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DOE OSTI2022

IMPROVING THE ACCURACY OF COMPOSITE METHODS: A G4MP2 METHOD WITH G4-LIKE ACCURACY AND IMPLICATIONS FOR MACHINE LEARNING

G4MP2 theory has proven to be a reliable and accurate quantum chemical composite method for the calculation of molecular energies using an approximation based on second-order perturbation theory to lower computational costs compared to G4 theory. However, it has been found to have significantly increased errors when applied to larger organic molecules with 10 or more nonhydrogen atoms. We report here on an investigation of the cause of the failure of G4MP2 theory for such larger molecules. One source of error is found to be the "higher-level correction (HLC)", which is meant to correct for deficiencies in correlation contributions to the calculated energies. This is because the HLC assumes that the contribution is independent of the element and the type of bonding involved, both of which become more important with larger molecules. We address this problem by adding an atom-specific correction, dependent on atom type but not bond type, to the higher-level correction. We find that a G4MP2 method that incorporates this modification of the higher-level correction, referred to as G4MP2A, becomes as accurate as G4 theory (for computing enthalpies of formation) for a test set of molecules with less than 10 nonhydrogen atoms as well as a set with 10-14 such atoms, the set of molecules considered here, with a much lower computational cost. The G4MP2A method is also found to significantly improve ionization potentials and electron affinities. Finally, we implemented the G4MP2A energies in a machine learning method to predict molecular energies.

Dandu, Naveen↗

DOE OSTI2022

Deep learning methods for obtaining photometric redshift estimations from images

ABSTRACT Knowing the redshift of galaxies is one of the first requirements of many cosmological experiments, and as it is impossible to perform spectroscopy for every galaxy being observed, photometric redshift (photo-z) estimations are still of particular interest. Here, we investigate different deep learning methods for obtaining photo-z estimates directly from images, comparing these with ‘traditional’ machine learning algorithms which make use of magnitudes retrieved through photometry. As well as testing a convolutional neural network (CNN) and inception-module CNN, we introduce a novel mixed-input model that allows for both images and magnitude data to be used in the same model as a way of further improving the estimated redshifts. We also perform benchmarking as a way of demonstrating the performance and scalability of the different algorithms. The data used in the study comes entirely from the Sloan Digital Sky Survey (SDSS) from which 1 million galaxies were used, each having 5-filtre (ugriz) images with complete photometry and a spectroscopic redshift which was taken as the ground truth. The mixed-input inception CNN achieved a mean squared error (MSE) =0.009, which was a significant improvement ($30{{\ \rm per\ cent}}$) over the traditional random forest (RF), and the model performed even better at lower redshifts achieving a MSE = 0.0007 (a $50{{\ \rm per\ cent}}$ improvement over the RF) in the range of z < 0.3. This method could be hugely beneficial to upcoming surveys, such as Euclid and the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), which will require vast numbers of photo-z estimates produced as quickly and accurately as possible.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

A sixth order Mehrstellen scheme with an application to the Method of Local Corrections for the 3D Poisson equation

We present a sixth order finite difference scheme for Poisson’s equation when discretized with the compact 27-point stencil based on Mehrstellen corrections of the forcing function term f. Our approach results in a sixth order accurate solution error as opposed to a fourth-order error imposed by the classical Mehrstellen correction for the 19-point and 27-point stencils. The present study is a continuation of former work of Spotz and Carey (1996) on compact finite difference schemes for Poisson’s equation where sixth order convergence may be obtained under the assumption that the fourth order derivatives of f are determined analytically. Specifically, we show that sixth order convergence can still be attained when only values of f at grid points are available. The sixth order Mehrstellen scheme is further coupled with a Method of Local Corrections (MLC) 3D Poisson solver improving to sixth order accuracy the results reported in Kavouklis and Colella (2019). The MLC test case considered involves an adaptive grid that comprises 7.5 billion cells.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Domain Adaptive Graph Neural Networks for Constraining Cosmological Parameters Across Multiple Data Sets

Deep learning models have been shown to outperform methods that rely on summary statistics, like the power spectrum, in extracting information from complex cosmological data sets. However, due to differences in the subgrid physics implementation and numerical approximations across different simulation suites, models trained on data from one cosmological simulation show a drop in performance when tested on another. Similarly, models trained on any of the simulations would also likely experience a drop in performance when applied to observational data. Training on data from two different suites of the CAMELS hydrodynamic cosmological simulations, we examine the generalization capabilities of Domain Adaptive Graph Neural Networks (DA-GNNs). By utilizing GNNs, we capitalize on their capacity to capture structured scale-free cosmological information from galaxy distributions. Moreover, by including unsupervised domain adaptation via Maximum Mean Discrepancy (MMD), we enable our models to extract domain-invariant features. We demonstrate that DA-GNN achieves higher accuracy and robustness on cross-dataset tasks (up to $28\%$ better relative error and up to almost an order of magnitude better $\chi^2$). Using data visualizations, we show the effects of domain adaptation on proper latent space data alignment. This shows that DA-GNNs are a promising method for extracting domain-independent cosmological information, a vital step toward robust deep learning for real cosmic survey data.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

How Should Researchers Measure Perovskite-Based Monolithic Multijunction Solar Cells’ Performance? A Calibration Lab's Perspective

Perovskite multijunctions (PVSK MJs) have made remarkable progress with monolithic PVSK/PVSK tandems surpassing the efficiency of single-junction (1 J) PVSK cells and PVSK/Si cells reported to exceed the 30% efficiency mark. These efficiencies are reported at standard test conditions (STC), established by the photovoltaic (PV) community to facilitate comparison between devices and technologies. Herein, it is discussed why an accurate STC performance measurement for a MJ is more complicated than for a 1 J cell and the special aspects to be considered when measuring the current-voltage characteristics and the performance of PVSK-containing MJ cells are emphasized. It is discussed why a spectrally adjustable solar simulator is needed and the sequence of accurate performance measurement, namely measurement of the spectral response of each junction, adjustment of the spectrum, and appropriate protocols for measuring the power output of the device at STC, is presented. For all these, common errors and pitfalls that sometime lead to misleading interpretation of the results are presented, and the methods to evaluate the accuracy of the data when a spectrally adjustable solar simulator is not available are recommended. Finally, first step is taken toward recommending performance measurement approaches when high throughput is required as will eventually be in a production line.

14 SOLAR ENERGY↗

DOE OSTI2022

UAE6 - Wind Tunnel Tests Data - UAE6 - Sequence E - Raw Data

Sequence E: Yaw Releases (P) This test sequence used a downwind, rigid turbine with a 3.4° cone angle. The wind speeds ranged from 7 m/s to 17 m/s. Initial yaw angles of ±90° were achieved. The blade tip pitch was 3°. The rotor rotated at 72 RPM. Blade and probe pressure measurements were collected. The teeter dampers were replaced with rigid links, and these two channels were flagged as not applicable by setting the measured values in the data file to –99999.99 Nm. The teeter link load cell was pre-tensioned to 40,000 N. The turbine was positioned at each specified yaw angle. A 30- second data set was collected with the yaw brake engaged. These points used a letter for the last digit beginning with A and proceeding through the alphabet as repeat points were needed. These points were plotted and compared to ascertain the functionality of the instrumentation. The files ending in numbers beginning with 0 and increasing with each repetition represent yaw release points. Once the fixed-position yaw test was complete, the yaw drive was engaged to hold the turbine. The yaw brake was released, and the yaw drive was disabled allowing the turbine to yaw freely. The yaw drive was disabled about 5 seconds into the campaign, and the turbine was allowed to yaw freely for the rest of the 30-second duration. When the yaw drive is disabled, no torque is applied to the motor, and the inertia and yawing force of the nacelle and rotor overcomes the friction and inertia of the yaw gear and motor. The yaw releases were repeated five times at each condition. Four additional campaigns were collected to determine the turbine’s natural yaw error by releasing the brake at 0° yaw error. These file names use the E designation, followed by two digits for wind speed, followed by XXXX, followed by the repetition digit.

17 WIND ENERGY↗

DOE OSTI2024

Weak-form latent space dynamics identification

Recent work in data-driven modeling has demonstrated that a weak formulation of model equations enhances the noise robustness of a wide range of computational methods. In this paper, we demonstrate the power of the weak form to enhance the LaSDI (Latent Space Dynamics Identification) algorithm, a recently developed data-driven reduced order modeling technique. We introduce a weak form-based version WLaSDI (Weak-form Latent Space Dynamics Identification). WLaSDI first compresses data, then projects onto the test functions and learns the local latent space models. Notably, WLaSDI demonstrates significantly enhanced robustness to noise. With WLaSDI, the local latent space is obtained using weak-form equation learning techniques. Compared to the standard sparse identification of nonlinear dynamics (SINDy) used in LaSDI, the variance reduction of the weak form guarantees a robust and precise latent space recovery, hence allowing for a fast, robust, and accurate simulation. We demonstrate the efficacy of WLaSDI vs. LaSDI on several common benchmark examples including viscid and inviscid Burgers', radial advection, and heat conduction. For instance, in the case of 1D inviscid Burgers' simulations with the addition of up to 100% Gaussian white noise, the relative error remains consistently below 6% for WLaSDI, while it can exceed 10,000% for LaSDI. Similarly, for radial advection simulations, the relative errors stay below 15% for WLaSDI, in stark contrast to the potential errors of up to 10,000% with LaSDI. Moreover, speedups of several orders of magnitude can be obtained with WLaSDI. For example applying WLaSDI to 1D Burgers' yields a 140X speedup compared to the corresponding full order model.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Standardized nomenclature for photovoltaic connectors

Photovoltaic (PV) systems rely on discrete connectors for the efficient and safe flow of power from module to module and from strings to combiner boxes and inverters. Despite their functional importance, no common nomenclature for PV connectors currently exists, resulting in confusion and miscommunication. Misunderstood terms like "MC4 compatible", "cross-mating", "intermating", "female", and "male" can lead to installation and maintenance errors and compromise system reliability. We believe a standardized terminology will reduce confusion, help support installation best practices, aid in maintenance and repair, inform next-generation designs, and provide a technical basis for improved codes and standards. To that end, we are proposing a standardized glossary for 4 mm PV connectors (the most common type of connector used in PV applications) based on, and validated by, a Sandia National Laboratories' investigation that included the following sources: 1) a comprehensive review of official documents from 20 connector manufacturers, including schematics, datasheets, installation manuals, and catalogs, as well as relevant patents; 2) two rounds of surveys distributed to stakeholders, including connector manufacturers, engineers, asset owners, test labs, and researchers; and 3) visual examination of 25 different models of 4 mm single-pole DC PV connectors to document variations in design and functionality. This work provides a foundation for establishing a clear and consistent terminology for PV connectors that will in turn enable progress toward greater reliability and collaboration across the industry.

14 SOLAR ENERGY↗

DOE OSTI2020

ROM-Based Surrogate Systems Modeling of EBR-II

We report the System Analysis Module (SAM), developed and maintained by Argonne National Laboratory, is designed to provide whole-plant transient safety analysis capabilities for a number of advanced non-light water reactors, including sodium-cooled fast reactor (SFR), lead-cooled fast reactor (LFR), and molten salt reactor (MSR)/fluoride-salt-cooled high-temperature reactor (FHR) designs. SAM is primarily constructed as a systems-level analysis tool, with the potential to incorporate reduced order models from three-dimensional computational fluid dynamics (CFD) simulations to improve characterization of complex, multidimensional physics. It is recognized that the computational expense associated with CFD can be intractable for various engineering analyses, such as uncertainty quantification, inference, and design optimization. This paper explores the reducibility of a SAM model using recent advances in randomized linear algebra techniques, which attempt to find recurring patterns in the various realizations generated by a model after randomly perturbing all its input parameters. The reduction is described in terms of fewer degrees of freedom (DOFs), referred to as the active DOFs, for the model variables such as input model parameters and model responses. The results indicate that there is significant room for additional reduction that may be leveraged for additional computational gains when employing SAM for engineering-intensive analyses that require repeated model executions. Different from physics-based reduction approaches, the proposed approach allows one to estimate upper bounds on the reduction errors, which are rigorously developed in this work. Finally, different methods for surrogate model construction, such as regression and neural network-based training, are employed to correlate the input and output active DOFs, which are related back to the original variables using matrix-based linear transformations.

42 ENGINEERING↗

DOE OSTI2022

Experimental testing of a control barrier function on an automated vehicle in live multi-lane traffic

This paper experimentally tests an implementation of a control barrier function (CBF) designed to guarantee a minimum time-gap in car following on an automated vehicle (AV) in live traffic, with a majority occurring on freeways. The CBF supervises a nominal unsafe PID controller on the AV’s velocity. The experimental testing spans two months of driving, of which 1.9 hours of data is collected in which the CBF and nominal controller are active. We find that violations of the guaranteed minimum time-gap are observed, as measured by the vehicle’s on-board radar unit. There are two distinct causes of the violations. First, in multi-lane traffic, Cut-ins from other vehicles represent external disturbances that can immediately violate the minimum guaranteed time gap provided by the CBF. When cut-ins occur, the CBF does eventually return the vehicle to a safe time gap. Second, even when cut-ins do not occur, system model inaccuracies (e.g., sensor error and delay, actuator error and delay) can lead to violations of the minimum time-gap. These violations are small relative to the violations that would have occurred using only the unsafe nominal control law.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2022

Quantification of Lanthanides in a Molten Salt Reactor Surrogate Off-Gas Stream Using Laser-Induced Breakdown Spectroscopy

To enable the deployment of molten salt reactor technology, the development of off-gas treatment systems and advanced monitoring tools capable of operating with high temperatures and radiation fields while delivering near real-time information is necessary. Here, we aim to fulfill this requirement and proposes laser-induced breakdown spectroscopy (LIBS) for monitoring molten salt aerosol streams. A sheath gas measuring method was developed to protect optical elements from aerosol particles and to ensure a relatively constant aerosol stream for measurement. An aqueous system was studied to demonstrate the utility of LIBS for monitoring possible fission products in an aerosol stream: Gd, Nd, and Sm up to 2000 parts per million (ppm). A calibration model was built using partial least squares (PLS) regression with five, six, and nine latent variables for Gd, Nd, and Sm, respectively. This calibration model successfully estimated the concentrations of three test samples, which were validated with inductively charged plasma optical emission spectroscopy measurements at a 99.9% confidence interval. To enhance these models, a genetic algorithm was used to filter the spectra before entering the PLS model, thereby limiting the spectral features being regressed to those with greater correlations to concentration. This allowed for the number of latent variables used in the PLS models to be reduced to four, three, and three for Gd, Nd, and Sm, respectively. Finally, the genetic algorithm-filtered PLS models were used to predict the concentrations of the aerosol stream on a real-time dataset and resulted in a 73%, 18%, and 25% improvement in root mean squared error of prediction compared to the original PLS models developed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Towards Pareto optimal high entropy hydrides via data-driven materials discovery

The ability to rapidly screen material performance in the vast space of high entropy alloys is of critical importance to efficiently identify optimal hydride candidates for various use cases. Given the prohibitive complexity of first principles simulations and large-scale sampling required to rigorously predict hydrogen equilibrium in these systems, we turn to compositional machine learning models as the most feasible approach to screen on the order of tens of thousands of candidate equimolar high entropy alloys (HEAs). Critically, we show that machine learning models can predict hydride thermodynamics and capacities with reasonable accuracy (e.g. a mean absolute error in desorption enthalpy prediction of ~5 kJ mol H 2 –1 ) and that explainability analyses capture the competing trade-offs that arise from feature interdependence. We can therefore elucidate the multi-dimensional Pareto optimal set of materials, i.e., where two or more competing objective properties can't be simultaneously improved by another material. This provides rapid and efficient down-selection of the highest priority candidates for more time-consuming density functional theory investigations and experimental validation. Various targets were selected from the predicted Pareto front (with saturation capacities approaching two hydrogen per metal and desorption enthalpy less than 60 kJ mol H 2 –1 ) and were experimentally synthesized, characterized, and tested amongst an international collaboration group to validate the proposed novel hydrides. Finally, additional top-predicted candidates are suggested to the community for future synthesis efforts, and we conclude with an outlook on improving the current approach for the next generation of computational HEA hydride discovery efforts.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Novel Data Driven Noise Emulation Framework using Deep Neural Network for Generating Synthetic PMU Measurements

Sensors play a critical role in supporting day-to-day grid operations and they are essential to operator’s decision-making process. Furthermore, sensors and sensor behaviors need to be emulated with grid simulations to perform modeling studies and to design cutting edge power systems applications. Ensuring the accurate behavior of these applications requires accurate emulation of sensors and pertinent signals. However, most grid simulators and modeling tools assume either zero error scenarios or simplistic noise models that may not always correlate to real-world sensors. To address the above issue, this work presents an initial study on the noise characteristics of phasor measurement units (PMUs), along with models for recreating their unique noise signatures. The proposed methods (both analytical and machine-learning-based) provide a substantial increase in a sensor’s model fidelity, a feature that can be leveraged by an end-user application to yield more accurate system representations. The proposed methods were then applied to micro PMU data from the EPFL microgrid campus to extract sensor noise profiles. This data was used to train a deep learning model, which was tested to emulate the noise characteristics present in actual signals. Based on the observed results and the employed data-driven methodology, the proposed methods may be adapted to replicate the behavior of other grid sensors and power new applications capable of detecting sensor degradation and eventual device failures in near real-time.

PMU, noise emulation, synthetic measurements, deep↗

DOE OSTI2024

Electroweak three-body decays in the presence of two- and three-body bound states

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Evaluation of CMIP6 GCMs Over the CONUS for Downscaling Studies

Despite the necessity of Global Climate Models (GCMs) sub-selection in downscaling studies, an objective approach for their selection is currently lacking. Building on the previously established concepts in GCMs evaluation frameworks, we develop a weighted averaging technique to remove the redundancy in the evaluation criteria and rank 37 GCMs from the sixth phase of the Coupled Models Intercomparison Project over the contiguous United States. GCMs are rated based on their average performance across 66 evaluation measures in the historical period (1981–2014) after each metric is weighted between zero and one, depending on its uniqueness. The robustness of the outcome is tested by repeating the process with the empirical orthogonal function analysis in which each GCM is ranked based on its sum of distances from the reference in the principal component space. The two methodologies work in contrasting ways to remove the metrics redundancy but eventually develop similar GCMs rankings. A disparity in GCMs' behavior related to their sensitivity to the size of the evaluation suite is observed, highlighting the need for comprehensive multi-variable GCMs evaluation at varying timescales for determining their skillfulness over a region. The sub-selection goal is to use a representative set of skillful models over the region of interest without substantial overlap in their future climate responses and modeling errors in representing historical climate. Additional analyses of GCMs' independence and spread in their future projections provide the necessary information to objectively select GCMs while keeping all aspects of necessity in view.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

RhizoNet segments plant roots to assess biomass and growth for enabling self-driving labs

Abstract Flatbed scanners are commonly used for root analysis, but typical manual segmentation methods are time-consuming and prone to errors, especially in large-scale, multi-plant studies. Furthermore, the complex nature of root structures combined with noisy backgrounds in images complicates automated analysis. Addressing these challenges, this article introduces RhizoNet, a deep learning-based workflow to semantically segment plant root scans. Utilizing a sophisticated Residual U-Net architecture, RhizoNet enhances prediction accuracy and employs a convex hull operation for delineation of the primary root component. Its main objective is to accurately segment root biomass and monitor its growth over time. RhizoNet processes color scans of plants grown in a hydroponic system known as EcoFAB, subjected to specific nutritional treatments. The root detection model using RhizoNet demonstrates strong generalization in the validation tests of all experiments despite variable treatments. The main contributions are the standardization of root segmentation and phenotyping, systematic and accelerated analysis of thousands of images, significantly aiding in the precise assessment of root growth dynamics under varying plant conditions, and offering a path toward self-driving labs.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Spirometric traits show quantile-dependent heritability, which may contribute to their gene-environment interactions with smoking and pollution

Background: “Quantile-dependent expressivity” refers to a genetic effect that is dependent upon whether the phenotype (e.g., spirometric data) is high or low relative to its population distribution. Forced vital capacity (FVC), forced expiratory volume in 1 second (FEV 1 ), and the FEV 1 /FVC ratio are moderately heritable spirometric traits. The aim of the analyses is to test whether their heritability (h 2 ) is constant over all quantiles of their distribution. Methods: Quantile regression was applied to the mean age, sex, height and smoking-adjusted spirometric data over multiple visits in 9,993 offspring-parent pairs and 1,930 sibships from the Framingham Heart Study to obtain robust estimates of offspring-parent (β OP ), offspring-midparent (β OM ), and full-sib regression slopes (β FS ). Nonparametric significance levels were obtained from 1,000 bootstrap samples. β OP s were used as simple indicators of quantile-specific heritability (i.e.,h 2 = 2β OP /(1+r spouse ), where r spouse was the correlation between spouses). Results: β OP ± standard error (SE) decreased by 0.0009 ± 0.0003 (P = 0.003) with every one-percent increment in the population distribution of FEV 1 /FVC, i.e., β OP ± SE were: 0.182 ± 0.031, 0.152 ± 0.015; 0.136 ± 0.011; 0.121 ± 0.013; and 0.099 ± 0.013 at the 10th, 25th, 50th, 75th, and 90th percentiles of the FEV 1 /FVC distribution, respectively. These correspond to h 2 ± SEs of 0.350 ± 0.060 at the 10th, 0.292 ± 0.029 at the 25th, 0.262 ± 0.020 at the 50th, 0.234 ± 0.025 at the 75th, and 0.191 ± 0.025 at the 90th percentiles of the FEV 1 /FVC ratio. Maximum mid-expiratory flow (MMEF) h 2 ± SEs increased 0.0025 ± 0.0007 (P = 0.0004) with every one-percent increment in its distribution, i.e.: 0.467 ± 0.046, 0.467 ± 0.033, 0.554 ± 0.038, 0.615 ± 0.042, and 0.675 ± 0.060 at the 10th, 25th, 50th, 75th, and 90th percentiles of its distribution. This was due to forced expiratory flow at 75% of FVC (FEF75%), whose quantile-specific h 2 increased an average of 0.0042 ± 0.0008 for every one-percent increment in its distribution. It is speculated that previously reported gene-environment interactions may be partially attributable to quantile-specific h 2 , i.e., greater heritability in individuals with lower FEV 1 /FVC due to smoking or airborne particles exposure vs. nonsmoking, unexposed individuals. Conclusion: Heritabilities of FEV 1 /FVC, MMEF, and FEF75% from quantile-regression of offspring-parent and sibling spirometric data suggest their quantile-dependent expressivity.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Gravitational waves and galaxies cross-correlations: a forecast on GW biases for future detectors

ABSTRACT Gravitational waves (GWs) have rapidly become important cosmological probes since their first detection in 2015. As the number of detected events continues to rise, upcoming instruments like Einstein Telescope (ET) and Cosmic Explorer (CE) will observe millions of compact binary mergers. These detections, coupled with galaxy surveys by instruments such as the Dark Spectroscopic Energy Instrument (DESI), Euclid, and the Vera Rubin Observatory, will provide unique information on the large-scale structure of the universe by cross-correlating GWs with the distribution of galaxies hosting them. In this paper, we focus on how cross-correlations constrain the clustering bias of GWs emitted by the coalescence of binary black holes (BBHs). This parameter links BBHs to the underlying dark matter distribution, hence informing us how they populate galaxies. Using a multitracer approach, we forecast the precision of these measurements under different survey combinations. Our results indicate that current GW detectors will have limited precision, with measurement errors as high as $\displaystyle \sim 50~{{\ \rm per\ cent}}$. However, third-generation detectors like ET, when cross-correlated with Legacy Survey of Space and Time (LSST) data, can improve clustering bias measurements to within 2.5 per cent. Furthermore, we demonstrate that these cross-correlations can enable a per cent-level measurement of the magnification lensing effect on GWs. Despite this, there is a degeneracy between magnification and evolution biases, which hinders the precision of both. This degeneracy is most effectively addressed by assuming knowledge of one bias or targeting an optimal redshift range of $\displaystyle 1 \lt z \lt 2.5$. Our analysis opens new avenues for studying the distribution of BBHs and testing the nature of gravity through large-scale structure.

Zazzera, Stefano (ORCID:0000000158979221)↗