are influenced by various covariates (such as the day of the week or temperature), SO frameworks typically disregard such side observations, wasting actionable information that could significantly enhance decision quality. Here, this article proposes a contextual SO (CSO) framework for UC under uncertain load, which can effectively exploit covariate observations in conjunction with a class of machine learning (ML) algorithms to improve the out-of-sample performance of UC decisions. It shows how three ML algorithms, adaptive boosting, gradient boosted trees, and extreme gradient boosting, can be used to this end, constituting the first application of these algorithms in any CSO framework. Using real-world data harvested from the New York ISO grid, we measure the out-of-sample performance of the framework in terms of total operation cost, shed load values, locational marginal prices, and total payments by the loads, against several benchmark methods proposed in the literature. The article has an online companion (Yurdakul et al.), wherein we present additional results and lay out further mathematical formulations used in this work.

42 ENGINEERING↗
DOE OSTI2024

An Entropy-Based Test and Development Framework for Uncertainty Modeling in Level-Set Visualizations

We present a simple comparative framework for testing and developing uncertainty modeling in uncertain marching cubes implementations. The selection of a model to represent the probability distribution of uncertain values directly influences the memory use, run time, and accuracy of an uncertainty visualization algorithm. We use an entropy calculation directly on ensemble data to establish an expected result and then compare the entropy from various probability models, including uniform, Gaussian, histogram, and quantile models. Our results verify that models matching the distribution of the ensemble indeed match the entropy. We further show that fewer bins in nonparametric histogram models are more effective whereas large numbers of bins in quantile models approach data accuracy.

Sisneros, Robert↗
DOE OSTI2020

Integrating the evidence for a terrestrial carbon sink caused by increasing atmospheric CO 2

Atmospheric carbon dioxide concentration ([CO 2 ]) is increasing, which increases leaf-scale photosynthesis and intrinsic water-use efficiency. These direct responses have the potential to increase plant growth, vegetation biomass, and soil organic matter; transferring carbon from the atmosphere into terrestrial ecosystems (a carbon sink). A substantial global terrestrial carbon sink would slow the rate of [CO 2 ] increase and thus climate change. However, ecosystem CO 2 -responses are complex or confounded by concurrent changes in multiple agents of global change and evidence for a [CO 2 ]-driven terrestrial carbon sink can appear contradictory. In this work, we synthesise theory and broad, multi-disciplinary evidence for the effects of increasing [CO 2 ] (iCO 2 ) on the global terrestrial carbon sink. Evidence suggests a substantial increase in global photosynthesis since pre-industry. Established theory, supported by experiments, indicates that iCO 2 is likely responsible for about half of the increase. Global carbon budgeting, atmospheric data, and forest inventories indicate a historical carbon sink, and these apparent iCO 2 -responses are high in comparison with experiments and theory. Plant mortality and soil carbon iCO 2 -responses are highly uncertain. In conclusion, a range of evidence supports a positive terrestrial carbon sink in response to iCO 2 , albeit with uncertain magnitude and strong suggestion of a role for additional agents of global change.

54 ENVIRONMENTAL SCIENCES↗