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At least 73 records · Page 4

Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques

Here, we study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in terms of number of random inputs and their probability distributions, which can be either known in closed form or provided through samples. We derive novel multifidelity Monte Carlo estimators which rely on a shared subspace between the high-fidelity and low-fidelity models where the parameters follow the same probability distribution, i.e., a standard Gaussian. We build the shared space employing normalizing flows to map different probability distributions into a common one, together with linear and nonlinear dimensionality reduction techniques, active subspaces and autoencoders, respectively, which capture the subspaces where the models vary the most. We then compose the existing low-fidelity model with these transformations and construct modified models with an increased correlation with the high-fidelity model, which therefore yield multifidelity estimators with reduced variance. A series of numerical experiments illustrate the properties and advantages of our approaches.

97 MATHEMATICS AND COMPUTING↗

On the Stability Analysis of Astrophysical Cooling Functions

To model the temperature evolution of optically thin astrophysical environments at MHD scales, radiative and collisional cooling rates are typically either pretabulated or fit into a functional form and then input into MHD codes as a radiative loss function. Thermal balance requires estimates of the analogous heating rates, which are harder to calculate, and due to uncertainties in the underlying dissipative heating processes these rates are often simply parameterized. The resulting net cooling function defines an equilibrium curve that varies with density and temperature. Such cooling functions can make the gas prone to thermal instability (TI), which will cause departures from equilibrium. There has been no systematic study of thermally unstable parameter space for nonequilibrium states. Motivated by our recent finding that there is a related linear instability, catastrophic cooling instability, that can dominate over TI, here we carry out such a study. We show that Balbus instability criteria for TI can be used to define a critical cooling rate, Λ c , that permits a nonequilibrium analysis of cooling functions through the mapping of TI zones. We furthermore illustrate how thermal conduction modifies the shape of TI zones. Upon applying a Λ c -based stability analysis to coronal loop simulations, we find that loops undergoing periodic episodes of coronal rain formation are linearly unstable to catastrophic cooling instability, while TI is stabilized by thermal conduction.

79 ASTRONOMY AND ASTROPHYSICS↗

Data Driven Optimization Framework for Volt-age Regulation in Distribution Systems

This letter proposes a data-driven optimization framework for voltage regulation problems to address the challenge of model inaccuracy and parameter varying. To achieve online voltage optimization, the recursive kernel regression and interior point methods are integrated. The IEEE 123-Bus system and EPRI Ckt5 feeder are selected to validate the effectiveness of the proposed data-driven optimization framework. The proposed method is also compared with a linear function based method.

Hong, Tianqi↗

A Fast, Two-dimensional Gaussian Process Method Based on Celerite: Applications to Transiting Exoplanet Discovery and Characterization

Gaussian processes (GPs) are commonly used as a model of stochastic variability in astrophysical time series. In particular, GPs are frequently employed to account for correlated stellar variability in planetary transit light curves. The efficient application of GPs to light curves containing thousands to tens of thousands of data points has been made possible by recent advances in GP methods, including the celerite method. Here we present an extension of the celerite method to two input dimensions where, typically, the second dimension is small. This method scales linearly with the total number of data points when the noise in each large dimension is proportional to the same celerite kernel and only the amplitude of the correlated noise varies in the second dimension. We demonstrate the application of this method to the problem of measuring precise transit parameters from multiwavelength light curves and show that it has the potential to improve transit parameters measurements by orders of magnitude. Applications of this method include transit spectroscopy and exomoon detection, as well a broader set of astronomical problems.

79 ASTRONOMY AND ASTROPHYSICS↗

Network-Wide Traffic Signal Control Using Bilinear System Modeling and Adaptive Optimization

This study proposes a new multi-input multi-output optimal bilinear signal control method in which a bilinear dynamic model approximation is used to capture the nonlinear dynamics of the urban traffic networks. With signal green time splits as the control input and traffic delay changes as the output for each intersections in the network, a bilinear system model was developed, which, on the basis of linear system modeling, takes interactions among traffic delays and signal timing splits into consideration. Based on the bilinear system modeling framework, we conducted two steps in each time interval to derive traffic control strategies: (1) we used the normalized least-squared algorithm to estimate system parameters; and (2) we solved an online optimization problem to obtain the updated traffic control inputs for the signal timing that minimizes future traffic delays. We evaluated the proposed method in a microscopic traffic simulation environment (VISSIM) with a 35-intersection network of Bellevue city in Washington. Two different traffic demand patterns: (1) normal traffic demands; and (2) time-varying traffic demands were simulated to compare the performance of different control strategies. Experimental results show that (1) the proposed bilinear system model can better describe traffic system dynamics than linear-model based methods, such as our previously developed linear-quadratic regulator control; and (2) the proposed method outperforms the state-of-the-art signal control strategies, namely the max-pressure and the self-organizing traffic light control methods. We have also shown that the proposed method is applicable to all other possible network layouts and signal controller phasing structures.

42 ENGINEERING↗

Dynamically morphing microchannels in liquid crystal elastomer coatings containing disclinations

Liquid crystal elastomers (LCEs) hold a major promise as a versatile material platform for smart soft coatings, since their orientational order can be predesigned to program a desired dynamic profile. In this work, we introduce temperature-responsive dynamic coatings based on LCEs with arrays of singular defects-disclinations that run parallel to the surface. The disclinations form in response to antagonistic patterns of the molecular orientation at the top and bottom surfaces, imposed by the plasmonic mask photoalignment. Upon heating, an initially flat LCE coating develops linear microchannels located above each disclination. The stimulus that causes a non-flat profile of LCE coatings upon heating is the activation force induced by the gradients of molecular orientation around disclinations. To describe the formation of microchannels and their thermal response, we adopt a Frank-Oseen model of disclinations in patterned director field and propose a linear elasticity theory to connect the complex spatially-varying molecular orientation to the displacements of the LCE. The thermo-responsive surface profiles predicted by the theory and by the finite element modeling are in good agreement with the experimental data; in particular, higher gradients of molecular orientation produce a stronger modulation of the coating profile. The elastic theory and the finite element simulations allow us to estimate the material parameter that characterizes the elastomer coating’s response to the thermal activation. The disclinations containing LCEs show potential as soft dynamic coatings with a predesigned responsive surface profile.

36 MATERIALS SCIENCE↗

Large Eddy Simulations of the Atmospheric Boundary Layer Over Satellite‐Sensed Sea Ice Maps

Surface heterogeneity in the marginal ice zone (MIZ) causes multiscale secondary atmospheric circulations that are challenging to model or observe. The absence or inadequate representation of these circulations in ocean‐atmosphere exchange schemes in climate models is partially responsible for the underestimation of Arctic sea ice loss. Observationally, such circulations obfuscate the interpretation of polar atmospheric chemistry measurements, among others. To address this open challenge, large‐eddy simulations are conducted over real‐world satellite‐sensed sea ice maps with an ice‐sea temperature contrast, as well as over idealizations of these maps that alter the ice pattern but conserve its fraction, showing that the ice fraction of a surface is not sufficient to predict the surface heat flux. In a second suite of simulations, three other heterogeneity metrics (representing the surface fragmentation, patch edge tortuosity, and patch size variability) are introduced to complement the ice fraction in describing the surface. Simulations varying these parameters suggest that they also significantly impact surface‐air interactions. A roughness contrast is then added to the surface temperature contrast, indicating that the contribution of roughness changes to the resulting atmospheric circulations is less pronounced than that of thermal heterogeneity. Based on these results, we illustrate, using a multi‐linear regression on these map features, that MIZ surface parameterizations in Earth Systems Models can be improved if they account for these various characteristics of the sea‐ice patterns.

54 ENVIRONMENTAL SCIENCES↗

Models of bars − II. Exponential profiles

ABSTRACT We present a new model for galactic bars with exponentially falling major axis luminosity profiles and Gaussian cross-sections. This is based on the linear superposition of Gaussian potential–density pairs with an exponential weight function, using an extension of the method originally introduced by Long & Murali. We compute the density, potential, and forces, using Gaussian quadrature. These quantities are given as explicit functions of position. There are three independent scaled bar parameters that can be varied continuously to produce bespoke bars of a given mass and shape. We categorize the effective potential by splitting a reduced parameter space into six regions. Unusually, we find bars with three stable Lagrange points on the major axis are possible. Our model reveals a variety of unexpected orbital structure, including a bifurcating x1 orbit coexisting with a stable x4 orbit. Propeller orbits are found to play a dominant role in the orbital structure, and we find striking similarities between our bar configuration and the model of Kaufmann & Contopoulos. We find a candidate orbital family, sired from the propeller orbits, that may be responsible for the observed high-velocity peaks in the Milky Way’s bar. As a cross-check, we inspect, for the first time, the proper motions of stars in the high-velocity peaks, which also match our suggested orbital family well. This work adds to the increasing body of evidence that real galactic bars may be supported at least partly by propeller orbits rather than solely by elliptical-like orbits of the x1 family.

McGough, D. P.↗

Bayesian reduced-order deep learning surrogate model for dynamic systems described by partial differential equations

We propose a reduced-order deep-learning surrogate model for dynamic systems described by time-dependent partial differential equations. This method employs space–time Karhunen–Loève expansions (KLEs) of the state variables and space-dependent KLEs of space-varying parameters to identify the reduced (latent) dimensions. Subsequently, a deep neural network (DNN) is used to map the parameter latent space to the state variable latent space. An approximate Bayesian method is developed for uncertainty quantification (UQ) in the proposed KL-DNN surrogate model. The KL-DNN method is tested for the linear advection–diffusion and nonlinear diffusion equations, and the Bayesian approach for UQ is compared with the deep ensembling (DE) approach, commonly used for quantifying uncertainty in DNN models. It was found that the approximate Bayesian method provides a more informative distribution of the PDE solutions in terms of the coverage of the reference PDE solutions (the percentage of nodes where the reference solution is within the confidence interval predicted by the UQ methods) and log predictive probability. The DE method is found to underestimate uncertainty and introduce bias. For the nonlinear diffusion equation, we compare the KL-DNN method with the Fourier Neural Operator (FNO) method and find that KL-DNN is 10% more accurate and needs less training time than the FNO method.

97 MATHEMATICS AND COMPUTING↗

Process parameters and system responses in friction extrusion

We report friction extrusion is an emerging manufacturing process that imparts improved properties and unique microstructures to materials. In this study, the effects of die features (i.e., the absence or presence of die face scrolling) and process parameters (i.e., die rotational speeds and feed rates) on response variables (e.g., extrusion force, torque, power, and temperature) were investigated. During this work, wires with good integrity and similar geometries were extruded over a range of experimental trials with different rotational speeds and feed rates at a constant extrusion ratio. The extrusion force linearly varies with die advance per revolution, which is the ratio of feed rate and rotational speed. The extrusion energy per kilogram mass of extrudate varies non-linearly and asymptotically such that energy consumption is highest at the lowest feed rate and lowest at the highest feed rate. Additionally relationships among other variables (i.e., die advance per revolution, torque, power heat input, and temperature) also were evaluated to elucidate their interdependences.

42 ENGINEERING↗

Induced Polarization of Clayey Rocks and Soils: Non‐Linear Complex Conductivity Models

Abstract The past decades have witnessed the increased applications of induced polarization (IP) method in the critical zone studies with ubiquitous clay minerals. Although IP outperforms traditional electrical and electromagnetic methods through its unique ability to measure quadrature conductivity, the nonlinearity that quadrature conductivity behaves with salinities and frequencies greatly tortures IP practitioners, as (a) salinity‐dependency makes the quadrature conductivity a varyingly unstable parameter to quantitatively estimate hydraulic properties and clay content; (b) frequency‐dependent Cole‐Cole and Debye/Warburg decomposition models, although mathematically sound, physically mingle the properties of pore water and clay minerals and are empirical in nature. From basic principles, we demonstrate that quadrature conductivity remains a hybrid property involving both clay and water, and develop relevant models to distinguish them. Our models are validated by theories, experiments, simulations, and comparisons, all of which proclaim considerable advantages over previous models and offer the prospect of quantitative applications.

58 GEOSCIENCES↗

Constrained model calibration of grain structure dependent spall dynamics in shock-loaded tantalum

Here, we perform a gas gun experiment by shock loading tantalum samples of varying grain structures to assess the suitability of a numerical model for simulating spall behavior. The observed differences in spall strength, as well spallation and re-compression history, are not captured in uncalibrated hydrodynamic simulations. An optimization is performed on the Johnson spall model to determine the best parameters that fit the observed trends. Linear stability analysis is employed to motivate bounds on those parameters. Herein, optimized simulations agree well with the experimental results, reproducing pullback depth and recompression timescales across the different samples tested. Further, the observed pullback time of the single crystal sample was found to imply, via the stability analysis, a percolation threshold in good agreement with the theoretical value for a body centered cubic lattice. Therefore, the combined linear stability and percolation analysis shows promise and may be applied to other materials with diverse microstructures. Collectively, the findings demonstrate that the model is suitable for reproducing spall-induced free surface behavior across various microstructures, but also points to caution in using model coefficients for uncalibrated microstructures.

58 GEOSCIENCES↗

Closed Loop Geothermal Working Group: GeoCLUSTER App, Subsurface Simulation Results, and Publications

To better understand the heat production, electricity generation performance, and economic viability of closed-loop geothermal systems in hot-dry rock, the Closed-Loop Geothermal Working Group -- a consortium of several national labs and academic institutions has tabulated time-dependent numerical solutions and levelized cost results of two popular closed-loop heat exchanger designs (u-tube and co-axial). The heat exchanger designs were evaluated for two working fluids (water and supercritical CO2) while varying seven continuous independent parameters of interest (mass flow rate, vertical depth, horizontal extent, borehole diameter, formation gradient, formation conductivity, and injection temperature). The corresponding numerical solutions (approximately 1.2 million per heat exchanger design) are stored as multi-dimensional HDF5 datasets and can be queried at off-grid points using multi-dimensional linear interpolation. A Python script was developed to query this database and estimate time-dependent electricity generation using an organic Rankine cycle (for water) or direct turbine expansion cycle (for CO2) and perform a cost assessment. This document aims to give an overview of the HDF5 database file and highlights how to read, visualize, and query quantities of interest (e.g., levelized cost of electricity, levelized cost of heat) using the accompanying Python scripts. Details regarding the capital, operation, and maintenance and levelized cost calculation using the techno-economic analysis script are provided. This data submission will contain results from the Closed Loop Geothermal Working Group study that are within the public domain, including publications, simulation results, databases, and computer codes. GeoCLUSTER is a Python-based web application created using Dash, an open-source framework built on top of Flask that streamlines the building of data dashboards. GeoCLUSTER provides users with a collection of interactive methods for streamlining the exploration and visualization of an HDF5 dataset. The GeoCluster app and database are contained in the compressed file geocluster_vx.zip, where the "x" refers to the version number. For example, geocluster_v1.zip is Version 1 of the app. This zip file also contains installation instructions. **To use the GeoCLUSTER app in the cloud, click the link to "GeoCLUSTER on AWS" in the Resources section below. To use the GeoCLUSTER app locally, download the geocluster_vx.zip to your computer and uncompress this file. When uncompressed this file comprises two directories and the geocluster_installation.pdf file. The geo-data app contains the HDF5 database in condensed format, and the GeoCLUSTER directory contains the GeoCLUSTER app in the subdirectory dash_app, as app.py. The geocluster_installation.pdf file provides instructions on installing Python, the needed Python modules, and then executing the app.

15 GEOTHERMAL ENERGY↗

Tabulated Database of Closed-Loop Geothermal Systems Performance for Cloud-Based Technical and Economic Modeling of Heat Production and Electricity Generation: Preprint

To better understand the heat production, electricity generation performance and economic viability of closed loop geothermal systems in hot-dry-rock, the Closed Loop Geothermal Group, a consortium of several national labs and academic institutions has tabulated time-dependent numerical solutions and levelized cost results of two popular closed loop heat exchanger designs (u-tube and co-axial). The heat exchanger designs were evaluated for two working fluids (water and super-critical CO2) while varying seven continuous independent parameters of interest (i.e., mass flow rate, vertical depth, horizontal extent, borehole diameter, formation gradient, formation conductivity, and injection temperature). The corresponding numerical solutions (approximately 1.2 million per heat exchanger design) are stored as multi-dimensional HDF5 datasets and can be queried at off-grid points using multi-dimensional linear interpolation. A Python script was developed to query this database and estimate time-dependent electricity generation using an Organic Rankine cycle (for water) or direct turbine expansion cycle (for CO2) and perform a cost assessment. This document aims to give an overview of the HDF5 database file and highlights how to read, visualize, and query quantities of interest (e.g., levelized cost of electricity, levelized cost of heat) using the accompanying python scripts. Details regarding the capital, operation, and maintenance and levelized cost calculation using the TEA (techno-economic analysis) script are provided.

co-axial↗

The Q 10 of in situ microbial soil respiration varies with mean annual temperature, precipitation, pH, and plant cover: a meta-analysis and spatial prediction of Q 10

The temperature sensitivity of soil microbial respiration, commonly quantified using the Q 10 coefficient, is a key parameter in carbon cycle models. Uncovering how environmental factors affect in situ Q 10 values can therefore provide critical insight into potential shifts in global carbon stocks under climate change. We collected data from previously published field experiments that measured soil microbial respiration across a range of temperatures. We hypothesized that the Q 10 coefficient of in situ soil microbial respiration would vary based on environmental factors including mean annual temperature (MAT), mean annual precipitation (MAP), plant cover type, pH, soil C:N, and latitude. Linear regression revealed that Q 10 correlates negatively with MAT and MAP and positively with pH and absolute latitude. Additionally, average Q 10 varied significantly across different plant cover types; it was highest in mountain grasslands and lowest in tropical moist forests. Variation in microbial Q 10 across environmental factors may arise from underlying mechanisms such as enzyme kinetics, substrate availability and complexity, and microbial adaptation. To capture patterns in Q 10 more comprehensively, we developed a multiple linear regression model of Q 10 based on the most individually significant environmental drivers and applied it to public datasets to generate a global map of predicted Q 10 . Q 10 was higher in high-latitude and high-altitude regions, where large permafrost carbon stores are vulnerable to thawing and decomposition. We also compared fits between the Q 10 equation and a model produced from macromolecular rate theory (MMRT). We found that the MMRT model had the superior fit and may be better suited to model temperature sensitivity of complex biological reactions. Overall, our results emphasize that relationships between microbial Q 10 and environmental variables should be accounted for in climate models. Incorporating these variations in the Q 10 parameter, rather than using a fixed value, will help predict whether CO 2 emissions will be buffered or exacerbated by soil microbial respiration under climate change.

54 ENVIRONMENTAL SCIENCES↗

Flow and Arching of Biomass Particles in Wedge-Shaped Hoppers

Poor understanding of the flow behavior of granular biomass material poses great challenges for the bioenergy industry, as the equipment functioning time is significantly reduced by handling issues like screw feeder clogging and hopper arching. In this work, the flow behavior of loblolly pine chips, including the mass flow rate and the critical outlet width, in a wedge-shaped hopper is investigated by combining physical experiments and numerical simulations. Comprehensive characterization of the flow response affected by the two material attributes (initial packing, particle density) and the three operational parameters (hopper outlet width, hopper inclination, and surcharge) is conducted. The results show that the hopper outlet width linearly controls the mass flow rate while the hopper inclination angle controls the critical outlet size. The packing determines whether the flow is smooth or surging, and the surcharge-induced compaction creates flow impedance. The magnitude of these influences varies from a slender hopper with a low inclination angle to a flat-bottom silo. These findings provide guidance for hopper operation in the material handling industry and shed light on the construction of a novel design method for material handling equipment in biorefineries.

09 BIOMASS FUELS↗

Multi-objective optimization of peel and shear strengths in ultrasonic metal welding using machine learning-based response surface methodology

Ultrasonic metal welding (UMW) is a solid-state joining technique with varied industrial applications. Despite of its numerous advantages, UMW has a relative narrow operating window and is sensitive to variations in process conditions. As such, it is imperative to quantitatively characterize the influence of welding parameters on the resulting joint quality. The quantification model can be subsequently used to optimize the parameters. Conventional response surface methodology (RSM) usually employs linear or polynomial models, which may not be able to capture the intricate, nonlinear input-output relationships in UMW. Furthermore, some UMW applications call for simultaneous optimization of multiple quality indices such as peel strength, shear strength, electrical conductivity, and thermal conductivity. To address these challenges, this paper develops a machine learning (ML)-based RSM to model the input-output relationships in UMW and jointly optimize two quality indices, namely, peel and shear strengths. The performance of various ML methods including spline regression, Gaussian process regression (GPR), support vector regression (SVR), and conventional polynomial regression models with different orders is compared. A case study using experimental data shows that GPR with radial basis function (RBF) kernel and SVR with RBF kernel achieve the best prediction accuracy. The obtained response surface models are then used to optimize a compound joint strength indicator that is defined as the average of normalized shear and peel strengths. In addition, the case study reveals different patterns in the response surfaces of shear and peel strengths, which has not been systematically studied in the literature. While developed for the UMW application, the method can be extended to other manufacturing processes.

42 ENGINEERING↗

Comparing the influence of cation order and composition in simulated Zn(Sn, Ge)N 2 on structure, elastic moduli, and polarization for solid state lighting

Alloying and site ordering play complementary roles in dictating a material’s properties. However, deconvolving the impacts of these separate phenomena can be challenging. In this work, we simulate structures of Zn(Sn,Ge)N 2 with varied Sn content and site ordering to determine the impacts of order and composition on structural and electronic properties. We assess the formation enthalpy, lattice parameters, elastic constants, spontaneous polarization, and piezoelectric coefficients. In mostly disordered structures (order parameters ranging from 0.2 to 0.4), the formation enthalpy exhibits local extrema as a function of the order parameter, deviating from the more linear trends seen in both fully disordered and fully ordered systems. This anomalous deviation from the otherwise linear trend in formation enthalpy with order manifests in each of the other properties calculated. This range of order parameters of interest may be caused by a transition in the ordering of the quaternary material similar to phase changes seen in ternary compounds but stretched over a region inclduing 20% of the order parameter range. Most parameters calculated are more sensitive to order than to composition in the limited composition range tested; however, the lattice parameter c, piezoelectric coefficient e 33 , and elastic moduli C 12 , C 13 , and C 23 are more sensitive to composition. Of the properties compared, the piezoelectric coefficients are influenced most significantly by changes in both the composition and order parameter. Lattice parameters undergo the smallest changes with order and composition, but these small differences appear to impart large trends in the other properties. Better understanding the effects of disorder and group IV alloying in Zn(Sn,Ge)N 2 allows for more accurate modeling of characteristics of this material system for solid state lighting and other applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗