Search NASA⌕ Search

SEARCH · Search NASA

Results for “variable order”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 991 records · Page 55
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Reactive transport in the complex heterogeneous alluvial aquifer of Fortymile Wash, Nevada

Yucca Mountain, Nevada, had been extensively investigated as a potential deep geologic repository for storing high-level nuclear wastes. Previous field investigations of stratified alluvial aquifer downstream of the site revealed that there is a hierarchy of sedimentary facies types. There is a corresponding log conductivity and reactive surface area subpopulations within each facies at each scale of sedimentary architecture. Here in this paper, we use a Lagrangian-based transport model in order to analyze radionuclide dispersion in the saturated alluvium of Fortymile Wash, Nevada. First, we validate the Lagrangian model using high-resolution flow and reactive transport simulations. Then, we used the validated model to investigate how each scale of sedimentary architecture may affect long-term radionuclide transport at Yucca Mountain. Results show that the reactive solute dispersion developed by the Lagrangian model matches the ensemble average of numerical simulations well. The link between the alluvium spatial variability and reactive solute dispersion at different spatiotemporal scales is demonstrated using the Lagrangian model. Finally, the longitudinal dispersivity of the reactive plume can be on the order of hundreds to thousands of meters, and it may not reach its asymptotic value even after 10,000 years of travel time and 2–3 km of travel distance.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Stellarator equilibrium axis-expansion to all orders in distance from the axis for arbitrary plasma beta

A systematic theory of the asymptotic expansion of the magnetohydrostatics (MHS) equilibrium in the distance from the magnetic axis is developed to include arbitrary smooth currents near the magnetic axis. Compared with the vacuum and the force-free system, an additional magnetic differential equation must be solved to obtain the pressure-driven currents. It is shown that there exist variables in which the rest of the MHS system closely mimics the vacuum system. Thus, a unified treatment of MHS fields is possible. The mathematical structure of the near-axis expansions to arbitrary order is examined carefully to show that the double-periodicity of physical quantities in a toroidal domain can be satisfied order by order. The essential role played by the leading-order Birkhoff–Gustavson normal form in solving the magnetic differential equations is highlighted. Several explicit examples of vacuum, force-free and MHS equilibrium in different geometries are presented.

Physics↗
DOE OSTI2018

Numerical similarity solution for a variable coefficient K(m, n) equation

A technique for finding numerical similarity solutions to an initial boundary value problem (IBVP) for generalized K(m, n) equations is described. The equation under consideration is nonlinear and has variable coefficients. The original problem is transformed with the aid of Lie symmetries to an initial value problem (IVP) for a nonlinear third-order ordinary differential equation. The existence and uniqueness of the solution are examined, and the problem is consequently solved with the aid of a finite-difference scheme for various values of the governing parameters. In lieu of an exact symbolic solution, the scheme is validated by comparing the numerical solutions with the approximate analytic solutions obtained with the aid of the method of successive approximations in their region of validity. The accuracy, efficiency, and consistency of the scheme are demonstrated. Numerical solutions to the original initial boundary value problem are constructed for selected parameter values with the aid of the transforms. The qualitative behavior of the solutions as a function of the governing parameters is analyzed, and it is found that the examined IBVPs for generalized K(m, n) equations with variable coefficients that are functions of time, do not admit solitary wave or compacton solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

BROAD ABSORPTION LINE VARIABILITY ON MULTI-YEAR TIMESCALES IN A LARGE QUASAR SAMPLE

We present a detailed investigation of the variability of 428 C IV and 235 Si IV broad absorption line (BAL) troughs identified in multi-epoch observations of 291 quasars by the Sloan Digital Sky Survey-I/II/III. These observations primarily sample rest-frame timescales of 1-3.7 yr over which significant rearrangement of the BAL wind is expected. We derive a number of observational results on, e.g., the frequency of BAL variability, the velocity range over which BAL variability occurs, the primary observed form of BAL-trough variability, the dependence of BAL variability upon timescale, the frequency of BAL strengthening versus weakening, correlations between BAL variability and BAL-trough profiles, relations between C IV and Si IV BAL variability, coordinated multi-trough variability, and BAL variations as a function of quasar properties. We assess implications of these observational results for quasar winds. Our results support models where most BAL absorption is formed within an order-of-magnitude of the wind-launching radius, although a significant minority of BAL troughs may arise on larger scales. We estimate an average lifetime for a BAL trough along our line-of-sight of a few thousand years. BAL disappearance and emergence events appear to be extremes of general BAL variability, rather than being qualitatively distinct phenomena. We derive the parameters of a random-walk model for BAL EW variability, finding that this model can acceptably describe some key aspects of EW variability. The coordinated trough variability of BAL quasars with multiple troughs suggests that changes in 'shielding gas' may play a significant role in driving general BAL variability.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

The magnetic ordering in high magnetoresistance Mn-doped ZnO thin films

Here, we studied the nature of magnetic ordering in Mn-doped ZnO thin films that exhibited ferromagnetism at 300 K and superparamagnetism at 5 K. We directly inter-related the magnetisation and magnetoresistance by invoking the polaronpercolation theory and variable range of hopping conduction below the metal-to-insulator transition. By obtaining a qualitative agreement between these two models, we attribute the ferromagnetism to the s-d exchange-induced spin splitting that was indicated by large positive magnetoresistance (~40 %). Low temperature superparamagnetism was attributed to the localization of carriers and non-interacting polaron clusters. This analysis can assist in understanding the presence or absence of ferromagnetism in doped/un-doped ZnO.

36 MATERIALS SCIENCE↗
DOE OSTI2015

SU-E-J-262: Variability in Texture Analysis of Gynecological Tumors in the Context of An 18F-FDG PET Adaptive Protocol

Purpose: This study examines the effect on texture analysis due to variable reconstruction of PET images in the context of an adaptive FDG PET protocol for node positive gynecologic cancer patients. By measuring variability in texture features from baseline and intra-treatment PET-CT, we can isolate unreliable texture features due to large variation. Methods: A subset of seven patients with node positive gynecological cancers visible on PET was selected for this study. Prescribed dose varied between 45–50.4Gy, with a 55–70Gy boost to the PET positive nodes. A baseline and intratreatment (between 30–36Gy) PET-CT were obtained on a Siemens Biograph mCT. Each clinical PET image set was reconstructed 6 times using a TrueX+TOF algorithm with varying iterations and Gaussian filter. Baseline and intra-treatment primary GTVs were segmented using PET Edge (MIM Software Inc., Cleveland, OH), a semi-automatic gradient-based algorithm, on the clinical PET and transferred to the other reconstructed sets. Using an in-house MATLAB program, four 3D texture matrices describing relationships between voxel intensities in the GTV were generated: co-occurrence, run length, size zone, and neighborhood difference. From these, 39 textural features characterizing texture were calculated in addition to SUV histogram features. The percent variability among parameters was first calculated. Each reconstructed texture feature from baseline and intra-treatment per patient was normalized to the clinical baseline scan and compared using the Wilcoxon signed-rank test in order to isolate variations due to reconstruction parameters. Results: For the baseline scans, 13 texture features showed a mean range greater than 10%. For the intra scans, 28 texture features showed a mean range greater than 10%. Comparing baseline to intra scans, 25 texture features showed p <0.05. Conclusion: Variability due to different reconstruction parameters increased with treatment, however, the majority of texture features showed significant changes during treatment independent of reconstruction effects.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Multiscale and Machine Learning Modeling for Process-informed Microstructure Prediction in Additively Manufactured Materials Using MALAMUTE

Advanced Materials and Manufacturing Technologies (AMMT) program under the Department of Energy Office of Nuclear Energy, aims to develop and qualify additively-manufactured materials for nuclear applications. The key challenges to these efforts are the microstructural variabilities observed on the AM products and their impact on the properties and performance of the material in extreme environments. AMMT is using a combination of high-through-put experimental and modeling techniques to accelerate the qualification efforts. Conventionally, in-situ and ex-situ characterizations and testing are performed to correlate different aspects of the AM process to the final product and its performance. However, adopting a trial-and-error approach to experimentally evaluate the vast range of process parameters required to capture the microstructural variabilities is cost-prohibitive. Modeling and simulation provide a comparatively inexpensive way to understand and correlate the microstructural evolution to the processing conditions. The modeling and simulation work-packages within the AMMT program aims to use physics-based and machine learning modeling capabilities to develop a digital twin for AM that can correlate the process conditions to the final product and establish a process-structure-property-performance (PSPP) correlation for AM materials. The melting and subsequent solidification that occurs during the AM process is a complex phenomenon that requires multiscale multiphysics analysis. Idaho National Laboratory’s (INL) Multiphysics Object-Oriented Simulation Environment (MOOSE), specifically the MOOSE Application Library for Advanced Manufacturing UTilitiEs (MALAMUTE) software, provides an ideal platform for developing the multiphysics multiscale model to explore the intricacies of the microstructural evolution during the AM processes within a single framework. Furthermore, given that such full-fidelity simulations can be computationally intensive, reduced order models are necessary to explore the PSPP space for AM materials in an efficient, reliable, and cost-effective way. This work package focuses on understanding the role of process variabilities on the various microstructural characteristics of the AM materials. Microstructures unique to AM materials, such as compositional micro-heterogeneity and dislocation cells, are of particular interest here since they can influence the creep properties and radiation performance. In fiscal year (FY) 24, we significantly advanced upon our work in the last fiscal year, both on physics-based and ML models. The alloy solidification model available in MOOSE has been extended to incorporate the thermodynamic properties and free energy relevant to 316SS. The model demonstrates the Cr segregation that occurs during solidifcation. It is demonstrated that rate of solidification and solute segregation is primarily influence by the cooling rate dictating the level of freezing. This work captures the microstructural variabilities at the subgrain level that are often missing in the part-scale models. With an aim to connect the microstructural evolution model to realistic process conditions, a reduced order model is developed for predicting the thermal conditions around meltpool from high-fidelity process simulations. Furthermore, machine learning approach is used to accelerate the temperature prediction during the AM process. In the following years, MALAMUTE will be used to connect different aspects of the models and quantitatively predict the microstructural evolution. The developed ML-based surrogate model will consider the process conditions as the input to predict the microstructural features in a cost-effective way. The generated microstructures can be used by other work packages under AMMT to evaluate the properties and environmental response of the material at the mesoscale. Thus, this work help identify the key microstructural features at the subgrain level that are significant in property/performance prediction of the AM products. This work will provide inputs to the large-scale process variability models to reevaluate and validate assumptions/simplifications made in the part-scale models. Furthermore, through active learning this work will help identify the data need from both modeling and experimental sides for development of a robust digital twin for AM.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Evidence for Abnormal H α Variability During Near-transit Observations of HD 189733 b

Changes in levels of stellar activity can mimic absorption signatures in transmission spectra from circumplanetary material. Thus, it is critical to understand the frequency and magnitude of these changes in order to attribute any particular signal to the circumplanetary environment. We present short-cadence, high-resolution out-of-transit H α spectra for the hot Jupiter host HD 189733 in order to establish the frequency and magnitude of intrinsic stellar variations in the H α line core. We find that changes in the line core strength similar to those observed immediately pre- and post-transit in two independent data sets are uncommon. This suggests that the observed near-transit signatures are either due to absorption of circumplanetary material or they occur preferentially in time, very near planetary transits. In either case, the evidence for abnormal H α variability is strengthened, though the short-cadence out-of-transit data do not argue for circumplanetary absorption versus stellar activity caused by a star–planet interaction. Further out-of-transit monitoring at higher signal-to-noise would be useful to more strictly constrain the frequency of the near-transit changes in the H α line core.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Neutron diffraction study of monoclinic brannerite-type CoV{sub 2}O{sub 6}

A variable-temperature powder neutron diffraction study of the monoclinic brannerite-type CoV{sub 2}O{sub 6} (space group C2/m, a=9.2531(2), b=3.5040(1), c=6.6201(1) A and {beta}=111.617(1) Degree-Sign at 300 K) is reported. No structural transition is observed down to 4 K, but a magnetostriction accompanying antiferromagnetic order at T{sub N}=15 K is discovered. Antiferromagnetic order observed below T{sub N} has an a Multiplication-Sign b Multiplication-Sign 2c supercell in which Co{sup 2+} moments of magnitude 4.77(4) {mu}{sub B} at 4 K lie in the ac plane and are ferromagnetically coupled within chains of edge-sharing CoO{sub 6} octahedra parallel to b. Ferromagnetic chains are coupled antiferromagnetically to neighbouring chains in the a and c directions, and a model for the interchain order in the reported 1/3 magnetization plateau region is proposed. - Graphical abstract: Antiferromagnetic order of Co{sup 2+} moments in monoclinic brannerite type CoV2O6 results in a magnetostriction at the 15 K Neel transition. An alternative coupling between ferromagnetic chains is proposed to account for a 1/3 magnetization plateau in this material. Highlights: Black-Right-Pointing-Pointer Variable-temperature powder neutron diffraction study of the monoclinic brannerite-type CoV{sub 2}O{sub 6} is reported. Black-Right-Pointing-Pointer Magnetostriction accompanying antiferromagnetic order at T{sub N}=15 K in monoclinic CoV{sub 2}O{sub 6} is discovered. Black-Right-Pointing-Pointer Antiferromagnetic order in a Multiplication-Sign b Multiplication-Sign 2c supercell of CoV{sub 2}O{sub 6} is determined. Black-Right-Pointing-Pointer Model for spin order in the reported 1/3 magnetization plateau of CoV{sub 2}O{sub 6} is proposed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Moving beyond the constraints of chemistry via crystal structure discovery with isotropic multiwell pair potentials

The rigid constraints of chemistry-dictated by quantum mechanics and the discrete nature of the atom-limit the set of observable atomic crystal structures. What structures are possible in the absence of these constraints? Here, we systematically crystallize one-component systems of particles interacting with isotropic multiwell pair potentials. We investigate two tunable families of pairwise interaction potentials. Our simulations self-assemble a multitude of crystal structures ranging from basic lattices to complex networks. Sixteen of the structures have natural analogs spanning all coordination numbers found in inorganic chemistry. Fifteen more are hitherto unknown and occupy the space between covalent and metallic coordination environments. The discovered crystal structures constitute targets for self-assembly and expand our understanding of what a crystal structure can look like.

crystal structures↗
DOE OSTI2023

Evidence for Black Holes in Green Peas from WISE Colors and Variability

We explore the presence of active galactic nuclei (AGNs)/black holes in Green Pea galaxies (GPs), motivated by the presence of high-ionization emission lines such as He ii and [Ne iii] in their optical spectra. In order to identify AGN candidates, we used mid-infrared (MIR) photometric observations from the all-sky Wide-field Infrared Survey Explorer (WISE) mission for a sample of 1004 GPs. Considering only >5σ detections with no contamination from neighboring sources in AllWISE, we select 31 GPs out of 134 as candidate AGNs based on a stringent three-band WISE color diagnostic. Using multi-epoch photometry in W1 and W2 bands based on time-resolved unWISE coadd images, we find two sources exhibiting variability in both the WISE bands among 112 GPs with W1 ≤16 mag and no contamination from neighboring sources in unWISE. These two variable sources were selected as AGNs by the WISE three-band color diagnostic as well. Compared to variable AGN fractions observed among low-mass galaxy samples in previous studies, we find a higher fraction (~1.8%) of MIR variable sources among GPs, which demonstrates the uniqueness and importance of studying these extreme objects. Through this work, we demonstrate that MIR diagnostics are promising tools to select AGNs that may be missed by other selection techniques (including optical emission-line ratios and X-ray emission) in star formation-dominated, low-mass, low-metallicity galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Regime dependence of cloud condensate variability observed at the Atmospheric Radiation Measurement Sites

Microphysical processes and cloud–radiation interaction occur on spatial scales of variability smaller than those represented explicitly in global weather forecasting and climate models. It is therefore necessary to parametrize the unresolved heterogeneity of humidity and cloud condensate in order to predict process rates accurately. Ground‐based observations from the Atmospheric Radiation Measurement sites located in various climatic regions of the world provide a source of high‐temporal‐resolution observations of cloud condensate. A number of different retrieval products for cloud condensate are assessed for the different geographical regions, years and seasons. The retrieval reliability varies with cloud type, but for cloud categories largely unaffected by precipitation a comparison across sites and longer time periods is possible. These observations confirm previously documented variability behaviour as a function of cloud fraction, but also reveal a systematic regime dependence that is not captured by existing parametrizations. Condensate variability measured as a fractional standard deviation (FSD) in warm boundary‐layer clouds is greater in the Tropics than in mid and high latitudes for scenes with comparable cloud type and fraction, with the observed FSD varying from 1.2 in the Tropics to 0.4 in the Arctic. A parametrization of the FSD of cloud liquid condensate based on the grid‐box mean total water amount and cloud fraction is formulated and shown to capture the observed range of FSD values better across different geographical sites and different seasons. The regime dependence of FSD for cirrus cloud is less pronounced than that for liquid clouds and is found largely to agree with FSD values previously derived from satellite observations.

Ahlgrimm, Maike↗
DOE OSTI2022

Shock Formation and Vorticity Creation for 3d Euler

Abstract We analyze the shock formation process for the 3D nonisentropic Euler equations with the ideal gas law, in which sound waves interact with entropy waves to produce vorticity. Building on our theory for isentropic flows in [3, 4], we give a constructive proof of shock formation from smooth initial data. Specifically, we prove that there exist smooth solutions to the nonisentropic Euler equations which form a generic stable shock with explicitly computable blowup time, location, and direction. This is achieved by establishing the asymptotic stability of a generic shock profile in modulated self‐similar variables, controlling the interaction of wave families via: (i) pointwise bounds along Lagrangian trajectories, (ii) geometric vorticity structure, and (iii) high‐order energy estimates in Sobolev spaces. © 2022 Wiley Periodicals LLC.

Mathematics↗
DOE OSTI2012

Renewable Generation, Integration of

The integration of renewable generation consists of all of the changes in power system operations that are required in order to allow renewable generation sources to play a significant role in the electricity system. The impacts are mostly due to variable generation (VG), like wind and solar power. Historically these technologies have been labeled as intermittent generation, but recent trendsprefer the label variable generation. Variable generators have a maximum available generation limit that changes with time (variability) and this limit is not known with perfect accuracy (uncertainty). This uncertainty and variability is in addition to that of the existing system and can therefore create additional challenges for grid operators to maintain their current levels of reliability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2012

Renewable Generation, Integration of

The integration of renewable generation consists of all of the changes in power system operations that are required in order to allow renewable generation sources to play a significant role in the electricity system. The impacts are mostly due to variable generation (VG), like wind and solar power. Historically these technologies have been labeled as intermittent generation, but recent trends prefer the label variable generation. Variable generators have a maximum available generation limit that changes with time (variability) and this limit is not known with perfect accuracy (uncertainty). This uncertainty and variability is in addition to that of the existing system and can therefore create additional challenges for grid operators to maintain their current levels of reliability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Neon diffusion kinetics and implications for cosmogenic neon paleothermometry in feldspars

Observations of cosmogenic neon concentrations in feldspars can potentially be used to constrain the surface exposure duration or surface temperature history of geologic samples. The applicability of cosmogenic neon to either application depends on the temperature-dependent diffusivity of neon isotopes. Here in this work, we investigate the kinetics of neon diffusion in feldspars of different compositions and geologic origins through stepwise degassing experiments on single, proton-irradiated crystals. To understand the potential causes of complex diffusion behavior that is sometimes manifest as nonlinearity in Arrhenius plots, we compare our results to argon stepwise degassing experiments previously conducted on the same feldspars. Many of the feldspars we studied exhibit linear Arrhenius behavior for neon whereas argon degassing from the same feldspars did not. This suggests that nonlinear behavior in argon experiments is an artifact of structural changes during laboratory heating. However, other feldspars that we examined exhibit nonlinear Arrhenius behavior for neon diffusion at temperatures far below any known structural changes, which suggests that some preexisting material property is responsible for the complex behavior. In general, neon diffusion kinetics vary widely across the different feldspars studied, with estimated activation energies (E a ) ranging from 83.3 to 110.7 kJ/mol and apparent pre-exponential factors (D 0 ) spanning three orders of magnitude from 2.4 ×10 -3 to 8.9 × 10 -1 cm 2 s -1 . Finally, as a consequence of this variability, the ability to reconstruct temperatures or exposure durations from cosmogenic neon abundances will depend on both the specific feldspar and the surface temperature conditions at the geologic site of interest.

58 GEOSCIENCES↗
DOE OSTI2023

Oxidation rates and redox stabilization of ferrous iron in trioctahedral smectites

Iron(II)-bearing trioctahedral smectites (saponites) form during anoxic alteration of basaltic rock. They are predicted to have been widespread on the early Earth and are observed in the oceanic subsurface today. Smectite structures, including the occupancy of sites in the octahedral sheet, affect iron redox behavior but the rates and products of trioctahedral smectite oxidation have been largely unexplored to date. In this study we synthesized two Fe(II)-bearing trioctahedral smectites, one moderate (22 wt% Fe) and one high (27 wt% Fe) in iron content. We then examined the rate, extent, and products of their oxidation by dissolved oxygen, nitrite, and hydrogen peroxide. Dissolved oxygen caused partial oxidation of Fe(II) in the smectites with 14 to 43% of Fe(II) unoxidized after 20 to 30 days of exposure. The rate and extent of oxidation correlated with the dissolved oxygen concentration and the Fe(II) content of the clay. The incomplete oxidation in these experiments is consistent with the mixed-valent trioctahedral smectites observed in oxidized natural samples but contrasts with the complete reoxidation by oxygen shown by chemically- or microbially-reduced dioctahedral smectites. Oxidation of structural Fe(II) by 5 mmol L -1 nitrite was negligible for the moderate-iron smectite and yielded only ~17% oxidation after 54 days of reaction for the high-iron smectite. Hydrogen peroxide caused rapid and near-complete oxidation of both clays. Powder X-ray diffraction, variable-temperature Mössbauer spectroscopy, and extended X-ray absorption fine structure spectroscopy together detected no crystalline or short-range-ordered secondary phases and show that oxidized iron remained in the trioctahedral smectite structure. The recalcitrant Fe(II) pool in oxidized trioctahedral smectites exists in less distorted sites than Fe(II) in the initial clays. Its unreactive nature at prolonged reaction times indicates an elevated redox potential generated by the local coordination environment. Slower oxidation rates create a larger recalcitrant Fe(II) pool, suggesting kinetic competition between oxidation and a process involved in redox stabilization, such as electron exchange between octahedral iron sites or deprotonation of hydroxyl groups in the structure. The resistance to complete oxidation of trioctahedral ferrous smectites and their full retention of iron demonstrates that transitions from anoxic to oxic conditions generate mixed-valence smectites rather than a mixture of new phases. Identifying the diagenetic products of mixed-valent trioctahedral smectites may provide an indicator in the rock record of past redox cycling. In conclusion, substantial portions of structural Fe(II) in trioctahedral smectites display slow abiotic oxidation kinetics and represent potential electron donors for both microaerophilic iron oxidizing and nitrate-reducing, iron-oxidizing microorganisms in altered mafic rocks and related settings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Variational Bayesian strategies for high-dimensional, stochastic design problems

This paper is concerned with a lesser-studied problem in the context of model-based, uncertainty quantification (UQ), that of optimization/design/control under uncertainty. The solution of such problems is hindered not only by the usual difficulties encountered in UQ tasks (e.g. the high computational cost of each forward simulation, the large number of random variables) but also by the need to solve a nonlinear optimization problem involving large numbers of design variables and potentially constraints. We propose a framework that is suitable for a class of such problems and is based on the idea of recasting them as probabilistic inference tasks. To that end, we propose a Variational Bayesian (VB) formulation and an iterative VB–Expectation-Maximization scheme that is capable of identifying a local maximum as well as a low-dimensional set of directions in the design space, along which, the objective exhibits the largest sensitivity. We demonstrate the validity of the proposed approach in the context of two numerical examples involving thousands of random and design variables. In all cases considered the cost of the computations in terms of calls to the forward model was of the order of 100 or less. The accuracy of the approximations provided is assessed by information-theoretic metrics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗