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DOE OSTI2021

A Nonstationary and Non-Gaussian Moving Average Model for Solar Irradiance

Historically, power has flowed from large power plants to customers. Increasing penetration of distributed energy resources such as solar power from rooftop photovoltaic has made the distribution network a two-way-street with power being generated at the customer level. The incorporation of renewables introduces additional uncertainty and variability into the power grid. Distribution network operation studies are being adapted to include renewables; however, such studies require high quality solar irradiance data that adequately reflect realistic meteorological variability. Data from satellite-based products are spatially complete, but temporally coarse, whereas solar irradiances exhibit high frequency variation at very fine timescales. We propose a new stochastic method for temporally downscaling global horizontal irradiance (GHI) to 1 min resolution, but we do not consider the spatial aspect due to limited availability of the in situ irradiance measurements. Solar irradiance's first and second-order structures vary diurnally and seasonally, and our model adapts to such nonstationarity. Empirical irradiance data exhibits highly non-Gaussian behavior; we develop a nonstationary and non-Gaussian moving average model that is shown to capture realistic solar variability at multiple timescales. We also propose a new estimation scheme based on Cholesky factors of empirical autocovariance matrices, bypassing difficult and inaccessible likelihood-based approaches. The model is demonstrated for a case study of three locations that are located in diverse climates through the United States. The model is compared against competitors from the literature and is shown to provide better uncertainty and variability quantification on testing data.

Cholesky factor↗

DOE OSTI2024

Predicting responses to climate change using a joint species, spatially dependent physiologically guided abundance model

Abstract Predicting the effects of warming temperatures on the abundance and distribution of organisms under future climate scenarios often requires extrapolating species–environment correlations to climatic conditions not currently experienced by a species, which can result in unrealistic predictions. For poikilotherms, incorporating species' thermal physiology to inform extrapolations under novel thermal conditions can result in more realistic predictions. Furthermore, models that incorporate species and spatial dependencies may improve predictions by capturing correlations present in ecological data that are not accounted for by predictor variables. Here, we present a joint species, spatially dependent physiologically guided abundance (jsPGA) model for predicting multispecies responses to climate warming. The jsPGA model uses a basis function approach to capture both species and spatial dependencies. We apply the jsPGA model to predict the response of eight fish species to projected climate warming in thousands of lakes in Minnesota, USA. By the end of the century, the cold‐adapted species was predicted to have high probabilities of extirpation across its current range—with 10% of lakes currently inhabited by this species having an extirpation probability >0.90. The remaining species had varying levels of predicted changes in abundance, reflecting differences in their thermal physiology. Though the model did not identify many strong species dependencies, the variation in estimated spatial dependence across species suggested that accounting for both dependencies was important for predicting the abundance of these fishes. The jsPGA model provides a new tool for predicting changes in the abundance, distribution, and extirpation probability of poikilotherms under novel thermal conditions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Convective Momentum Transport and Its Impact on the Madden‐Julian Oscillation in E3SM‐MMF

Abstract Convective momentum transport (CMT) is the process of vertical redistribution of horizontal momentum by small‐scale turbulent flows from moist convection. Traditional general circulation models (GCMs) and their multiscale modeling framework (MMF) versions poorly represent CMT due to insufficient information of subgrid‐scale flows at each GCM grid. Here the explicit scalar momentum transport (ESMT) scheme for representing CMT is implemented in the Energy Exascale Earth System Model‐Multiscale Modeling Framework (E3SM‐MMF) with embedded 2‐D cloud‐resolving models (CRMs), and verified against E3SM‐MMF simulations with 3‐D CRMs and observations. The results show that representing CMT by ESMT helps reduce climatological mean precipitation model bias over the western Pacific and the ITCZ regions, which is attributed to the weakened mean easterlies over the Pacific. Also, CMT from simulations with 2‐D and 3‐D CRMs impose a similar impact on Kelvin waves by reducing their variability and slowing down their phase speed, but opposite impacts on the Madden‐Julian Oscillation (MJO) variability. The ESMT scheme readily captures the climatological mean spatial patterns of the zonal and meridional components of CMT and their variability across multiple time scales, but shows some differences in estimating its magnitude. CMT mainly affects the MJO by decelerating its winds in the free troposphere, but accelerates its near‐surface winds. This study serves as a prototype for implementing CMT scheme in the MMF simulations, highlighting its crucial role in reducing model bias in mean state and spatiotemporal variability.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Gaussian process analysis of electron energy loss spectroscopy data: multivariate reconstruction and kernel control

Abstract Advances in hyperspectral imaging including electron energy loss spectroscopy bring forth the challenges of exploratory and physics-based analysis of multidimensional data sets. The multivariate linear unmixing methods generally explore similarities in the energy dimension, but ignore correlations in the spatial domain. At the same time, Gaussian process (GP) explicitly incorporate spatial correlations in the form of kernel functions but is computationally intensive. Here, we implement a GP method operating on the full spatial domain and reduced representations in the energy domain. In this multivariate GP, the information between the components is shared via a common spatial kernel structure, while allowing for variability in the relative noise magnitude or image morphology. We explore the role of kernel constraints on the quality of the reconstruction, and suggest an approach for estimating them from the experimental data. We further show that spatial information contained in higher-order components can be reconstructed and spatially localized.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Nth-plant supply: corn stover supplies and costs in a fleet of biorefineries

Feedstock cost and cost variability is expected to increase with the number of biorefineries. To quantify this effect, this spatial-economic analysis simulates feedstock cost and cost variability of an industry based on corn stover as a function of the number of biorefineries. Results are reported for nine scenarios (a base case and sensitivity analysis of four variables – harvest efficiency, sustainability constraints, opportunity cost, and corn grain yield) under deterministic and stochastic simulations, assuming biorefineries using 658 000 Mg (725 000 tons) year- 1 of corn stover in 2019. The resulting supply curves are highly elastic (i.e. little change in cost) for the first 50 of the 121 biorefineries, with price increases in subsequent biorefineries depending on scenario. In the base-case deterministic scenario, weighted-average stover costs are $66 Mg -1 ($60 ton- 1 ), $69 Mg -1 ($62 ton -1 ), and $156 Mg -1 ($142 ton -1 ), at the first, 60th, and 121st biorefineries, respectively. The stochastic simulations, subject to observed 30-year corn yield variability, follow a similar pattern, with price distributions that vary by scenario. The base-case stochastic simulations illustrate minimal cost variability for the first 60 biorefineries, but rapid increases in cost variability in the second half of potential biorefineries, with similar patterns observed in the other scenarios. Of the four variables explored, price was most sensitive to harvest efficiency, followed by sustainability constraints, corn yield, and opportunity cost. Results suggest that, under conventional logistics, about half of the US corn stover resource is reliably available with minimum cost increase and variability. Interactive visualization is available at https://doi.org/10.11578/1828779.

09 BIOMASS FUELS↗

DOE OSTI2022

Increased signal-to-noise ratios within experimental field trials by regressing spatially distributed soil properties as principal components

Environmental variability poses a major challenge to any field study. Researchers attempt to mitigate this challenge through replication. Thus, the ability to detect experimental signals is determined by the degree of replication and the amount of environmental variation, noise, within the experimental system. A major source of noise in field studies comes from the natural heterogeneity of soil properties which create microtreatments throughout the field. In addition, the variation within different soil properties is often nonrandomly distributed across a field. We explore this challenge through a sorghum field trial dataset with accompanying plant, microbiome, and soil property data. Diverse sorghum genotypes and two watering regimes were applied in a split-plot design. We describe a process of identifying, estimating, and controlling for the effects of spatially distributed soil properties on plant traits and microbial communities using minimal degrees of freedom. Importantly, this process provides a method with which sources of environmental variation in field data can be identified and adjusted, improving our ability to resolve effects of interest and to quantify subtle phenotypes.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2022

Standoff Infrared Measurements of Chemical Plume Dynamics in Complex Terrain Using a Combination of Active Swept-ECQCL Laser Spectroscopy with Passive Hyperspectral Imaging

Chemical plume detection and modeling in complex terrain present numerous challenges. We present experimental results from outdoor releases of two chemical tracers (sulfur hexafluoride and Freon-152a) from different locations in mountainous terrain. Chemical plumes were detected using two standoff instruments collocated at a distance of 1.5 km from the plume releases. A passive long-wave infrared hyperspectral imaging system was used to show time- and space-resolved plume transport in regions near the source. An active infrared swept-wavelength external cavity quantum cascade laser system was used in a standoff configuration to measure quantitative chemical column densities with high time resolution and high sensitivity along a single measurement path. Both instruments provided chemical-specific detection of the plumes and provided complementary information over different temporal and spatial scales. The results show highly variable plume propagation dynamics near the release points, strongly dependent on the local topography and winds. Effects of plume stagnation, plume splitting, and plume mixing were all observed and are explained based on local topographic and wind conditions. Measured plume column densities at distances ~100 m from the release point show temporal fluctuations over ~1 s time scales and spatial variations over ~1 m length scales. The results highlight the need for high-speed and spatially resolved measurement techniques to provide validation data at the relevant spatial and temporal scales required for high-fidelity terrain-aware microscale plume propagation models.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

On the Emergence of Human Influence on Surface Air Temperature Changes Over India

Human activities in terms of greenhouse gas (GHG) emissions and aerosols resulting from the combustion of fossil fuels have been shown to have affected the temperature of the Earth on global and continental scales. The surface air temperature (TAS) over India has also been observed to be increasing over the last 100 years. Understanding the underlying causes of regional climate change over India can help in developing appropriate mitigation and adaptation strategies. Differentiating signals of externally forced climate changes from the noise of natural internal variability generally becomes more difficult as spatial scale reduces. Therefore detecting and attributing the influence of external forcings such as GHGs and aerosols is harder at local and regional scales. In this study, we applied a detection and attribution (D&A) method to study annual and seasonal mean TAS over the Indian region. We found that the observed warming over India from 1906 to 2005 cannot be explained by natural climate variability alone. We found that the warming is largely driven by the increase in GHGs, and partially offset by regional anthropogenic emissions of aerosols. These results were confirmed for the shorter 1956–2005 period, but results were sensitive to the choice of observational data set. Furthermore, the changes cannot be explained by internal climate variability or natural external forcings alone, but are compatible with the responses to combined anthropogenic GHG and aerosol forcings.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Spatially resolved polarization swings in the supermassive binary black hole candidate OJ 287 with first Event Horizon Telescope observations

We present the first Event Horizon Telescope 1.3 mm observations of the supermassive binary black hole candidate OJ 287. The observations achieved an unprecedented angular resolution of 18 μas and reveal significant structural and polarization variability over just five days, marking the shortest timescale on which such changes have been directly imaged in this source. The inner jet exhibits a twisted ridgeline structure, with features displaying apparent superluminal motions up to about 22 c. The linear polarization maps reveal three main polarized features whose electric-vector position angles (EVPAs) change substantially over the time span of our observations, including a component with a radial polarization consistent with being produced by a recollimation shock. Most notably, we directly resolved two innermost jet components whose EVPAs rotate in opposite directions. The faster component, moving at 2.4 ± 0.9 μas/day (17.4 ± 6.5 c), exhibits counterclockwise EVPA swings of roughly 3.7° per day, while the slower component, with a proper motion of 1.4 ± 0.3 μas/day (10.2 ± 2.2 c), rotates clockwise at approximately 2.5° per day. Previous studies inferred helical magnetic fields in AGN jets from time-resolved or integrated polarization variability but lacked the angular resolution to directly image this effect. Our results provide spatially resolved evidence that a helical magnetic field threads the jet’s collimation and acceleration zone, ruling out models based on the superposition of unresolved components. Our analysis suggests that propagating shocks interact with a Kelvin–Helmholtz plasma instability, illuminating different phases of the helical magnetic field and producing the observed polarization spatial and temporal variability. Moreover, our model naturally accounts for the more rapid polarization rotation observed in the faster moving component. Our model predicts even more rapid swings in polarization, which could be tested with future observations featuring a more densely sampled time coverage.

OJ 287↗

DOE OSTI2026

Dynamical Downscaling of Earth System Model Data for Energy System Analysis

Assessing energy resources (e.g., solar, wind, and hydro) under future scenarios requires datasets with sufficient spatial and temporal detail to capture variability and extreme events. While global-scale Earth System Model (ESM) projections are widely used, their coarse resolution limits direct application to regional energy system analyses. Dynamical downscaling offers a robust approach to generate physically consistent, fine-scale datasets that better represent local atmospheric processes impacting energy resources. In this work, we present a two-stage approach for producing high-resolution historical and future projections over the contiguous United States (CONUS). First, we optimize the Weather Research and Forecasting (WRF) model configuration for energy-relevant variables - solar irradiance, wind speed, and precipitation - by conducting ERA5-driven simulations at 8-km and 28-km resolution. Multiple physics schemes and model configurations within the WRF are evaluated against observational datasets including the National Solar Radiation Database (NSRDB), the Parameter-elevation Regressions on Independent Slopes Model (PRISM), and the Stage IV multi-radar/multi-sensor precipitation product for the CONUS domain. Using the best-performing configuration, we dynamically downscale MPI-ESM1-2-HR simulations for 2000-2060 under SSP2-4.5 and SSP5-8.5 scenarios at 4-km spatial and hourly temporal resolution. This presentation will provide a comprehensive analysis of the results from multiple numerical experiments and high-resolution ESM projections. In addition, we will discuss potential applications of our high-resolution datasets within the energy sector and outline future research avenues dedicated to evaluating how extreme weather events influence system performance and resilience.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics

Standard approaches for uncertainty quantification in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic three-dimensional simulations. Here, we propose an efficient uncertainty quantification framework utilizing a multilevel multifidelity Monte Carlo (MLMF) estimator to improve the accuracy of hemodynamic quantities of interest while maintaining reasonable computational cost. This is achieved by leveraging three cardiovascular model fidelities, each with varying spatial resolution to rigorously quantify the variability in hemodynamic outputs. We employ two low-fidelity models (zero- and one-dimensional) to construct several different estimators. Our goal is to investigate and compare the efficiency of estimators built from combinations of these two low-fidelity model alternatives and our high-fidelity three-dimensional models. We demonstrate this framework on healthy and diseased models of aortic and coronary anatomy, including uncertainties in material property and boundary condition parameters. Our goal is to demonstrate that for this application it is possible to accelerate the convergence of the estimators by utilizing a MLMF paradigm. Therefore, we compare our approach to single fidelity Monte Carlo estimators and to a multilevel Monte Carlo approach based only on three-dimensional simulations, but leveraging multiple spatial resolutions. We demonstrate significant, on the order of 10 to 100 times, reduction in total computational cost with the MLMF estimators. We also examine the differing properties of the MLMF estimators in healthy versus diseased models, as well as global versus local quantities of interest. As expected, global quantities such as outlet pressure and flow show larger reductions than local quantities, such as those relating to wall shear stress, as the latter rely more heavily on the highest fidelity model evaluations. Similarly, healthy models show larger reductions than diseased models. In all cases, our workflow coupling Dakota’s MLMF estimators with the SimVascular cardiovascular modeling framework makes uncertainty quantification feasible for constrained computational budgets.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Quantifying the influence of natural climate variability on in situ measurements of seasonal total and extreme daily precipitation

Abstract While various studies explore the relationship between individual sources of climate variability and extreme precipitation, there is a need for improved understanding of how these physical phenomena simultaneously influence precipitation in the observational record across the contiguous United States. In this work, we introduce a single framework for characterizing the historical signal (anthropogenic forcing) and noise (natural variability) in seasonal mean and extreme precipitation. An important aspect of our analysis is that we simultaneously isolate the individual effects of seven modes of variability while explicitly controlling for joint inter-mode relationships. Our method utilizes a spatial statistical component that uses in situ measurements to resolve relationships to their native scales; furthermore, we use a data-driven procedure to robustly determine statistical significance. In Part I of this work we focus on natural climate variability: detection is mostly limited to DJF and SON for the modes of variability considered, with the El Niño/Southern Oscillation, the Pacific–North American pattern, and the North Atlantic Oscillation exhibiting the largest influence. Across all climate indices considered, the signals are larger and can be detected more clearly for seasonal total versus extreme precipitation. We are able to detect at least some significant relationships in all seasons in spite of extremely large (> 95%) background variability in both mean and extreme precipitation. Furthermore, we specifically quantify how the spatial aspect of our analysis reduces uncertainty and increases detection of statistical significance while also discovering results that quantify the complex interconnected relationships between climate drivers and seasonal precipitation.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Controlling matric potential in microfluidics to examine microbial dynamics in unsaturated porous media

The use of microfluidics for the study of soil microbial ecology is an emerging field. Most microfluidic studies of biological systems, however, have been performed under fully saturated conditions that are not representative of natural soil. Therefore, while microfluidics offer many unique capabilities that other methodologies cannot, they are not currently suited to address the effects of matric potential, an important variable defining the microbial moisture niche. Here, a methodology is presented that allows the user to control the aqueous conditions within microfluidic networks by manipulating matric potential using a hanging water column. The method relies on hydrophilic surface treatment of the microfluidic device using polyvinyl alcohol (PVA) and incorporating a bed of small pores at the network boundaries, which serve as a porous ceramic plate analogue (PPA). The method was validated on a simple capillary bundle and then on a more complex pore network. A water retention curve, exhibiting hysteresis, was generated for the pore network over a narrow matric potential range of 0 to – 5 kPa. Both the drainage and wetting curves were reproducible, as were the spatial configuration and the number of fragmented moisture niches in the pore network, particularly on the drainage curve. In contrast, the wetting curve exhibited greater variability in spatial configuration due to the “ink bottle effect,” where capillarity was interrupted by wider pore bodies. Ultimately, the methodology provides realistic pore-scale moisture conditions that can be easily manipulated and maintained, enabling new opportunities to explore soil biophysics and microbial biogeography in unsaturated porous media. As a brief example, images showing the localization of fluorescently tagged Pantoea sp. YR343 at −4.3 kPa are presented, highlighting bacterial distributions in water films and air-water interfaces.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

A general spatial-temporal framework for short-term building temperature forecasting at arbitrary locations with crowdsourcing weather data

Weather forecasting has been a critical component to predict and control building energy consumption for better building energy management. Without accessibility to other data sources, the onsite observed temperatures or the airport temperatures are used in forecast models. In this paper, we present a novel approach by utilizing the crowdsourcing weather data from neighboring personal weather stations (PWS) to improve the weather forecast accuracy around buildings using a general spatial-temporal modeling framework. The final forecast is based on the ensemble of local forecasts for the target location using neighboring PWSs. Our approach is distinguished from existing literature in various aspects. First, we leverage the crowdsourcing weather data from PWS in addition to public data sources. In this way, the data is at much finer time resolution (e.g., at 5-minute frequency) and spatial resolution (e.g., arbitrary location vs grid). Second, our proposed model incorporates spatial-temporal correlation information of weather variables between the target building and a set of neighboring PWSs so that underlying correlations can be effectively captured to improve forecasting performance. Here, we demonstrate the performance of the proposed framework by comparing to the benchmark models on temperature forecasting for a building located at an arbitrary location at San Antonio, Texas, USA. In general, the proposed model framework equipped with machine learning technique such as Random Forest can improve forecasting by 50% compares with persistent model and has 90% chance to outperform airport forecast in short-term forecasting. In a real-time setting, the proposed model framework can provide more accurate temperature forecasting results compared with using airport temperature forecast for most forecast horizon. Moreover, we analyze the sensitivity of model parameters to gain insights on how crowdsourcing data from the neighboring personal weather stations impacts forecasting performance. Finally, we implement our model in other cities such as Syracuse and Chicago to test the model's performance in different landforms and climate types.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Nitrogen fixation rates in the Guinea Dome and the equatorial upwelling regions in the Atlantic Ocean

Abstract Biological nitrogen fixation is a key process balancing the loss of combined nitrogen in the marine nitrogen cycle. Its relevance in upwelling or high nutrient regions is still unclear, with the few available studies in these regions of the ocean reporting rates that vary widely from below detection limit to > 100 nmol N L −1 d −1 . In the eastern tropical Atlantic Ocean, two open ocean upwelling systems are active in boreal summer. One is the seasonal equatorial upwelling, where the residual phosphorus associated with aged upwelled waters is suggested to enhance nitrogen fixation in this season. The other is the Guinea Dome, a thermal upwelling dome. We conducted two surveys along 23° W across the Guinea Dome and the Equator from 15° N to 5° S in September 2015 and August–September 2016 with high latitudinal resolution (20–60 nm between stations). The abundance of Trichodesmium colonies was characterized by an Underwater Vision Profiler 5 and the total biological nitrogen fixation in the euphotic layer was measured using the 15 N 2 technique. The highest abundances of Trichodesmium colonies were found in the area of the Guinea Dome (9°–15° N) with a maximum of 3 colonies L −1 near the surface. By contrast, colonies were almost absent in the Equatorial band between 2° N and 5° S. The highest nitrogen fixation rate was measured at the northern edge of the Guinea Dome in 2016 (ca. 31 nmol N L −1 d −1 ). In this region, where diazotrophs thrived on a sufficient supply of both phosphorus and iron, a patchy distribution was unveiled by our increased spatial resolution scheme. In the Equatorial band, rates were considerably lower, ranging from below detection limit to ca. 4 nmol N L −1 d −1 , with a clear difference in magnitude between 2015 (rates close to zero) and 2016 (average rates around 2 nmol N L −1 d −1 ). This difference seemed triggered by a contrasting supply of phosphorus between years. Our study stresses the importance of surveys with sampling at fine-scale spatial resolution, and shows unexpected high variability in the rates of nitrogen fixation in the Guinea Dome, a region where diazotrophy is a significant process supplying new nitrogen into the euphotic layer.

Fernández-Carrera, Ana (ORCID:0000000183470996)↗

DOE OSTI2024

A multi-objective optimization model for cropland design considering profit, biodiversity, and ecosystem services

More sustainable agricultural methods are needed to alleviate the decreases in biodiversity and ecosystem services that have occurred because of industrial agriculture. One such method is the inclusion of alternative crops into croplands that can support biodiversity, reduce erosion and chemical runoff, and sequester carbon in the soil. However, the question of where such crops should be planted to balance competing economic and environmental objectives remains open. To this end, we develop a mixed-integer quadratically constrained program to optimize the layout of a cropland considering economic, biodiversity, greenhouse gas emissions, and water quality objectives. We include spatially varying fertilization as a decision variable in addition to crop establishment location. We further include the effect of core area and edges between different crops on biodiversity. To demonstrate the applicability of the model, we apply it to an example field, showing how the optimal cropland design changes as a decision-maker prioritizes different objectives and as edges have different impacts on biodiversity.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

System-of-systems optimization of hydrogen infrastructure for heavy-duty freight corridors: The interstate 10 case study

Medium and heavy-duty freight transportation requires hydrogen energy infrastructure that is cost-effective, operationally reliable, spatially coherent, and resilient to demand variability along major corridors. This paper presents an integrated hydrogen corridor planning framework using Oak Ridge National Laboratory's OR-AGENT that couples freight-driven, route-resolved hydrogen demand modeling with optimized station siting, sizing, and station-level techno-economic analysis. The framework is demonstrated for the Interstate 10 freight corridor and the Houston-to-Los-Angeles region. Hydrogen demand is derived from high-resolution origin–destination freight data, duty-cycle characterization, and physics-based energy consumption modeling. Candidate refueling sites are selected from existing heavy-duty diesel fueling locations and optimized subject to onboard storage and station capacity constraints. Resulting station throughputs are evaluated using established techno-economic models for electrolytic hydrogen production and dispensing infrastructure. Results show that a regional, portfolio-level aggregation, average dispensed electrolytic hydrogen cost of $6.87–$7.26/kg is currently feasible, and is strongly influenced by demand density and utilization.

Sujan, Vivek [ORNL] (ORCID:0000000269882342)↗

DOE OSTI2021

Optimal design of acoustic metamaterial cloaks under uncertainty

In this work, we consider the problem of optimal design of an acoustic cloak under uncertainty and develop scalable approximation and optimization methods to solve this problem. The design variable is taken as an infinite-dimensional spatially-varying field that represents the material property, while an additive infinite-dimensional random field represents the variability of the material property or the manufacturing error. Discretization of this optimal design problem results in high-dimensional design variables and uncertain parameters. To solve this problem, we develop a computational approach based on a Taylor approximation and an approximate Newton method for optimization, which is based on a Hessian derived at the mean of the random field. We show our approach is scalable with respect to the dimension of both the design variables and uncertain parameters, in the sense that the necessary number of acoustic wave propagations is essentially independent of these dimensions, for numerical experiments with up to one million design variables and half a million uncertain parameters. Additionally, we demonstrate that, using our computational approach, an optimal design of the acoustic cloak that is robust to material uncertainty is achieved in a tractable manner. The optimal design under uncertainty problem is posed and solved for the classical circular obstacle surrounded by a ring-shaped cloaking region, subjected to both a single-direction single-frequency incident wave and multiple-direction multiple-frequency incident waves. Finally, we apply the method to a deterministic large-scale optimal cloaking problem with complex geometry, to demonstrate that the approximate Newton method’s Hessian computation is viable for large, complex problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗