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Results for “Variational inference”
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Posterior Covariance Matrix Approximations
Here, the Davis equation of state (EOS) is commonly used to model thermodynamic relationships for high explosive (HE) reactants. Typically, the parameters in the EOS are calibrated, with uncertainty, using a Bayesian framework and Markov Chain Monte Carlo (MCMC) methods. However, MCMC methods are computationally expensive, especially for complex models with many parameters. This paper provides a comparison between MCMC and less computationally expensive Variational methods (Variational Bayesian and Hessian Variational Bayesian) for computing the posterior distribution and approximating the posterior covariance matrix based on heterogeneous experimental data. All three methods recover similar posterior distributions and posterior covariance matrices. This study demonstrates that for this EOS parameter calibration application, the assumptions made in the two Variational methods significantly reduce the computational cost but do not substantially change the results compared to MCMC.
CONCURRENT, CONDENSED STEIN VARIATIONAL GRADIENT DESCENT FOR UNCERTAINTY QUANTIFICATION OF NEURAL NETWORKS
In this work, we propose a Stein variational gradient descent (SVGD) method to concurrently sparsify, train, and provide uncertainty quantification (UQ) of a complexly parameterized model, such as a neural network (NN). It employs a graph reconciliation and condensation process to reduce complexity and increase similarity in the Stein ensemble of parameterizations. Therefore, the proposed concurrent, condensed SVGD (ccSVGD) method can provide UQ on parameters, not just outputs. Furthermore, the parameter reduction speeds up the convergence of the Stein gradient descent as it reduces the combinatorial complexity by aligning and differentiating the sensitivity to parameters. These properties are demonstrated with an illustrative example and an application to a mechanical response representation problem in solid mechanics.
Xenon in the Protoplanetary Disk (PPD), in Two Planets, and a Comet
Isotopic anomalies in several elements, as recently observed in meteorites, are generally interpreted to indicate nonequilibrium environments in the protoplanetary disk (PPD). Here we study reported Xe isotopic compositions on planets Earth and Mars, in a comet, and in meteorites for precursor discrepancies. Abundance variations of inferred presolar nano-diamonds, the carrier phase of the Xe-HL component, appear to be the primary source of nonuniformity of Xe precursors in the PPD, together with mechanisms of mass-dependent fractionation. While planet Mars kept a record of initial solar Xe isotopic abundances, such a record is missing for planet Earth. Xe isotopic abundances in paleo-atmospheres of both planets represent secondary reservoirs that show mass-dependent fractionation effects, but the inferred compositions of their PPD precursors differ: Mars atmospheric precursor Xe had solar isotopic composition, while Earth’s Xe precursor is consistent with a PPD reservoir of low nano-diamond abundance. Strong mass-dependent fractionation effects are observed in Xe components of IAB irons and in Yamato carbonaceous (CY) chondrites, and show that fractionation mechanisms are not restricted to planetary atmospheres. These records show that Xe isotopes in solar system reservoirs are useful tracers of evolutionary processes and of nonequilibrated presolar components in the PPD.
SQUID Readout of a High-$Q$ Superconducting $LC$ Resonator
We demonstrate the readout of a superconducting $LC$ resonator, with $Q \approx 2 \times 10^{6}$ at approximately 250 kHz, using a dc SQUID followed by a SQUID series-array amplifier readout chain. We find that $Q$ depends on the SQUID flux-bias point, increasing near the shallow-slope point of the SQUID modulation curve and decreasing near the steep-slope point, consistent with the previously observed SQUID damping effects. From this variation, we infer the SQUID effective input impedance. We further infer the effective temperature of the resonator circuit from the resonance peak in the noise spectrum and show that it also depends on the SQUID flux-bias point, suggesting a possible contribution from SQUID back-action noise. This system provides a working prototype for future experiments based on lumped-element resonators with SQUID readout, in particular low-mass axion searches within the DMRadio program.
Aided Active Learning (AAL) for Enhanced Critical Heat Flux Prediction
Accurate prediction of critical heat flux (CHF) is crucial for the safe and efficient operation of nuclear reactors. Traditional CHF modeling methods often require extensive experimental data, which are hard to obtain. This study introduces the Aided Active Learning (AAL) framework, which strategically minimizes data requirements without sacrificing model accuracy. Unlike conventional Active Learning (AL), AAL introduces an additional step of randomly selecting a subset from the sample pool before applying the query strategy. To evaluate the performance of AAL, two query strategies—uncertainty-based sampling and error-reduction sampling—were evaluated across the following models: random forest (RF), feedforward neural network (FNN), and variational feedforward neural network (vFNN). The proposed framework demonstrated that AAL effectively reduces the number of training samples needed to achieve comparable predictive accuracy. For the RF model, AL required only 710 samples to achieve an R2 score of 0.98, as compared to the 4,785 samples needed by random sampling. Similarly, the FNN model achieved the same R2 score with just 355 samples when using AL, a significant improvement over the 825 samples required by random sampling. In case of uncertainty-based sampling strategy, vFNN attained an R2 of 0.98 with 3,420 samples, reducing the sample requirement by 47% relative to the 6,440 samples needed for random sampling. Its performance suggests that larger training data are required to fully leverage its uncertainty quantification capabilities.
Global variation in vegetation carbon use efficiency inferred from eddy covariance observations
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Optimal Bayesian supervised domain adaptation for RNA sequencing data
Abstract Motivation When learning to subtype complex disease based on next-generation sequencing data, the amount of available data is often limited. Recent works have tried to leverage data from other domains to design better predictors in the target domain of interest with varying degrees of success. But they are either limited to the cases requiring the outcome label correspondence across domains or cannot leverage the label information at all. Moreover, the existing methods cannot usually benefit from other information available a priori such as gene interaction networks. Results In this article, we develop a generative optimal Bayesian supervised domain adaptation (OBSDA) model that can integrate RNA sequencing (RNA-Seq) data from different domains along with their labels for improving prediction accuracy in the target domain. Our model can be applied in cases where different domains share the same labels or have different ones. OBSDA is based on a hierarchical Bayesian negative binomial model with parameter factorization, for which the optimal predictor can be derived by marginalization of likelihood over the posterior of the parameters. We first provide an efficient Gibbs sampler for parameter inference in OBSDA. Then, we leverage the gene-gene network prior information and construct an informed and flexible variational family to infer the posterior distributions of model parameters. Comprehensive experiments on real-world RNA-Seq data demonstrate the superior performance of OBSDA, in terms of accuracy in identifying cancer subtypes by utilizing data from different domains. Moreover, we show that by taking advantage of the prior network information we can further improve the performance. Availability and implementation The source code for implementations of OBSDA and SI-OBSDA are available at the following link. https://github.com/SHBLK/BSDA. Supplementary information Supplementary data are available at Bioinformatics online.
Monitoring Seasonal Shear Wave Velocity Changes in the Top 6 m at Garner Valley in Southern California With Borehole Data
Abstract Subsurface structures play important roles in seismic ground motion, crustal hydrology, stability of the built environment, and more. Constraining temporal changes of subsurface shear wave velocity ( V S ) can provide useful information to all these topics and the growing field of hydrological monitoring with seismic velocity. Using borehole records at Garner Valley, CA, we estimate seasonal subsurface V S variations from impulse response functions (IRFs) of earthquake data (2005–2018) along with IRFs and cross‐correlation of cross‐hole experiment data (2015–2018). The inferred V S variations are up to ∼25% in the top 6 m and ∼10% at 2–5 m in depth. The V S variations correlate strongly with the water table depth changes, suggesting that the changes are mostly due to fluctuations of pore pressure in the shallow material. The shallow velocity changes alter the near‐surface conditions, can affect seismic hazard estimation, and may be improperly attributed to deeper processes without careful analysis.
An x-ray penumbral imager for measurements of electron–temperature profiles in inertial confinement fusion implosions at OMEGA
Hot-spot shape and electron temperature (T e ) are key performance metrics used to assess the efficiency of converting shell kinetic energy into hot-spot thermal energy in inertial confinement fusion implosions. X-ray penumbral imaging offers a means to diagnose hot-spot shape and T e , where the latter can be used as a surrogate measure of the ion temperature (T i ) in sufficiently equilibrated hot spots. We have implemented a new x-ray penumbral imager on OMEGA. We demonstrate minimal line-of-sight variations in the inferred T e for a set of implosions. Furthermore, we demonstrate spatially resolved T e measurements with an average uncertainty of 10% with 6 μm spatial resolution.
Soil incubation methods lead to large differences in inferred methane production temperature sensitivity
Abstract Quantifying the temperature sensitivity of methane (CH 4 ) production is crucial for predicting how wetland ecosystems will respond to climate warming. Typically, the temperature sensitivity (often quantified as a Q 10 value) is derived from laboratory incubation studies and then used in biogeochemical models. However, studies report wide variation in incubation-inferred Q 10 values, with a large portion of this variation remaining unexplained. Here we applied observations in a thawing permafrost peatland (Stordalen Mire) and a well-tested process-rich model ( ecosys ) to interpret incubation observations and investigate controls on inferred CH 4 production temperature sensitivity. We developed a field-storage-incubation modeling approach to mimic the full incubation sequence, including field sampling at a particular time in the growing season, refrigerated storage, and laboratory incubation, followed by model evaluation. We found that CH 4 production rates during incubation are regulated by substrate availability and active microbial biomass of key microbial functional groups, which are affected by soil storage duration and temperature. Seasonal variation in substrate availability and active microbial biomass of key microbial functional groups led to strong time-of-sampling impacts on CH 4 production. CH 4 production is higher with less perturbation post-sampling, i.e. shorter storage duration and lower storage temperature. We found a wide range of inferred Q 10 values (1.2–3.5), which we attribute to incubation temperatures, incubation duration, storage duration, and sampling time. We also show that Q 10 values of CH 4 production are controlled by interacting biological, biochemical, and physical processes, which cause the inferred Q 10 values to differ substantially from those of the component processes. Terrestrial ecosystem models that use a constant Q 10 value to represent temperature responses may therefore predict biased soil carbon cycling under future climate scenarios.
Graph link prediction in computer networks using Poisson matrix factorisation
Graph link prediction is an important task in cybersecurity: relationships between entities within a computer network, such as users interacting with computers or system libraries and the corresponding processes that use them, can provide key insights into adversary behaviour. Poisson matrix factorisation (PMF) is a popular model for link prediction in large networks, particularly useful for its scalability. In this article PMF is extended to include scenarios that are commonly encountered in cybersecurity applications. Specifically, an extension is proposed to explicitly handle binary adjacency matrices and include known categorical covariates associated with the graph nodes. A seasonal PMF model is also presented to handle seasonal networks. To allow the methods to scale to large graphs, variational methods are discussed for performing fast inference. The results show an improved performance over the standard PMF model and other statistical network models.
Testing Hidden Assumptions of Representativeness in Reach-Scale Studies of Hyporheic Exchange
Field studies of hyporheic exchange in mountain systems are often conducted using short study reaches and a limited number of observations. It is common practice to assume these study reaches represent hyporheic exchange at larger scales or different sites and to infer general relationships among potential causal mechanisms from the limited number of observations. However, these assumptions of representativeness are rarely tested. In this study, we develop numerical models from four segments of mountain streams in different geomorphologic settings and extract shorter reaches to test how representative exchange metrics are in shorter reaches compared to their reference segments. We also map the locations of the representative reaches to determine if a pattern exists based on location. Finally, we compare variance of these shorter within-site reaches to 29 additional reaches across the same basin to understand the impacts of inferring causal mechanisms, for example, the expectation that wide and narrow valley bottoms will yield different hyporheic exchange patterns. Our results show that the location and length strategy of the study reach must be considered before assuming an exchange metric to be representative of anything other than the exact segment studied. Further, it is necessary to quantify within and between site variations before making causal inferences based on observable characteristics, such as valley width or stream morphology. Our findings have implications for future field practices and how those practices are translated into models.
Can the Rate of a Catalytic Turnover Be Altered by Ligands in the Absence of Direct Binding Interactions?
Second sphere coordination effects ubiquitous in enzymatic catalysis occur through direct interactions, either covalent or non-covalent, with reaction intermediates and transition states. Here, we present herein evidence of indirect second sphere coordination effects in which ligation of water/alkanols far removed from the primary coordination sphere of the active site nevertheless alter energetic landscapes within catalytic redox cycles in the absence of direct physicochemical interactions with surface species mediating catalytic turnovers. Density functional theory, in situ X-ray absorption and infrared spectroscopy, and a wide array of steady-state and transient CO oxidation rate data suggest that the presence of peripheral water renders oxidation half-cycles within two-electron redox cycles over μ m -oxo-bridged trimers in MIL-100(M) more kinetically demanding. Communication between ligated water and the active site appears to occur through the Fe-O-Fe backbone, as inferred from spin density variations on the central μ m -oxygen 'junction'. Evidence is provided for the generality of these second sphere effects in that they influence different types of redox half-cycles or metals, and can be amplified or attenuated through choice of coordinating ligand. Specifically in the case of MIL-100(M) materials, the Cr isostructure can be made to kinetically mimic the Fe variant by disproportionately hindering oxidation half-cycles relative to the reduction half-cycles. Kinetic and spectroscopic inferences presented here significantly expand both the conceptual definition of second sphere effects as well as the palette of synthetic levers available for tuning catalytic redox performance through chemical ligation.
Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach
The finite element method (FEM) is widely used to simulate a variety of physics phenomena. Approaches that integrate FEM with neural networks (NNs) are typically leveraged as an alternative to conducting expensive FEM simulations in order to reduce the computational cost without significantly sacrificing accuracy. However, these methods can produce biased predictions that deviate from those obtained with FEM, since these hybrid FEM-NN approaches rely on approximations trained using physically relevant quantities. In this work, an uncertainty estimation framework is introduced that leverages ensembles of Bayesian neural networks to produce diverse sets of predictions using a hybrid FEM-NN approach that approximates internal forces on a deforming solid body. The uncertainty estimator developed herein reliably infers upper bounds of bias/variance in the predictions for a wide range of interpolation and extrapolation cases using a three-element FEM-NN model of a bar undergoing plastic deformation. This proposed framework offers a powerful tool for assessing the reliability of physics-based surrogate models by establishing uncertainty estimates for predictions spanning a wide range of possible load cases.
A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates
This work develops a new multi delity ensemble Kalman lter (MFEnKF) algorithm based on linear control variate framework. The approach allows for rigorous multi delity extensions of the EnKF, where the uncertainty in coarser delities in the hierarchy of models represent control variates for the uncertainty in ner delities. Small ensembles of high delity model runs are com- plemented by larger ensembles of cheaper, lower delity runs, to obtain much improved analyses at only small additional computational costs. We investigate the use of reduced order models as coarse delity control variates in the MFEnKF, and provide analyses to quantify the improvements over the traditional ensemble Kalman lters. We apply these ideas to perform data assimilation with a quasi-geostrophic test problem, using direct numerical simulation and a corresponding POD-Galerkin reduced order model. Numerical results show that the two- delity MFEnKF provides better analyses than existing EnKF algorithms at comparable or reduced computational costs.
Resource selection functions based on hierarchical generalized additive models provide new insights into individual animal variation and species distributions
Habitat selection studies are designed to generate predictions of species distributions or inference regarding general habitat associations and individual variation in habitat use. Such studies frequently involve either individually indexed locations gathered across limited spatial extents and analyzed using resource selection functions (RSFs) or spatially extensive locational data without individual resolution typically analyzed using species distribution models. Both analytical methodologies have certain desirable features, but analyses that combine individual- and population-level inference with flexible non-linear functions may provide improved predictions while accounting for individual variation. Here, we describe how RSFs can be fit using hierarchical generalized additive models (HGAMs) using widely available software, providing a means to explore individual variation in habitat associations and to generate species distribution maps. We used GPS tracking data from golden eagles Aquila chrysaetos from across eastern North America with four environmental predictors to generate monthly distribution models. We considered three model structures that assumed different amounts of individual variation in the functional relationship between predictors and habitat use and used k-fold cross-validation to compare model performance. Models accounting for individual variability in shape and smoothness of functional responses performed best. Eagles exhibited the least amount of individual variation in response to land cover variables during winter months, with most individuals more closely adhering to the population-level trend. During the summer months, eagles exhibited more substantial individual variation in shape and smoothness of the functional relationships, suggesting some need to account for individual variation in eagle habitat use for both inferential and predictive purposes, during this time of year. Because they allow users to blend flexible functions with random effects structures and are well-supported by a variety of software platforms, we believe that HGAMs provide a useful addition to the suite of analyses used for modeling habitat associations or predicting species distributions.
Measurements of low-mode asymmetries in the areal density of laser-direct-drive deuterium–tritium cryogenic implosions on OMEGA using neutron spectroscopy
Areal density is one of the key parameters that determines the confinement time in inertial confinement fusion experiments, and low-mode asymmetries in the compressed fuel are detrimental to the implosion performance. The energy spectra from the scattering of the primary deuterium–tritium (DT) neutrons off the compressed cold fuel assembly are used to investigate low-mode nonuniformities in direct-drive cryogenic DT implosions at the Omega Laser Facility. For spherically symmetric implosions, the shape of the energy spectrum is primarily determined by the elastic and inelastic scattering cross sections for both neutron-deuterium and neutron-tritium kinematic interactions. Two highly collimated lines of sight, which are positioned at nearly orthogonal locations around the OMEGA target chamber, record the neutron time-of-flight signal in the current mode. An evolutionary algorithm is being used to extract a model-independent energy spectrum of the scattered neutrons from the experimental neutron time-of-flight data and is used to infer the modal spatial variations (l = 1) in the areal density. Experimental observations of the low-mode variations of the cold-fuel assembly (ρL 0 + ρL 1 ) show good agreement with a recently developed model, indicating a departure from the spherical symmetry of the compressed DT fuel assembly. As a result, another key signature that has been observed in the presence of a low-mode variation is the broadening of the kinematic end-point due to the anisotropy of the dense fuel conditions.