The multifaceted nature of uncertainty in structure-property linkage with crystal plasticity finite element model
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Tran, Anh↗
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QUESTS: Quick Uncertainty and Entropy from STructural Similarity
QUESTS provides a strategy to quantify the uncertainty and the information content (entropy) of datasets of atomistic simulations. The code implements the calculation of a descriptor, compares information contents of datasets, verifies whether given structures are contained in specific datasets, and more. This code base enables better design of training sets for machine learning force fields as well as understanding some thermodynamic properties of materials.
Schwalbe Koda, Daniel↗
Earth System Reanalysis in Support of Climate Model Improvements
Recent climate model developments, established through increased model resolution, have led to substantial improvements in model simulations of the time-evolving, coupled Earth system and its subcomponents. However, regardless of resolution, climate models will always produce climate features and variability that differ from the real world and will be prone to biases. This is due to many remaining uncertainties, such as in parametric and structural model uncertainty, in the initial conditions prescribed, and in the prescribed (scenario) forcing which varies on decadal to centennial timescales. Further model improvements are expected to arise specifically from improved representation of physical processes realized through model-data fusion. This will create an unprecedented opportunity to better exploit a large array of Earth observations, from in situ measurements to weather radars and satellite observations, as the resolved scales of the models approach those of the observations. For this, climate DA will be the central tool to bring models and observations into consistency, by improving initial conditions, inferring uncertain model parameters and structure, and quantifying uncertainty. Generally, there will be advantages and complementarities of adjoint-based smoother approaches, ensemble-based filter approaches, or new ML-inspired approaches. Yet, the ever-increasing model resolution will present growing challenges arising from computational cost, calling for new ways of performing data assimilation and model optimization. Using the complementarity in a hybrid approach, blending tools and concepts from variational, ensemble and ML methods might be what is required in the future. In this context ML could be important to handle non-linear responses, and to better approximate non-Gaussian distributions.
54 ENVIRONMENTAL SCIENCES↗
Sparse Bayesian mass mapping with uncertainties: hypothesis testing of structure
ABSTRACT A crucial aspect of mass mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present a new method to reconstruct maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type l1-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time, these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artefacts of the reconstruction. Here, we present this new formalism, and demonstrate the method on simulations, before applying the developed formalism to two observational data sets of the Abell 520 cluster. Initial reconstructions of the Abell 520 catalogues reported the detection of an anomalous ‘dark core’ – an overdense region with no optical counterpart – which was taken to be evidence for self-interacting dark matter. In our Bayesian framework, it is found that neither Abell 520 data set can conclusively determine the physicality of such dark cores at $99{{\ \rm per\ cent}}$ confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data.
Price, M. A.↗
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↗
Temperature Uncertainty Modeling with Proxy Structural Data as Geostatistical Constraints for Well Siting: An Example Applied to Granite Springs Valley, NV, USA
Utilizing existing temperature and structural information around Granite Springs Valley, Nevada, we build 3D stochastic temperature models with the aim of evaluating the 3D uncertainty of temperature and choosing between candidate exploration well locations . The data used to support the modeling are measured temperatures and structural proxies from 3D geologic modeling, the latter considered "secondary" data. Two stochastic geostatistical techniques are explored for incorporating the structural proxies: cosimulation and local varying mean. With both the cosimulation and local varying mean methods, many equally likely temperature models (i.e., realizations) are produced, from which temperature probability profiles are calculated at candidate well locations. To aid in choosing between the candidate locations, two quantities summarize the temperature probabilities: Vprior and entropy. Vprior quantifies the likelihood for economic temperatures at each candidate location, whereas entropy identifies where new information has the most potential to reduce uncertainty. In general, the cosimulation realizations have smoother spatial structure, and extrapolate high temperatures at candidate locations that are located along the direction of the longest spatial correlation, which are down dip from existing temperature logs. The smooth realizations result in tight temperature probability profiles that are easier to interpret, but they have unrealistic temperature reversals in some locations because the cosimulation technique does not enforce a conductive geothermal gradient as a baseline (i.e., linearly increasing temperature with depth). The local varying mean results produce realizations with more realistic geothermal gradients, with temperatures increasing downward since a depth-temperature relationship is included. However, because they have much noisier spatial nature compared to cosimulation, it is harder to interpret the temperature probability profiles. The different local varying mean results allow the geologist to determine which proxy (e.g., dilation versus distance to fault termination) should be used given the specific geothermal system. In general, Vprior from local varying mean results identify locations that are close to high values for the structural proxies: areas with highe r probabilities for higher temperatures. The entropy results identify where uncertainty is greatest and therefore new drilling information could be most useful. Though these techniques provide useful information, even when applied to areas of sparse data, our comp arison of these two techniques demonstrates the need for new geothermal geostatistics techniques that combine the advantages of these two methods and that are tailored to the spatial uncertainty issues inherent in geothermal exploration.
3D temperature modeling↗
Temperature uncertainty modelling with proxy structural data as geostatistical constraints for well siting: an example applied to Granite Springs Valley, NV, USA
Utilizing existing temperature and structural geology information around Granite Springs Valley, Nevada, we build 3D stochastic temperature models with the aims of evaluating the 3D uncertainty of temperature and choosing between candidate exploration well locations. The data used to support the modelling are measured temperatures and structural proxies from 3D geologic modelling (distance to fault, distance to fault intersections and terminations, Coulomb stress change and dilation tendency), the latter considered ‘secondary’ data. Two stochastic geostatistical techniques are explored for incorporating the structural proxies: cosimulation and local varying mean. With both the cosimulation and local varying mean methods, many equally-likely temperature models (i.e. realizations) are produced, from which temperature probability profiles are calculated at candidate well locations. To aid in choosing between the candidate locations, two quantities summarize the temperature probabilities: V prior and entropy. V prior quantifies the likelihood for economic temperatures at each candidate location, whereas entropy identifies where new information has the most potential to reduce uncertainty. In general, the cosimulation realizations have smoother spatial structure, and extrapolate high temperatures at candidate locations that are located along the direction of the longest spatial correlation, which are down dip from existing temperature logs. The smooth realizations result in tight temperature probability profiles that are easier to interpret, but they have unrealistic temperature reversals in some locations because of the dipping ellipsoid shape created and that the cosimulation technique does not enforce a conductive geothermal gradient as a baseline (i.e. linearly increasing temperature with depth). The local varying mean results produce realizations with more realistic geothermal gradients, with temperatures increasing downward since a depth-temperature relationship is included. However, because they have much noisier spatial nature compared to cosimulation, it is harder to interpret the temperature probability profiles. The different local varying mean results allow the geologist to determine which proxy (e.g. dilation v. distance to fault termination) should be used given the specific geothermal system. In general, V prior from local varying mean results identify locations that are close to high values for the structural proxies: areas with higher probabilities for higher temperatures. The entropy results identify where uncertainty is greatest and therefore new drilling information could be most useful. Though these techniques provide useful information, even when applied to areas of sparse data, our comparison of these two techniques demonstrates the need for new geothermal geostatistics techniques that combine the advantages of these two methods and that are tailored to the spatial uncertainty issues inherent in geothermal exploration.
15 GEOTHERMAL ENERGY↗
Multi-faceted uncertainty quantification for structure-property relationship with crystal plasticity finite element.
Abstract not provided.
Tran, Anh↗
Sparse Data Machine Learning Integration with Theory, Experiment and Uncertainty Quantification: Process-Structure-Property-Performance of Friction Deformation Processing
Computer vision and deep learning tools that advance the ability to establish processing-structure-property-performance (PSPP) relations are presented. The Bayesian binning method for image segmentation enables quantitative analysis of microstructural features in an automated way, while the analysis of shapes and relative orientation of these features reveals local deformation maps indicative of both, material flow and residual stresses due to materials processing. The deep learning method leads to the previous knowledge agnostic mapping of empirically observed microstructural zones in friction stir welding (FSW) process and synthetic microstructure generation capability that is statistically equivalent to experimentally collected data.
97 MATHEMATICS AND COMPUTING↗
The multifaceted uncertainty nature of structure-property linkage with crystal plasticity finite element model.
Abstract not provided.
Tran, Anh↗
Uncertainties in ab initio nuclear structure calculations with chiral interactions
We present theoretical ground state energies and their uncertainties for p -shell nuclei obtained from chiral effective field theory internucleon interactions as a function of chiral order, fitted to two- and three-body data only. We apply a Similary Renormalization Group transformation to improve the numerical convergence of the many-body calculations, and discuss both the numerical uncertainties arising from basis truncations and those from omitted induced many-body forces, as well as chiral truncation uncertainties. With complete Next-to-Next-to-Leading (N 2 LO) order two- and three-body interactions, we find significant overbinding for the ground states in the upper p -shell, but using higher-order two-body potentials, in combination with N 2 LO three-body forces, our predictions agree with experiment throughout the p -shell to within our combined estimated uncertainties. The uncertainties due to chiral order truncation are noticeably larger than the numerical uncertainties, but they are expected to become comparable to the numerical uncertainties at complete N 3 LO.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Quantifying structural errors in cloud condensation nuclei activity from reduced representation of aerosol size distributions
Aerosol effects on clouds and radiation are the dominant contribution to uncertainty in radiative forcing relative to the pre-industrial atmosphere. While previous studies have assessed the impact of parametric uncertainty on modeled forcing, structural errors from the numerical representation of particle distributions have not been well quantified. Here we present a framework for quantifying error in aerosol size distributions and cloud condensation nuclei activity, which we apply to the widely used 4-mode version of the Modal Aerosol Module (MAM4). Box model predictions from the MAM4 are evaluated against the Particle Monte Carlo Model for Simulating Aerosol Interactions and Chemistry (PartMC-MOSAIC), a benchmark model that tracks the evolution of individual particles. We show that size distributions simulated by MAM4 diverge from those simulated by PartMC-MOSAIC after only a few hours of aging by condensation and coagulation in polluted conditions, which leads to large errors in modeled cloud condensation nuclei concentrations. We find that differences between MAM4 and PartMC-MOSAIC are largest under polluted conditions, where the size distribution evolves rapidly though aging by condensation of semi-volatile substances and coagulation among particles. These findings suggest that structural error in modeled aerosol properties contributes to the large inter-model variability in aerosol radiative forcing.
Fierce, Laura M.↗
Evidence of a New Excited Charmed Baryon Decaying to Σ c ( 2455 ) 0 , + + π ±
We present the study of $\overline{B}$ 0 →Σ c (2455) 0,++ π ± $\overline{p}$ decays based on 772×10 6 B$\overline{B}$ events collected with the Belle detector at the KEKB asymmetric-energy e + e - collider. The Σ c (2455) 0,++ candidates are reconstructed via their decay to Λ$^{+}_{c}$π ∓ and Λ$^{+}_{c}$ decays to pK - π + , pK$^{0}_{S}$, and Λπ + final states. The corresponding branching fractions are measured to be $\mathscr{B}$($\overline{B}$ 0 →Σ c (2455) 0 π + $\overline{p}$)=(1.09±0.06±0.07)×10 -4 and $\mathscr{B}$($\overline{B}$ 0 →Σ c (2455) ++ π - $\overline{p}$)=(1.84±0.11±0.12)×10 -4 , which are consistent with the world average values with improved precision. A new structure is found in the M Σ c (2455) 0,++π± spectrum with a significance of 4.2σ including systematic uncertainty. The structure is possibly an excited Λ$^{+}_{c}$ and is tentatively named Λ c (2910) + . Its mass and width are measured to be (2913.8±5.6±3.8) MeV/c 2 and (51.8±20.0±18.8) MeV, respectively. The products of branching fractions for the Λ c (2910) + are measured to be $\mathscr{B}$($\overline{B}$ 0 →Λ c (2910) + $\overline{p}$) × $\mathscr{B}$(Λ c (2910) + →Σ c (2455) 0 π + )=(9.5±3.6±1.6) x 10 -6 and $\mathscr{B}$($\overline{B}$ 0 →Λ c (2910) + $\overline{p}$) × $\mathscr{B}$(Λ c (2910) + →Σ c (2455 )++ π - )=(1.24±0.35±0.10)×10 -5 . Here, the first and second uncertainties are statistical and systematic, respectively.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Incorporating geological structure into sensitivity analysis of subsurface contaminant transport
Simulating subsurface contaminant transport at the kilometer-scale often entails modeling reactive flow and transport within and through complex geologic structures. These structures are typically meshed by hand and as a result geologic structure is usually represented by one or a few deterministically generated geological models for uncertainty studies of flow and transport in the subsurface. Uncertainty in geologic structure can have a significant impact on contaminant transport. In this study, the impact of geologic structure on contaminant tracer transport in a shale formation is investigated for a simplified generic deep geologic repository for permanent disposal of spent nuclear fuel. An open-source modeling framework is used to perform a sensitivity analysis study on transport of two tracers from a generic spent nuclear fuel repository with uncertain location of the interfaces between the stratum of the geologic structure. The automated workflow uses sampled realizations of the geological structural model in addition to uncertain flow parameters in a nested sensitivity analysis. Concentration of the tracers at observation points within, in line with, and downstream of the repository are used as the quantities of interest for determining model sensitivity to input parameters and geological realization. Finally, the results of the study indicate that the location of strata interfaces in the geological structure has a first-order impact on tracer transport in the example shale formation, and that this impact may be greater than that of the uncertain flow parameters.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Diversifying Composition Leads to Hierarchical Composites with Design Flexibility and Structural Fidelity
Although significant progress has been made in the self-assembly of nanostructures, present successes heavily rely on precision in building block design, composition, and pair interactions. These requirements fundamentally limit our ability to synthesize macroscopic materials where the likelihood of impurity inclusion escalates and, more importantly, to access molecular-to-nanoscopic-to-microscopic-to-macroscopic hierarchies, since the types and compositions of building blocks vary at each stage. Inspired by biological blends and high-entropy alloys, we hypothesize that diversifying the blend’s composition can overcome these limitations. Increasing the number of components increases mixing entropy, leading to the dispersion of different components and, as a result, enhances interphase miscibility, weakens the dependence on specific pair interactions, and enables long-range cooperativity. This hypothesis is validated in complex blends containing small molecules, block copolymer-based supramolecules, and nanoparticles/colloidal particles. Hierarchically structured composites can be obtained with formulation flexibility in the filler selection and blend composition. It is worth noting that, by adding small molecules, we can solve the size constraint that plagues traditional block copolymer/nanoparticle blends. Detailed characterization and simulation further confirm that each component is distributed to locally mediate unfavorable interactions, cooperatively mitigate composition fluctuations, and retain structural fidelity. Furthermore, the blends have sufficient mobility to access tunable microstructures without compromising the order of the nanostructure. Besides establishing a kinetically viable pathway to release current constraints in the composite design and to navigate uncertainties during structure formation over multiple length scales, the present study demonstrates that entropy-driven behaviors can be realized in systems beyond high-entropy alloys despite inherent differences between metal alloys and organic/inorganic hybrids.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Reducing uncertainty of high-latitude ecosystem models through identification of key parameters
Abstract Climate change is having significant impacts on Earth’s ecosystems and carbon budgets, and in the Arctic may drive a shift from an historic carbon sink to a source. Large uncertainties in terrestrial biosphere models (TBMs) used to forecast Arctic changes demonstrate the challenges of determining the timing and extent of this possible switch. This spread in model predictions can limit the ability of TBMs to guide management and policy decisions. One of the most influential sources of model uncertainty is model parameterization. Parameter uncertainty results in part from a mismatch between available data in databases and model needs. We identify that mismatch for three TBMs, DVM-DOS-TEM, SIPNET and ED2, and four databases with information on Arctic and boreal above- and belowground traits that may be applied to model parametrization. However, focusing solely on such data gaps can introduce biases towards simple models and ignores structural model uncertainty, another main source for model uncertainty. Therefore, we develop a causal loop diagram (CLD) of the Arctic and boreal ecosystem that includes unquantified, and thus unmodeled, processes. We map model parameters to processes in the CLD and assess parameter vulnerability via the internal network structure. One important substructure, feed forward loops (FFLs), describe processes that are linked both directly and indirectly. When the model parameters are data-informed, these indirect processes might be implicitly included in the model, but if not, they have the potential to introduce significant model uncertainty. We find that the parameters describing the impact of local temperature on microbial activity are associated with a particularly high number of FFLs but are not constrained well by existing data. By employing ecological models of varying complexity, databases, and network methods, we identify the key parameters responsible for limited model accuracy. They should be prioritized for future data sampling to reduce model uncertainty.
54 ENVIRONMENTAL SCIENCES↗
Propagating sample variance uncertainties in redshift calibration: simulations, theory, and application to the COSMOS2015 data
ABSTRACT Cosmological analyses of galaxy surveys rely on knowledge of the redshift distribution of their galaxy sample. This is usually derived from a spectroscopic and/or many-band photometric calibrator survey of a small patch of sky. The uncertainties in the redshift distribution of the calibrator sample include a contribution from shot noise, or Poisson sampling errors, but, given the small volume they probe, they are dominated by sample variance introduced by large-scale structures. Redshift uncertainties have been shown to constitute one of the leading contributions to systematic uncertainties in cosmological inferences from weak lensing and galaxy clustering, and hence they must be propagated through the analyses. In this work, we study the effects of sample variance on small-area redshift surveys, from theory to simulations to the COSMOS2015 data set. We present a three-step Dirichlet method of resampling a given survey-based redshift calibration distribution to enable the propagation of both shot noise and sample variance uncertainties. The method can accommodate different levels of prior confidence on different redshift sources. This method can be applied to any calibration sample with known redshifts and phenotypes (i.e. cells in a self-organizing map, or some other way of discretizing photometric space), and provides a simple way of propagating prior redshift uncertainties into cosmological analyses. As a worked example, we apply the full scheme to the COSMOS2015 data set, for which we also present a new, principled SOM algorithm designed to handle noisy photometric data. We make available a catalogue of the resulting resamplings of the COSMOS2015 galaxies.
79 ASTRONOMY AND ASTROPHYSICS↗
a priori uncertainty quantification of reacting turbulence closure models using Bayesian neural networks
While many physics-based closure model forms have been posited for the sub-filter scale (SFS) in large eddy simulation (LES), vast amounts of data available from direct numerical simulations (DNS) create opportunities to leverage data-driven modeling techniques. Albeit flexible, data-driven models still depend on the dataset and the functional form of the model chosen. Increased adoption of such models requires reliable uncertainty estimates both in the data-informed and out-of-distribution regimes. Here, in this work, we employ Bayesian neural networks (BNNs) to capture both epistemic and aleatoric uncertainties in a reacting flow model. In particular, we model the filtered progress variable scalar dissipation rate which plays a key role in the dynamics of turbulent premixed flames. We demonstrate that BNN models can provide unique insights about the structure of uncertainty of the data-driven closure models. We also propose a method for the incorporation of out-of-distribution information in a BNN, which can be used for out-of-distribution query detection. The efficacy of the model is demonstrated by a priori evaluation on a dataset consisting of a variety of flame conditions and fuels.
97 MATHEMATICS AND COMPUTING↗