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At least 109 records · Page 6

Astrophysics & cosmology from line intensity mapping vs galaxy surveys

Line intensity mapping (LIM) proposes to efficiently observe distant faint galaxies and map the matter density field at high redshift. Building upon the formalism in a companion paper, we first highlight the degeneracies between cosmology and astrophysics in LIM. We discuss what can be constrained from measurements of the mean intensity and redshift-space power spectra. With a sufficient spectral resolution, the large-scale redshift-space distortions of the 2-halo term can be measured, helping to break the degeneracy between bias and mean intensity. With a higher spectral resolution, measuring the small-scale redshift-space distortions disentangles the 1-halo and shot noise terms. Additionally, cross-correlations with external galaxy catalogs or lensing surveys further break degeneracies. We derive requirements for experiments similar to SPHEREx, HETDEX, CDIM, COMAP and CONCERTO. We then revisit the question of the optimality of the LIM observables, compared to galaxy detection, for astrophysics and cosmology. We use a matched filter to compute the luminosity detection threshold for individual sources. We show that LIM contains information about galaxies too faint to detect, in the high-noise or high-confusion regimes. We quantify the sparsity and clustering bias of the detected sources and compare them to LIM, showing in which cases LIM is a better tracer of the matter density. We extend previous work by answering these questions as a function of Fourier scale, including for the first time the effect of cosmic variance, pixel-to-pixel correlations, luminosity-dependent clustering bias and redshift-space distortions.

79 ASTRONOMY AND ASTROPHYSICS↗

Constraints on Local Primordial Non-Gaussianity with 3D Velocity Reconstruction from the Kinetic Sunyaev-Zeldovich Effect

The cosmic velocity field is an unbiased probe of the total matter distribution but is challenging to measure directly at intermediate and high redshifts. The large-scale velocity field imprints a signal in the cosmic microwave background (CMB) through the kinetic Sunyaev-Zeldovich (kSZ) effect. We perform the first 3D reconstruction of the large-scale velocity field from the kSZ effect by applying a quadratic estimator to CMB temperature maps and the 3D positions of galaxies. We do so by combining CMB data from the fifth data release of the Atacama Cosmology Telescope (in combination with Planck) and a spectroscopic galaxy sample from the Sloan Digital Sky Survey. We then measure the galaxy-velocity cross-power spectrum and detect the presence of the kSZ signal at a signal-to-noise ratio of 7.2⁢𝜎. Using this galaxy-velocity cross-correlation alone, we constrain the amplitude of local primordial non-Gaussianity finding 𝑓 NL =−9⁢0$^{+210}_{−350}$. In conclusion, this pathfinder measurement sets the stage for joint galaxy-CMB kSZ constraints to significantly enhance the 𝑓 NL information obtained from galaxy surveys through sample variance cancellation.

79 ASTRONOMY AND ASTROPHYSICS↗

Variance Reduction within Implicit Monte Carlo Thermal Radiation Transport using the Local Importance Function Transform [Slides]

System of equations derived by Fleck and Cummings to model time-dependent thermal radiative transfer (TRT) problems: Solution of radiation specific intensity (I), non-linearly coupled to material internal energy (U); Absorption and re-emission approximated by effective scattering events. Useful for high-energy density physics simulations: i.e., astrophysics, inertial confinement fusion (ICF). Whereas deterministic methods are fully discretized and free of statistical noise, Monte Carlo methods allow for dynamic sampling of the phase space at the price of statistical noise; Monte Carlo methods are also characterized by a slow $\frac{1}{√Ν}$ convergence rate.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Stochasticity and robustness in spiking neural networks

Despite drawing inspiration from biological systems which are inherently noisy and variable, artificial neural networks have been shown to require precise weights to carry out the task which they are trained to accomplish. This creates a challenge when adapting these artificial networks to specialized execution platforms which may encode weights in a manner which restricts their accuracy and/or precision.Reflecting back on the non-idealities which are observed in biological systems, we investigated the effect these properties have on the robustness of spiking neural networks under perturbations to weights. First, we examined techniques extant in conventional neural networks which resemble noisy processes, and postulated they may produce similar beneficial effects in spiking neural networks. Second, we evolved a set of spiking neural networks utilizing biological non-idealities to solve a pole-balancing task, and estimated their robustness. We showed it is higher in networks using noisy neurons, and demonstrated that one of these networks can perform well under the variance expected when a hafnium-oxide based resistive memory is used to encode synaptic weights. Lastly, we trained a series of networks using a surrogate gradient method on the MNIST classification task. We confirmed that these networks demonstrate similar trends in robustness to the evolved networks. We discuss these results and argue that they display empirical evidence supporting the role of noise as a regularizer which can increase network robustness.

97 MATHEMATICS AND COMPUTING↗

A Self-learning Neural Network Approach for Radio Frequency Interference Detection and Removal in Radio Astronomy

In this work, we present a novel neural network (NN) method for the detection and removal of radio frequency interference (RFI) from the raw digitized signal in the signal processing chain of a typical radio astronomy experiment. The main advantage of our method is that it does not require a training set. Instead, our method relies on the fact that the true signal of interest coming from astronomical sources is thermal and therefore described as a Gaussian random process, which cannot be compressed. We employ a variational encoder/decoder network to find the compressible information in the data stream that can explain the most variance with the fewest degrees of freedom. We demonstrate it on a set of toy problems and stored ring buffers from the Baryon Mapping eXperiment prototype. We find that the RFI subtraction is effective at cleaning simulated time streams: While we find that the power spectra of the RFI-cleaned time streams output by the NN suffer from extra signal consistent with additive noise, we find that it is generally around percent level across the band and sub 10% in contaminated spectral channels even when RFI power is an order of magnitude larger than the signal. We discuss the advantages and limitations of this method and possible implementation in the front end of future radio experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

Data and scripts from: “Denoising autoencoder for reconstructing sensor observation data and predicting evapotranspiration: noisy and missing values repair and uncertainty quantification”

This data package includes data and scripts from the manuscript “Denoising autoencoder for reconstructing sensor observation data and predicting evapotranspiration: noisy and missing values repair and uncertainty quantification”.The study addressed common challenges faced in environmental sensing and modeling, including uncertain input data, missing sensor observations, and high-dimensional datasets with interrelated but redundant variables. Point-scaled meteorological and soil sensor observations were perturbed with noises and missing values, and denoising autoencoder (DAE) neural networks were developed to reconstruct the perturbed data and further predict evapotranspiration. This study concluded that (1) the reconstruction quality of each variable depends on its cross-correlation and alignment to the underlying data structure, (2) uncertainties from the models were overall stronger than those from the data corruption, and (3) there was a tradeoff between reducing bias and reducing variance when evaluating the uncertainty of the machine learning models.This package includes:(1) Four ipython scripts (.ipynb): “DAE_train.ipynb” trains and evaluates DAE neural networks, “DAE_predict.ipynb” makes predictions from the trained DAE models, “ET_train.ipynb” trains and evaluates ET prediction neural networks, and “ET_predict.ipynb” makes predictions from trained ET models.(2) One python file (.py): “methods.py” includes all user-defined functions and python codes used in the ipython scripts.(3) A “sub_models” folder that includes five trained DAE neural networks (in pytorch format, .pt), which could be used to ingest input data before being fed to the downstream ET models in ‘ET_train.ipynb” or ‘ET_predict.ipynb’.(4) Two data files (.csv). Daily meteorological, vegetation, and soil data is in “df_data.csv”, where “df_meta.csv” contains the location and time information of “df_data.csv”. Each row (index) in “df_meta.csv” corresponds to each row in “df_data.csv”. These data files are formatted to follow the data structure requirements and be directly used in the ipython scripts, and they have been shuffled chronologically to train machine learning models. The meteorological and soil data was collected using point sensors between 2019-2023 at(4.a) Three shrub-dominated field sites in East River, Colorado (named “ph1”, “ph2” and “sg5” in “df_meta.csv”, where “ph1” and “ph2” were located at PumpHouse Hillslopes, and “sg5” was at Snodgrass Mountain meadow) and(4.b) One outdoor, mesoscale, and herbaceous-dominated experiment in Berkeley, California (named “tb” in “df_meta.csv”, short for Smartsoils Testbed at Lawrence Berkeley National Lab).- See "df_data_dd.csv" and "df_meta_dd.csv" for variable descriptions and the Methods section for additional data processing steps. See "flmd.csv" and "README.txt" for brief file descriptions.- All ipython scripts and python files are written in and require PYTHON language software.

54 ENVIRONMENTAL SCIENCES↗

A Universal Power-law Prescription for Variability from Synthetic Images of Black Hole Accretion Flows

We present a framework for characterizing the spatiotemporal power spectrum of the variability expected from the horizon-scale emission structure around supermassive black holes, and we apply this framework to a library of general relativistic magnetohydrodynamic (GRMHD) simulations and associated general relativistic ray-traced images relevant for Event Horizon Telescope (EHT) observations of Sgr A*. We find that the variability power spectrum is generically a red-noise process in both the temporal and spatial dimensions, with the peak in power occurring on the longest timescales and largest spatial scales. When both the time-averaged source structure and the spatially integrated light-curve variability are removed, the residual power spectrum exhibits a universal broken power-law behavior. On small spatial frequencies, the residual power spectrum rises as the square of the spatial frequency and is proportional to the variance in the centroid of emission. Beyond some peak in variability power, the residual power spectrum falls as that of the time-averaged source structure, which is similar across simulations; this behavior can be naturally explained if the variability arises from a multiplicative random field that has a steeper high-frequency power-law index than that of the time-averaged source structure. We briefly explore the ability of power spectral variability studies to constrain physical parameters relevant for the GRMHD simulations, which can be scaled to provide predictions for black holes in a range of systems in the optically thin regime. We present specific expectations for the behavior of the M87* and Sgr A* accretion flows as observed by the EHT.

79 ASTRONOMY AND ASTROPHYSICS↗

Personalized and uncertainty-aware coronary hemodynamics simulations: From Bayesian estimation to improved multi-fidelity uncertainty quantification

Non-invasive simulations of coronary hemodynamics have improved clinical risk stratification and treatment outcomes for coronary artery disease, compared to relying on anatomical imaging alone. However, simulations typically use empirical approaches to distribute total coronary flow amongst the arteries in the coronary tree, which ignores patient variability, the presence of disease, and other clinical factors. Further, uncertainty in the clinical data often remains unaccounted for in the modeling pipeline. We present an end-to-end uncertainty-aware pipeline to (1) personalize coronary flow simulations by incorporating vessel-specific coronary flows as well as cardiac function; and (2) predict clinical and biomechanical quantities of interest with improved precision, while accounting for uncertainty in the clinical data. We assimilate patient-specific measurements of myocardial blood flow from clinical CT myocardial perfusion imaging to estimate branch-specific coronary artery flows. Simulated noise in the clinical data is used to estimate the joint posterior distributions of the model parameters using adaptive Markov Chain Monte Carlo sampling. Additionally, the posterior predictive distribution for the relevant quantities of interest is determined using a new approach combining multi-fidelity Monte Carlo estimation with non-linear, data-driven dimensionality reduction. This leads to improved correlations between high- and low-fidelity model outputs. Our framework accurately recapitulates clinically measured cardiac function as well as branch-specific coronary flows under measurement noise uncertainty. We observe substantial reductions in confidence intervals for estimated quantities of interest compared to single-fidelity Monte Carlo estimation and state-of-the-art multi-fidelity Monte Carlo methods. This holds especially true for quantities of interest that showed limited correlation between the low- and high-fidelity model predictions. In addition, the proposed multi-fidelity Monte Carlo estimators are significantly cheaper to compute than traditional estimators, under a specified confidence level or variance. The proposed pipeline for personalized and uncertainty-aware predictions of coronary hemodynamics is based on routine clinical measurements and recently developed techniques for CT myocardial perfusion imaging. The proposed pipeline offers significant improvements in precision and reduction in computational cost.

Bayesian parameter estimation↗

Uncertainty amplification due to density/refractive index gradients in background-oriented schlieren experiments

Here, we theoretically analyze the effect of density/refractive index gradients on the measurement precision of background-oriented schlieren (BOS) experiments by deriving the Cramer–Rao lower bound (CRLB) for the 2D centroid estimation process. A model is derived for the diffraction limited image of a dot viewed through a medium containing density gradients that includes the effect of the experimental parameters such as the magnification and f-number. It is shown using the model that nonlinearities in the density gradient field lead to blurring of the dot image. This blurring amplifies the effect of image noise on the centroid estimation process, leading to an increase in the CRLB and a decrease in the measurement precision. The ratio of position uncertainties of a dot in the reference and gradient images is shown to be a function of the ratio of the dot diameters and dot intensities. We termed this parameter the amplification ratio (A F ), and a methodology for reporting position uncertainties in tracking-based BOS measurements is proposed. The theoretical predictions of the dot position estimation variance from the CRLB are compared to ray tracing simulations, and agreement is obtained. The uncertainty amplification is also demonstrated on experimental BOS images of flow induced by a spark discharge, where it is seen that regions of high amplification ratio correspond to regions of density gradients. This analysis elucidates the dependence of the position uncertainty on density and refractive index gradient-induced distortion parameters, provides a methodology for accounting its effect on uncertainty quantification and provides a framework for optimizing experiment design.

42 ENGINEERING↗

Neural Network Prediction of Strong Lensing Systems with Domain Adaptation and Uncertainty Quantification

Modeling strong gravitational lenses is computationally expensive for the complex data from modern and next-generation cosmic surveys. Deep learning has emerged as a promising approach for finding lenses and predicting lensing parameters, such as the Einstein radius. Mean-variance Estimators (MVEs) are a common approach for obtaining aleatoric (data) uncertainties from a neural network prediction. However, neural networks have not been demonstrated to perform well on out-of-domain target data successfully - e.g., when trained on simulated data and applied to real, observational data. In this work, we perform the first study of the efficacy of MVEs in combination with unsupervised domain adaptation (UDA) on strong lensing data. The source domain data is noiseless, and the target domain data has noise mimicking modern cosmology surveys. We find that adding UDA to MVE increases the accuracy on the target data by a factor of about two over an MVE model without UDA. Including UDA also permits much more well-calibrated aleatoric uncertainty predictions. Advancements in this approach may enable future applications of MVE models to real observational data.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Finding Real Uncertainties From Physical Simulations

Modeling strong gravitational lenses is computationally expensive for the complex data from modern and next-generation cosmic surveys. Deep learning has emerged as a promising approach for finding lenses and predicting lensing parameters, such as the Einstein radius. Mean-variance Estimators (MVEs) are a common approach for obtaining aleatoric (data) uncertainties from a neural network prediction. However, neural networks have not been demonstrated to perform well on out-of-domain target data successfully - e.g., when trained on simulated data and applied to real, observational data. In this work, we perform the first study of the efficacy of MVEs in combination with unsupervised domain adaptation (UDA) on strong lensing data. The source domain data is noiseless, and the target domain data has noise mimicking modern cosmology surveys. We find that adding UDA to MVE increases the accuracy on the target data by a factor of about two over an MVE model without UDA. Including UDA also permits much more well-calibrated aleatoric uncertainty predictions. Advancements in this approach may enable future applications of MVE models to real observational data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Optimal Frequency-domain Analysis for Spacecraft Time Series: Introducing the Missing-data Multitaper Power Spectrum Estimator

While the Lomb–Scargle periodogram is foundational to astronomy, it has a significant shortcoming: the variance in the estimated power spectrum does not decrease as more data are acquired. Statisticians have a 60 yr history of developing variance-suppressing power spectrum estimators, but most are not used in astronomy because they are formulated for time series with uniform observing cadence and without seasonal or daily gaps. Here we demonstrate how to apply the missing-data multitaper power spectrum estimator to spacecraft data with uniform time intervals between observations but missing data during thruster fires or momentum dumps. The F-test for harmonic components may be applied to multitaper power spectrum estimates to identify statistically significant oscillations that would not rise above a white noise–based false alarm probability. Multitapering improves the dynamic range of the power spectrum estimate and suppresses spectral window artifacts. We show that the multitaper–F-test combination applied to Kepler observations of KIC 6102338 detects differential rotation without requiring iterative sinusoid fitting and subtraction. Significant signals reside at harmonics of both fundamental rotation frequencies and suggest an antisolar rotation profile. Next we use the missing-data multitaper power spectrum estimator to identify the oscillation modes responsible for the complex "scallop-shell" shape of the K2 light curve of EPIC 203354381. We argue that multitaper power spectrum estimators should be used for all time series with regular observing cadence.

79 ASTRONOMY AND ASTROPHYSICS↗

STITCHES: creating new scenarios of climate model output by stitching together pieces of existing simulations

Abstract. Climate model output emulation has long been attempted to support impact research, mainly to fill in gaps in the scenario space. Given the computational cost of running coupled earth system models (ESMs), which are usually the domain of supercomputers and require on the order of days to weeks to complete a century-long simulation, only a handful of different scenarios are usually chosen to externally force ESM simulations. An effective emulator, able to run on standard computers in times of the order of minutes rather than days could therefore be used to derive climate information under scenarios that were not run by ESMs. Lately, the necessity of accounting for internal variability has also made the availability of initial-condition ensembles, under a specific scenario, important, further increasing the computational demand. At least so far, emulators have been limited to simplified ESM-like output, either seasonal, annual, or decadal averages of basic quantities, like temperature and precipitation, often emulated independently of one another. With this work, we propose a more comprehensive solution to ESM output emulation. Our emulator, STITCHES, uses existing archives of earth system models' (ESMs) scenario experiments to construct ESM-like output under new scenarios or enrich existing initial-condition ensembles, which is what other emulators also aim to do. Importantly, however, STITCHES' output has the same characteristics of the ESM output it sets out to emulate: multivariate, spatially resolved, and high frequency, representing both the forced component and the internal variability around it. STITCHES extends the idea of time sampling – according to which climate outcomes are stratified by the global warming level at which they manifest themselves, irrespective of the scenario and time at which they occur – to the construction of a continuous history of ESM-like output over the whole 21st century, consistent with a 21st-century trajectory of global surface air temperature (GSAT) derived from the scenario that has been chosen as the target of the emulation. STITCHES does so by first splitting the target GSAT trajectory into decade-long windows, then matching each window in turn to a decade-long window within an existing model simulation from the available scenario runs according to its proximity to the target in absolute size of the temperature anomaly and its rate of change. A look-up table is therefore created of a sequence of existing experiment–time-window combinations that, when stitched together, create a GSAT trajectory “similar” to the target. Importantly, we can then stitch together much more than GSAT from these windows, i.e., any output that the ESM has saved for these existing experiment–time-window combinations, at any frequency and spatial scale available in its archive. We show that the stitching does not introduce artifacts in the great majority of cases (we look at temperature and precipitation at monthly frequency and on the native grid of the ESM and at an index of ENSO activity, the Southern Oscillation Index). This is true even if the criteria for the identification of the decades to be stitched together are chosen to work for a smoothed time series of annual GSAT, a result we expect given the larger amount of noise affecting most other variables at finer spatial scales and higher frequencies, which therefore are more “forgiving” of the stitching. We successfully test the method's performance over many ESMs and scenarios. Only a few exceptions surface, but these less-than-optimal outcomes are always associated with a scarcity of the archived simulations from which we can gather the decade-long windows that form the building blocks of the emulated time series. In the great majority of cases, STITCHES' performance is satisfactory according to metrics that reward consistency in trends, interannual and inter-ensemble variance, and autocorrelation structure of the time series stitched together. The method therefore can be used to create ESM-like output according to new scenarios, on the basis of a trajectory of GSAT produced according to that scenario, which could be easily obtained by a simple climate model. It can also be used to increase the size of existing initial-condition ensembles. There are aspects of our emulator that will immediately disqualify it for specific applications, like when climate information is needed whose characteristics result from accumulated quantities over windows of times longer than those used as pieces by STITCHES, droughts longer than a decade for example. But for many applications, we argue that a stitched product can satisfy the climate information needs of impact researchers. STITCHES cannot emulate ESM output from scenarios that result in GSAT trajectories outside of the envelope available in the archive, nor can it emulate trajectories with shapes different from existing ones (overshoots with negative derivative, for example). Therefore, the size and characteristics of the available archives of ESM output are the principal limitations for STITCHES' deployment. Thus, we argue for the possibility of designing scenario experiments within, for example, the next phase of the Coupled Model Intercomparison Project according to new principles, relieved of the need to produce a number of similar trajectories that vary only in radiative forcing strength but more strategically covering the space of temperature anomalies and rates of change.

54 ENVIRONMENTAL SCIENCES↗

From noise to information: The transfer function formalism for uncertainty quantification in reconstructing the nuclear density

The neutron distribution of neutron-rich nuclei provides critical information on the structure of finite nuclei and neutron stars. Parity violating experiments—such as PREX and CREX—provide a clean and largely model-independent determination of neutron densities. Such experiments, however, are challenging and expensive, which is why sound statistical arguments are required to maximize the information gained. We introduce a new framework, the “transfer function formalism,” aimed at uncertainty quantification, model selection, and experimental design in the context of neutron densities. The transfer functions (TFs) are built analytically by expressing the linear response of the objective function (e.g., χ2) to small perturbations of the data. Using the TF formalism, we are able to analyze the expected overall uncertainty—quantified in terms of bias and variance—of the mean square radius and interior density of 48 Ca and 208 Pb. Using relativistic mean field models as a proxy for the weak-charge density—and assuming that a total of five measurements could be performed on the weak form factor of 48 Ca and 208 Pb—we identify the optimal models and experimental locations that minimize the uncertainty in the extraction of the radius and interior density. We also explore the use of the TF formalism to understand the influence of prior distributions for the model parameters, as well as the optimization of model hyperparameters not constrained by the data. Here,we establish how the choice of experimental locations and the model that is used can have a significant impact on the final uncertainties of the extracted quantities of interest. For challenging experiments such as CREX and PREX, a proper quantification of such uncertainties is critical. We have demonstrated how the TF formalism provides several advantages for this type of analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. As a result, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem.

Lei, Jinlong↗

The Twins Embedding of Type Ia Supernovae. I. The Diversity of Spectra at Maximum Light

In this work, we study the spectral diversity of Type Ia supernovae (SNe Ia) at maximum light using high signal-to-noise spectrophotometry of 173 SNe Ia from the Nearby Supernova Factory. We decompose the diversity of these spectra into different extrinsic and intrinsic components, and we construct a nonlinear parameterization of the intrinsic diversity of SNe Ia that preserves pairings of "twin"SNe Ia. We call this parameterization the "Twins Embedding."Our methodology naturally handles highly nonlinear variability in spectra, such as changes in the photosphere expansion velocity, and uses the full spectrum rather than being limited to specific spectral line strengths, ratios, or velocities. We find that the time evolution of SNe Ia near maximum light is remarkably similar, with 84.6% of the variance in common to all SNe Ia. After correcting for brightness and color, the intrinsic variability of SNe Ia is mostly restricted to specific spectral lines, and we find intrinsic dispersions as low as ~0.02 mag between 6600 and 7200 Å. With a nonlinear three-dimensional model plus one dimension for color, we can explain 89.2% of the intrinsic diversity in our sample of SNe Ia, which includes several different kinds of "peculiar"SNe Ia. A linear model requires seven dimensions to explain a comparable fraction of the intrinsic diversity. We show how a wide range of previously established indicators of diversity in SNe Ia can be recovered from the Twins Embedding. In a companion article, we discuss how these results can be applied to the standardization of SNe Ia for cosmology.

79 ASTRONOMY AND ASTROPHYSICS↗

Fiber Bundle Morphisms as a Framework for Modeling Many-to-Many Maps

While it is not generally reflected in the `nice' datasets used for benchmarking machine learning algorithms, the real-world is full of processes that would be best described as many-to-many. That is, a single input can potentially yield many different outputs (whether due to noise, imperfect measurement, or intrinsic stochasticity in the process) and many different inputs can yield the same output (that is, the map is not injective). For example, imagine a sentiment analysis task where, due to linguistic ambiguity, a single statement can have a range of different sentiment interpretations while at the same time many distinct statements can represent the same sentiment. When modeling such a multivalued function $f: X \rightarrow Y$, it is frequently useful to be able to model the distribution on $f(x)$ for specific input $x$ as well as the distribution on fiber $f^{-1}(y)$ for specific output $y$. Such an analysis helps the user (i) better understand the variance intrinsic to the process they are studying and (ii) understand the range of specific input $x$ that can be used to achieve output $y$. Following existing work which used a fiber bundle framework to better model many-to-one processes we describe how morphisms of fiber bundles provide a template for building models which naturally capture the structure of many-to-many processes.

Coda, Elizabeth D.↗

Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms

The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. In conclusion, we numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs.

Derivative-free Optimization↗