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Results for “uncertain quantification”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Method of Distributions for Two‐Phase Flow in Heterogeneous Porous Media

Abstract Multiscale heterogeneity and insufficient characterization data for a specific subsurface formation of interest render predictions of multi‐phase fluid flow in geologic formations highly uncertain. Quantification of the uncertainty propagation from the geomodel to the fluid‐flow response is typically done within a probabilistic framework. This task is computationally demanding due to, for example, the slow convergence of Monte Carlo simulations (MCS), especially when computing the tails of a distribution that are necessary for risk assessment and decision‐making under uncertainty. The frozen streamlines method (FROST) accelerates probabilistic predictions of immiscible two‐phase fluid flow problems; however, FROST relies on MCS to compute the travel‐time distribution, which is then used to perform the transport (phase saturation) computations. To alleviate this computational bottleneck, we replace MCS with a deterministic equation for the cumulative distribution function (CDF) of travel time. The resulting CDF‐FROST approach yields the CDF of the saturation field without resorting to sampling‐based strategies. Our numerical experiments demonstrate the high accuracy of CDF‐FROST in computing the CDFs of both saturation and travel time. For the same accuracy, it is about 5 and 10 times faster than FROST and MCS, respectively.

Yang, Hyung Jun↗
DOE OSTI2021

Bayesian inference of the dense-matter equation of state encapsulating a first-order hadron-quark phase transition from observables of canonical neutron stars

The remarkable progress in recent multimessenger observations of both isolated neutron stars (NSs) and their mergers has provided some of the much needed data to improve our understanding about the equation of state (EOS) of dense neutron-rich matter. Various EOSs with or without some kinds of phase transitions from hadronic to quark matter (QM) have been widely used in many forward modelings of NS properties. Direct comparisons of these predictions with observational data sometimes also using χ 2 minimizations have provided very useful constraints on the model EOSs. Furthermore, it is normally difficult to perform uncertain quantifications and analyze correlations of the EOS model parameters involved in forward modelings especially when the available data are still very limited.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

CO 2 geological storage: Critical insights on plume dynamics and storage efficiency during long-term injection and post-injection periods

In the quest for net-zero greenhouse gas emission, CO 2 capture and storage technologies play a prominent role. Estimates suggest a potential of sequestering up to several thousand metric gigatons of CO 2 . However, some of the main challenges in its development are an assessment of reservoir-specific storage capacities due to variabilities and heterogeneities in the underlying properties (structure, formations, facies, petrophysics, reservoir architecture, and others) and understanding the migration of CO 2 in the subsurface. How much CO 2 can be stored in a reservoir, and how quickly can it be injected? What will be the dominant storing (trapping) mechanisms? These questions, among others, remain as challenges to the commercial deployment of this technology. This article critically investigates CO 2 plume characteristics and determines the evolving contributions of different trapping mechanisms during a 100-year injection period. Here, simulation results on the CO 2 plume dynamics indicate that lateral propagation is much larger than vertical propagation. The ratio of average lateral to vertical dispersion ranged between 6.3 and 18.8 for the cases investigated. On average, for all the scenarios investigated, the free phase (mobile supercritical CO 2 ) is the dominant trapping mechanism (in terms of the amount of CO 2 stored) during the injection period, accounting up to 45% of the CO 2 injected. Both residual (30%) and solubility (25%) trapping storage ratios decline with time during injection, and no significant mineral trapping appeared during the 100-year injection period. However, the behavior of CaCO 3 suggests a predominant dissolution of CaCO 3 , especially in the vicinity of the injection well.

03 NATURAL GAS↗
DOE OSTI2024

Quantifying Streambed Grain Size, Uncertainty, and Hydrobiogeochemical Parameters Using Machine Learning Model YOLO

Abstract Streambed grain sizes control river hydro‐biogeochemical (HBGC) processes and functions. However, measuring their quantities, distributions, and uncertainties is challenging due to the diversity and heterogeneity of natural streams. This work presents a photo‐driven, artificial intelligence (AI)‐enabled, and theory‐based workflow for extracting the quantities, distributions, and uncertainties of streambed grain sizes from photos. Specifically, we first trained You Only Look Once, an object detection AI, using 11,977 grain labels from 36 photos collected from nine different stream environments. We demonstrated its accuracy with a coefficient of determination of 0.98, a Nash–Sutcliffe efficiency of 0.98, and a mean absolute relative error of 6.65% in predicting the median grain size of 20 ground‐truth photos representing nine typical stream environments. The AI is then used to extract the grain size distributions and determine their characteristic grain sizes, including the 10th, 50th, 60th, and 84th percentiles, for 1,999 photos taken at 66 sites within a watershed in the Northwest US. The results indicate that the 10th, median, 60th, and 84th percentiles of the grain sizes follow log‐normal distributions, with most likely values of 2.49, 6.62, 7.68, and 10.78 cm, respectively. The average uncertainties associated with these values are 9.70%, 7.33%, 9.27%, and 11.11%, respectively. These data allow for the computation of the quantities, distributions, and uncertainties of streambed HBGC parameters, including Manning's coefficient, Darcy‐Weisbach friction factor, top layer interstitial velocity magnitude, and nitrate uptake velocity. Additionally, major sources of uncertainty in grain sizes and their impact on HBGC parameters are examined.

58 GEOSCIENCES↗
DOE OSTI2020

Deeply uncertain: comparing methods of uncertainty quantification in deep learning algorithms

We present a comparison of methods for uncertainty quantification (UQ) in deep learning algorithms in the context of a simple physical system. Three of the most common uncertainty quantification methods - Bayesian Neural Networks (BNN), Concrete Dropout (CD), and Deep Ensembles (DE) - are compared to the standard analytic error propagation. We discuss this comparison in terms endemic to both machine learning ("epistemic" and "aleatoric") and the physical sciences ("statistical" and "systematic"). The comparisons are presented in terms of simulated experimental measurements of a single pendulum - a prototypical physical system for studying measurement and analysis techniques. Our results highlight some pitfalls that may occur when using these UQ methods. For example, when the variation of noise in the training set is small, all methods predicted the same relative uncertainty independently of the inputs. This issue is particularly hard to avoid in BNN. On the other hand, when the test set contains samples far from the training distribution, we found that no methods sufficiently increased the uncertainties associated to their predictions. This problem was particularly clear for CD. In light of these results, we make some recommendations for usage and interpretation of UQ methods.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Deeply Uncertain: Comparing Methods of Uncertainty Quantification in Deep Learning Algorithms [Slides]

Deep learning is used in many applications in the physical sciences. In those sciences we are used to having uncertainty on every measurement or prediction. In the last years, many methods have been put forth for uncertainty quantification: Bayesian Neural Networks, Concrete Dropout, and Deep Ensembles. Uncertainty in deep learning is often divided into aleatoric or irreducible and epistemic or reducible. The problem remains: Which uncertainty quantification method should be chosen? How are those results interpreted?

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Design Under Uncertainty with Design-Dependent Uncertain Variables

Uncertainty quantification (UQ) can provide a more robust understanding of a system, leading to better informed decisions earlier in the design process. The additional information that UQ provides can be leveraged during a design optimization process known as design under uncertainty that, when incorporated with multidisciplinary design and optimization, can become computationally infeasible due to the large number of responses required for meaningful results. Previous work addressed reducing the computational expense in design under uncertainty by incorporating analytic derivatives throughout polynomial chaos expansion. Although this allows design under uncertainty to be feasible for more systems, some multidisciplinary systems have design-dependent uncertain variables. This paper details an implementation of design dependent uncertain variables in a manner than preserves derivatives required for efficient gradient-based optimization throughout the process. Two analytic examples of design-dependent uncertain variables are given: the first transforms a uniform uncertain variable with one design variable and the second transforms a normal uncertain variable with two design variables. The polynomial chaos expansion (PCE) results are comparable to both the Monte Carlo (MC) results and the analytic results for the two examples. A case study that maximizes the lift-to-drag ratio with a design-dependence between the wing leading edge sweep angle and uncertain parameter percentage of laminar flow is compared to a MC and alternative optimization formulations. This paper demonstrates that design-dependent uncertain variables are valid and hold throughout PCE.

Joanna N Schmidt↗
NASA NTRSDate not supplied

Design Under Uncertainty with Design-Dependent Uncertain Variables

Uncertainty quantification (UQ) can provide a more robust understanding of a system, leading to better informed decisions earlier in the design process. The additional information that UQ provides can be leveraged during a design optimization process known as design under uncertainty that, when incorporated with multidisciplinary design and optimization, can become computationally infeasible due to the large number of responses required for meaningful results. Previous work addressed reducing the computational expense in design under uncertainty by incorporating analytic derivatives throughout polynomial chaos expansion. Although this allows design under uncertainty to be feasible for more systems, some multidisciplinary systems have design-dependent uncertain variables. This paper details an implementation of design dependent uncertain variables in a manner than preserves derivatives required for efficient gradient-based optimization throughout the process. Two analytic examples of design-dependent uncertain variables are given: the first transforms a uniform uncertain variable with one design variable and the second transforms a normal uncertain variable with two design variables. The polynomial chaos expansion (PCE) results are comparable to both the Monte Carlo (MC) results and the analytic results for the two examples. A case study that maximizes the lift-to-drag ratio with a design-dependence between the wing leading edge sweep angle and uncertain parameter percentage of laminar flow is compared to a MC and alternative optimization formulations. This paper demonstrates that design-dependent uncertain variables are valid and hold throughout PCE.

robust design↗
DOE OSTI2023

Uncertain of uncertainties? A comparison of uncertainty quantification metrics for chemical data sets

Abstract With the increasingly more important role of machine learning (ML) models in chemical research, the need for putting a level of confidence to the model predictions naturally arises. Several methods for obtaining uncertainty estimates have been proposed in recent years but consensus on the evaluation of these have yet to be established and different studies on uncertainties generally uses different metrics to evaluate them. We compare three of the most popular validation metrics (Spearman’s rank correlation coefficient, the negative log likelihood (NLL) and the miscalibration area) to the error-based calibration introduced by Levi et al. ( Sensors 2022 , 22 , 5540). Importantly, metrics such as the negative log likelihood (NLL) and Spearman’s rank correlation coefficient bear little information in themselves. We therefore introduce reference values obtained through errors simulated directly from the uncertainty distribution. The different metrics target different properties and we show how to interpret them, but we generally find the best overall validation to be done based on the error-based calibration plot introduced by Levi et al. Finally, we illustrate the sensitivity of ranking-based methods (e.g. Spearman’s rank correlation coefficient) towards test set design by using the same toy model ferent test sets and obtaining vastly different metrics (0.05 vs. 0.65).

Rasmussen, Maria H.↗
DOE OSTI2020

Hyper-Differential Sensitivity Analysis of Uncertain Parameters in PDE-Constrained Optimization

Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose additional complexity, namely, uncertain parameters in the PDEs. Uncertainty quantification (UQ) is necessary to characterize, prioritize, and study the influence of these uncertain parameters. Sensitivity analysis, a classical tool in UQ, is frequently used to study the sensitivity of a model to uncertain parameters. In this article, we introduce "hyper-differential sensitivity analysis" which considers the sensitivity of the solution of a PDE-constrained optimization problem to uncertain parameters. Our approach is a goal-oriented analysis which may be viewed as a tool to complement other UQ methods in the service of decision making and robust design. We formally define hyper-differential sensitivity indices and highlight their relationship to the existing optimization and sensitivity analysis literatures. Assuming the presence of low rank structure in the parameter space, computational efficiency is achieved by leveraging a generalized singular value decomposition in conjunction with a randomized solver which converts the computational bottleneck of the algorithm into an embarrassingly parallel loop. Two multi-physics examples, consisting of nonlinear steady state control and transient linear inversion, demonstrate efficient identification of the uncertain parameters which have the greatest influence on the optimal solution.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2019

On the Calculation of Exact Cumulative Distribution Statistics for Burgers Equation

A mathematical procedure is presented for the calculation of exact cumulative distribution statistics for a viscosity-free variant of Burgers nonlinear partial differential equation (PDE) in one space dimension and time subject to sinusoidal initial data with uncertain (random variable) amplitude or phase shift. Analytical solutions of nonlinear PDEs with uncertain initial and/or boundary data are invaluable benchmarks in assessing approximate uncertainty quantification techniques. The Burgers equation solution with uncertain initial data results in nonsmooth solution behavior in both physical and random variable dimensions which provides a severe test for approximate uncertainty quantification techniques. Mathematical proofs are provided to verify that exact cumulative distribution statistics can be systematically and robustly obtained for all forward time.

Burgers↗
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 OSTI2022

Comprehensive uncertainty quantification (UQ) for full engineering models by solving probability density function (PDF) equation

This report details a new method for propagating parameter uncertainty (forward uncertainty quantification) in partial differential equations (PDE) based computational mechanics applications. The method provides full-field quantities of interest by solving for the joint probability density function (PDF) equations which are implied by the PDEs with uncertain parameters. Full-field uncertainty quantification enables the design of complex systems where quantities of interest, such as failure points, are not known apriori. The method, motivated by the well-known probability density function (PDF) propagation method of turbulence modeling, uses an ensemble of solutions to provide the joint PDF of desired quantities at every point in the domain. A small subset of the ensemble is computed exactly, and the remainder of the samples are computed with approximation of the driving (dynamics) term of the PDEs based on those exact solutions. Although the proposed method has commonalities with traditional interpolatory stochastic collocation methods applied directly to quantities of interest, it is distinct and exploits the parameter dependence and smoothness of the dynamics term of the governing PDEs. The efficacy of the method is demonstrated by applying it to two target problems: solid mechanics explicit dynamics with uncertain material model parameters, and reacting hypersonic fluid mechanics with uncertain chemical kinetic rate parameters. A minimally invasive implementation of the method for representative codes SPARC (reacting hypersonics) and NimbleSM (finite- element solid mechanics) and associated software details are described. For solid mechanics demonstration problems the method shows order of magnitudes improvement in accuracy over traditional stochastic collocation. For the reacting hypersonics problem, the method is implemented as a streamline integration and results show very good accuracy for the approximate sample solutions of re-entry flow past the Apollo capsule geometry at Mach 30.

42 ENGINEERING↗
NASA NTRS2020

Bias in CMIP6 Models as Compared to Observed Regional Dimming and Brightening

Anthropogenic aerosol emissions have increased considerably over the last century, but climate effects and quantification of the emissions are highly uncertain as one goes back in time. This uncertainty is partly due to a lack of observations in the pre-satellite era, making the observations we do have before 1990 additionally valuable. Aerosols suspended in the atmosphere scatter and absorb incoming solar radiation and thereby alter the Earth's surface energy balance. Previous studies show that Earth system models (ESMs) do not adequately represent surface energy fluxes over the historical era. We investigated global and regional aerosol effects over the time period 1961–2014 by looking at surface downwelling shortwave radiation (SDSR). We used observations from ground stations as well as multiple experiments from eight ESMs participating in the Coupled Model Intercomparison Project Version 6 (CMIP6). Our results show that this subset of models reproduces the observed transient SDSR well in Europe but poorly in China. We suggest that this may be attributed to missing emissions of sulfur dioxide in China, sulfur dioxide being a precursor to sulfate, which is a highly reflective aerosol and responsible for more reflective clouds. The emissions of sulfur dioxide used in the models do not show a temporal pattern that could explain observed SDSR evolution over China. The results from various aerosol emission perturbation experiments from DAMIP, RFMIP and AerChemMIP show that only simulations containing anthropogenic aerosol emissions show dimming, even if the dimming is underestimated. Simulated clear-sky and all-sky SDSR do not differ greatly, suggesting that cloud cover changes are not a dominant cause of the biased SDSR evolution in the simulations. Therefore we suggest that the discrepancy between modeled and observed SDSR evolution is partly caused by erroneous aerosol and aerosol precursor emission inventories. This is an important finding as it may help interpret whether ESMs reproduce the historical climate evolution for the right or wrong reason.

surface downwelling shortwave radiation (SDSR)↗
DOE OSTI2022

A general framework for quantifying uncertainty at scale

Abstract In many fields of science, comprehensive and realistic computational models are available nowadays. Often, the respective numerical calculations call for the use of powerful supercomputers, and therefore only a limited number of cases can be investigated explicitly. This prevents straightforward approaches to important tasks like uncertainty quantification and sensitivity analysis. This challenge can be overcome via our recently developed sensitivity-driven dimension-adaptive sparse grid interpolation strategy. The method exploits, via adaptivity, the structure of the underlying model (such as lower intrinsic dimensionality and anisotropic coupling of the uncertain inputs) to enable efficient and accurate uncertainty quantification and sensitivity analysis at scale. Here, we demonstrate the efficiency of this adaptive approach in the context of fusion research, in a realistic, computationally expensive scenario of turbulent transport in a magnetic confinement tokamak device with eight uncertain parameters, reducing the effort by at least two orders of magnitude. In addition, we show that this refinement method intrinsically provides an accurate surrogate model that is nine orders of magnitude cheaper than the high-fidelity model.

Farcaş, Ionuţ-Gabriel (ORCID:0000000238841580)↗
DOE OSTI2023

Assessing the nexus between groundwater and solar energy plants in a desert basin with a dual-model approach under uncertainty

Globally, many solar power plants and other types of renewable energy are being located in water-scarce regions. Many projects rely on groundwater resources whose sustainability is uncertain. In the Chuckwalla Basin in California, quantification of recharge and trans-valley underflow is needed to estimate the impacts of solar project withdrawals on the water table. However, such estimates are highly challenging due to data scarcity, heterogeneous soils and long residence times. Conventional assessment employs isolated groundwater models configured with crude and uniform estimates of recharge. Here, we employ a data-constrained surface subsurface processes model, PAWS+CLM, to provide an ensemble of recharges and underflows with perturbed parameters. Then, the Parameter Estimation (PEST) package is used to calibrate MODFLOW aquifer conductivity and filter out implausible recharges. The novel dual-model approach, potentially applicable in other arid regions, can effectively assimilate groundwater head observations, reject unrealistic parameters, and narrow the range of estimated drawdowns. Simulated recharge concentrates along alluvial fans at the mountain fronts and ephemeral washes where run-off water infiltrates. If an evenly distributed recharge was assumed, it resulted in under-estimated drawdown and larger uncertainty bounds. The withdrawals are approaching total inflow, suggesting the system will be nearing, if not exceeding, its sustainable groundwater production capacity, and a boom of such projects will not be sustainable. Especially, the cost/benefit of pumped-storage projects is called into question as the initial-fill phase depletes entire area’s recharge. Our study highlights the stress on groundwater resources of solar development, and that the speed of groundwater recovery does not indicate sustainability. Main point 1: A novel dual model approach, involving an integrated surface/subsurface model and a groundwater parameter-estimation model, was able to better constrain the model. Main point 2: The groundwater system may be nearing, if not exceeding, its sustainable groundwater production capacity and the speed of recovery is not indicative of sustainability. Main point 3: Results from using conventionally-assumed uniform recharge distort calibrated K fields and impacts assessment

14 SOLAR ENERGY↗
NASA NTRS2013

Sensitivity and Response of Bhutanese Glaciers to Atmospheric Warming

Glacierized change in the Himalayas affects river-discharge, hydro-energy and agricultural production, and Glacial Lake Outburst Flood potential, but its quantification and extent of impacts remains highly uncertain. Here we present conservative, comprehensive and quantitative predictions for glacier area and meltwater flux changes in Bhutan, monsoonal Himalayas. In particular, we quantify the uncertainties associated with the glacier area and meltwater flux changes due to uncertainty in climate data, a critical problem for much of High Asia. Based on a suite of gridded climate data and a robust glacier melt model, our results show that glacier area and meltwater change projections can vary by an order of magnitude for different climate datasets. However, the most conservative results indicate that, even if climate were to remain at the present-day mean values, almost 10% of Bhutan s glacierized area would vanish and the meltwater flux would drop by as much as 30%. Under the conservative scenario of an additional 1 C regional warming, glacier retreat is going to continue until about 25% of Bhutan s glacierized area will have disappeared and the annual meltwater flux, after an initial spike, would drop by as much as 65%. Citation

Rupper, Summer↗
NASA NTRS2018

Dynamics and Control of Quadcopter in Uncertain Environment

We consider problem of dynamics, control, and uncertainty quantification for quadcopter. We use the 6DOF model of quadcopter dynamics, linear quadratic regulator and linear quadratic Gaussian control of quadcopter in the presence of dynamical disturbances, measurement noise, hidden dynamical variables, dashing GPS signal, and wind gusts to predict quadcopter trajectory. We identify key sources of uncertainties and report on progress in development of a system that estimates the probability of safety-critical events using a set of algorithms based on the trajectory predictions.

uncertainty quantification↗