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At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Beyond the 3rd moment: a practical study of using lensing convergence CDFs for cosmology with DES Y3

ABSTRACT Widefield surveys probe clustered scalar fields – such as galaxy counts, lensing potential, etc. – which are sensitive to different cosmological and astrophysical processes. Constraining such processes depends on the statistics that summarize the field. We explore the cumulative distribution function (CDF) as a summary of the galaxy lensing convergence field. Using a suite of N-body light-cone simulations, we show the CDFs’ constraining power is modestly better than the second and third moments, as CDFs approximately capture information from all moments. We study the practical aspects of applying CDFs to data, using the Dark Energy Survey (DES Y3) data as an example, and compute the impact of different systematics on the CDFs. The contributions from the point spread function and reduced shear approximation are $\lesssim 1~{{\ \rm per\ cent}}$ of the total signal. Source clustering effects and baryon imprints contribute 1–10 per cent. Enforcing scale cuts to limit systematics-driven biases in parameter constraints degrade these constraints a noticeable amount, and this degradation is similar for the CDFs and the moments. We detect correlations between the observed convergence field and the shape noise field at 13σ. The non-Gaussian correlations in the noise field must be modelled accurately to use the CDFs, or other statistics sensitive to all moments, as a rigorous cosmology tool.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Exact wave solver for nonparaxial laser beam propagation

Simulations of inertial confinement fusion (ICF) experiments require high-fidelity models for laser beam propagation in a nonuniform plasma with varying index of refraction. We describe a new numerical wave solver that is applicable to centimeter-scale length plasmas encountered in indirect drive ICF applications. The one-way Helmholtz equation (OHE) generalizes the time-harmonic paraxial wave equation to large angles. Here, we present a methodology to numerically evaluate the exact solution to the OHE. This solution is computed by analytically advancing eigenfunctions of the one-way Helmholtz operator along a propagation direction and is applicable to any given index of a refraction profile. We compare our exact method with a commonly used approximate split-step technique for solving the OHE. As a test problem, we consider nonparaxial propagation of Gaussian and speckled beams in a plasma density channel with internal reflection. We find that the split-step approach incurs significant errors compared to the exact solution computed using the novel algorithm.

Belyaev, Mikhail A. (ORCID:0000000224908887)↗
DOE OSTI2025

Local primordial non-Gaussian bias from time evolution

Primordial non-Gaussianity (PNG) is a signature of fundamental physics in the early Universe that is probed by cosmological observations. Here, it is well known that the local type of PNG generates a strong signal in the two-point function of large-scale structure tracers, such as galaxies. This signal, often termed “scale-dependent bias” is a generic feature of modulation of gravitational structure formation by a large-scale mode. It is less well appreciated that the coefficient controlling this signal, b ϕ , is closely connected to the time evolution of the tracer number density. This correspondence between time evolution and local PNG can be simply explained for a universal tracer whose mass function only depends on peak height and, more generally, for nonuniversal tracers in the separate universe picture, which we validate in simulations. We also describe how to recover the bias of tracers subject to a survey selection function and perform a simple demonstration on simulated galaxies. Since the local PNG amplitude in n-point statistics ($f$ NL ) is largely degenerate with the coefficient b ϕ , this proof of concept study demonstrates that Galaxy survey data can allow for more optimal and robust extraction of local PNG information from upcoming surveys.

Sullivan, James M. [University of California, Berk↗
DOE OSTI2024

Simulations of Stochastic Fluid Dynamics near a Critical Point in the Phase Diagram

Here, we present simulations of stochastic fluid dynamics in the vicinity of a critical endpoint belonging to the universality class of the Ising model. This study is motivated by the challenge of modeling the dynamics of critical fluctuations near a conjectured critical endpoint in the phase diagram of quantum chromodynamics (QCD). We focus on the interaction of shear modes with a conserved scalar density, which is known as model H. We show that the observed dynamical scaling behavior depends on the correlation length and the shear viscosity of the fluid. As the correlation length is increased or the viscosity is decreased we observe a crossover from the dynamical exponent of critical diffusion, z≃4, to the expected scaling exponent of model H, z≃3. We use our method to investigate the time-dependent correlation function of non-Gaussian moments M n (t) of the order parameter. We find that the relaxation time depends in a nontrivial manner on the power n.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

QES-Plume v1.0: a Lagrangian dispersion model

Low-cost simulations providing accurate predictions of transport of airborne material in urban areas, vegetative canopies, and complex terrain are demanding because of the small-scale heterogeneity of the features influencing the mean flow and turbulence fields. Common models used to predict turbulent transport of passive scalars are based on the Lagrangian stochastic dispersion model. The Quick Environmental Simulation (QES) tool is a low-computational-cost framework developed to provide high-resolution wind and concentration fields in a variety of complex atmospheric-boundary-layer environments. Part of the framework, QES-Plume, is a Lagrangian dispersion code that uses a time-implicit integration scheme to solve the generalized Langevin equations which require mean flow and turbulence fields. Here, QES-Plume is driven by QES-Winds, a 3D fast-response model that computes mass-consistent wind fields around buildings, vegetation, and hills using empirical parameterizations, and QES-Turb, a local-mixing-length turbulence model. In this paper, the particle dispersion model is presented and validated against analytical solutions to examine QES-Plume’s performance under idealized conditions. In particular, QES-Plume is evaluated against a classical Gaussian plume model for an elevated continuous point-source release in uniform flow, the Lagrangian scaling of dispersion in isotropic turbulence, and a non-Gaussian plume model for an elevated continuous point-source release in a power-law boundary-layer flow. In these cases, QES-Plume yields a maximum relative error below 6 % when compared with analytical solutions. In addition, the model is tested against wind-tunnel data for a uniform array of cubical buildings. QES-Plume exhibits good agreement with the experiment with 99 % of matched zeros and 59 % of the predicted concentrations falling within a factor of 2 of the experimental concentrations. Furthermore, results also emphasize the importance of using high-quality turbulence models for particle dispersion in complex environments. Finally, QES-Plume demonstrates excellent computational performance.

58 GEOSCIENCES↗
DOE OSTI2020

Multi-fidelity machine-learning with uncertainty quantification and Bayesian optimization for materials design: Application to ternary random alloys

We present a scale-bridging approach based on a multi-fidelity (MF) machine-learning (ML) framework leveraging Gaussian processes (GP) to fuse atomistic computational model predictions across multiple levels of fidelity. Through the posterior variance of the MFGP, our framework naturally enables uncertainty quantification, providing estimates of confidence in the predictions. We used density functional theory as high-fidelity prediction, while a ML interatomic potential is used as low-fidelity prediction. Practical materials’ design efficiency is demonstrated by reproducing the ternary composition dependence of a quantity of interest (bulk modulus) across the full aluminum–niobium–titanium ternary random alloy composition space. The MFGP is then coupled to a Bayesian optimization procedure, and the computational efficiency of this approach is demonstrated by performing an on-the-fly search for the global optimum of bulk modulus in the ternary composition space. The framework presented in this manuscript is the first application of MFGP to atomistic materials simulations fusing predictions between density functional theory and classical interatomic potential calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

The Effect of the Prior and the Experimental Design on the Inference of the Precision Matrix in Gaussian Chain Graph Models

Here, we investigate whether (and how) experimental design could aid in the estimation of the precision matrix in a Gaussian chain graph model, especially the interplay between the design, the effect of the experiment and prior knowledge about the effect. Estimation of the precision matrix is a fundamental task to infer biological graphical structures like microbial networks. We compare the marginal posterior precision of the precision matrix under four priors: flat, conjugate Normal-Wishart, Normal-MGIG and a general independent. Under the flat and conjugate priors, the Laplace-approximated posterior precision is not a function of the design matrix rendering useless any efforts to find an optimal experimental design to infer the precision matrix. In contrast, the Normal-MGIG and general independent priors do allow for the search of optimal experimental designs, yet there is a sharp upper bound on the information that can be extracted from a given experiment. We confirm our theoretical findings via a simulation study comparing (i) the KL divergence between prior and posterior and (ii) the Stein’s loss difference of MAPs between random and no experiment. Our findings provide practical advice for domain scientists conducting experiments to better infer the precision matrix as a representation of a biological network.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Descriptor Aided Bayesian Optimization for Many-Level Qualitative Variables With Materials Design Applications

Abstract Engineering design often involves qualitative and quantitative design variables, which requires systematic methods for the exploration of these mixed-variable design spaces. Expensive simulation techniques, such as those required to evaluate optimization objectives in materials design applications, constitute the main portion of the cost of the design process and underline the need for efficient search strategies—Bayesian optimization (BO) being one of the most widely adopted. Although recent developments in mixed-variable Bayesian optimization have shown promise, the effects of dimensionality of qualitative variables have not been well studied. High-dimensional qualitative variables, i.e., with many levels, impose a large design cost as they typically require a larger dataset to quantify the effect of each level on the optimization objective. We address this challenge by leveraging domain knowledge about underlying physical descriptors, which embody the physics of the underlying physical phenomena, to infer the effect of unobserved levels that have not been sampled yet. We show that physical descriptors can be intuitively embedded into the latent variable Gaussian process approach—a mixed-variable GP modeling technique—and used to selectively explore levels of qualitative variables in the Bayesian optimization framework. This physics-informed approach is particularly useful when one or more qualitative variables are high dimensional (many-level) and the modeling dataset is small, containing observations for only a subset of levels. Through a combination of mathematical test functions and materials design applications, our method is shown to be robust to certain types of incomplete domain knowledge and significantly reduces the design cost for problems with high-dimensional qualitative variables.

Engineering↗
DOE OSTI2022

Inference for Nonparanormal Partial Correlation via Regularized Rank-Based Nodewise Regression

Abstract Partial correlation is a common tool in studying conditional dependence for Gaussian distributed data. However, partial correlation being zero may not be equivalent to conditional independence under non-Gaussian distributions. In this paper, we propose a statistical inference procedure for partial correlations under the high-dimensional nonparanormal (NPN) model where the observed data are normally distributed after certain monotone transformations. The NPN partial correlation is the partial correlation of the normal transformed data under the NPN model, which is a more general measure of conditional dependence. We estimate the NPN partial correlations by regularized nodewise regression based on the empirical ranks of the original data. A multiple testing procedure is proposed to identify the nonzero NPN partial correlations. The proposed method can be carried out by a simple coordinate descent algorithm for lasso optimization. It is easy-to-implement and computationally more efficient compared to the existing methods for estimating NPN graphical models. Theoretical results are developed to show the asymptotic normality of the proposed estimator and to justify the proposed multiple testing procedure. Numerical simulations and a case study on brain imaging data demonstrate the utility of the proposed procedure and evaluate its performance compared to the existing methods. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Integrated top-down process and voxel-based microstructure modeling for Ti-6Al-4V in laser wire direct energy deposition process

Laser-wire metal additive manufacturing (AM) is one of the ideal direct energy deposition (DED) processes for creating large-scale parts with a medium level of complexity. However, the DED process involves complex thermal signatures and wide length scales making the fabrication of realistic AM components and part qualification often reliant on experimental trial-and-error optimization. While experimental measurements over the full volume of a part are valuable and necessary, measuring the entire area of a part is significantly laborious and practically infeasible, particularly for large parts in terms of cost and rapid qualification. Therefore, in this work, we developed an effective thermal and microstructure modeling framework based on the Johnson–Mehl-Avrami-Kolmogorov (JMAK) and Koistinen & Marburger (KM) models through a top-down approach that considers plate distortion-affected thermal profiles. A voxel-by-voxel simulation method is used to predict individual phase fractions of Ti-6Al-4 V. The predicted results were validated through detailed metallurgical measurements. A combined voxel-by-voxel approach with a sparse data reconstruction technique produced a near-perfect reconstruction of the original data. This approach anticipates a significant reduction in data points and computation time and resources. Lastly, we conclude with potential extensions of this work to other modeling efforts.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Nearest neighbour distributions: New statistical measures for cosmological clustering

ABSTRACT The use of summary statistics beyond the two-point correlation function to analyse the non-Gaussian clustering on small scales, and thereby, increasing the sensitivity to the underlying cosmological parameters, is an active field of research in cosmology. In this paper, we explore a set of new summary statistics – the k-Nearest Neighbour Cumulative Distribution Functions (kNN-CDF). This is the empirical cumulative distribution function of distances from a set of volume-filling, Poisson distributed random points to the k-nearest data points, and is sensitive to all connected N-point correlations in the data. The kNN-CDF can be used to measure counts in cell, void probability distributions, and higher N-point correlation functions, all using the same formalism exploiting fast searches with spatial tree data structures. We demonstrate how it can be computed efficiently from various data sets – both discrete points, and the generalization for continuous fields. We use data from a large suite of N-body simulations to explore the sensitivity of this new statistic to various cosmological parameters, compared to the two-point correlation function, while using the same range of scales. We demonstrate that the use of kNN-CDF improves the constraints on the cosmological parameters by more than a factor of 2 when applied to the clustering of dark matter in the range of scales between 10 and $40\, h^{-1}\, {\rm Mpc}$. We also show that relative improvement is even greater when applied on the same scales to the clustering of haloes in the simulations at a fixed number density, both in real space, as well as in redshift space. Since the kNN-CDF are sensitive to all higher order connected correlation functions in the data, the gains over traditional two-point analyses are expected to grow as progressively smaller scales are included in the analysis of cosmological data, provided the higher order correlation functions are sensitive to cosmology on the scales of interest.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Data-Driven Closures and Assimilation for Stiff Multiscale Random Dynamics

Here, we introduce a data-driven and physics-informed framework for propagating uncertainty in stiff, multiscale random ordinary differential equations (RODEs) driven by correlated (colored) noise. Unlike systems subjected to Gaussian white noise, a deterministic equation for the joint probability density function (PDF) of RODE state variables does not exist in closed form. Moreover, such an equation would require as many phase-space variables as there are states in the RODE system. To alleviate this curse of dimensionality, we instead derive exact, albeit unclosed, reduced-order PDF (RoPDF) equations for low-dimensional observables/quantities of interest. The unclosed terms take the form of state-dependent conditional expectations, which are directly estimated from data at sparse observation times. However, for systems exhibiting stiff, multiscale dynamics, data sparsity introduces regression discrepancies that compound during RoPDF evolution. This is overcome by introducing a kinetic-like defect term to the RoPDF equation, which is learned by assimilating in sparse, low-fidelity RoPDF estimates. Two assimilation methods are considered, namely nudging and deep neural networks, which are successfully tested against Monte Carlo simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

On Transfer Learning Of Neural Networks Using Bi-Fidelity Data For Uncertainty Propagation

Due to their high degree of expressiveness, neural networks have recently been used as surrogate models for mapping inputs of an engineering system to outputs of interest. Once trained, neural networks are computationally inexpensive to evaluate and remove the need for repeated evaluations of computationally expensive models in uncertainty quantification applications. However, given the highly parameterized construction of neural networks, especially deep neural networks, accurate training often requires large amounts of simulation data that may not be available in the case of computationally expensive systems. In this paper, to alleviate this issue for uncertainty propagation, we explore the application of transfer learning techniques using training data generated from both high- and low-fidelity models. We explore two strategies for coupling these two datasets during the training procedure, namely, the standard transfer learning and the bi-fidelity-weighted learning. In the former approach, a neural network model mapping the inputs to the outputs of interest is trained based on the low-fidelity data. The high-fidelity data are then used to adapt the parameters of the upper layer(s) of the low-fidelity network, or train a simpler neural network to map the output of the low-fidelity network to that of the high-fidelity model. In the latter approach, the entire low-fidelity network parameters are updated using data generated via a Gaussian process model trained with a small high-fidelity dataset. The parameter updates are performed via a variant of stochastic gradient descent with learning rates given by the Gaussian process model. Using three numerical examples, we illustrate the utility of these bi-fidelity transfer learning methods where we focus on accuracy improvement achieved by transfer learning over standard training approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Probabilistic Data Association for Orbital-Element Estimation Using Multistage Expectation–Maximization

Tracking space objects is important for managing space traffic and predicting collisions, but is difficult in part due to data association and orbit model uncertainty. Expectation–maximization (EM) is a commonly used tracking method that has not been widely considered for tracking space objects. The technique consists of iteratively computing data association probabilities with a set of current element estimates, and updating estimates of the elements by solving a nonlinear weighted least-squares regression problem where the weights are the data association probabilities. In this paper, we demonstrate the use of EM for probabilistic data association and orbital-element estimation by applying the technique to simulated data from two angles-only tracking scenarios. In both scenarios, EM provides correct data associations and accurate maximum likelihood estimates of orbital elements. One scenario considers tracking a single object in clutter and quantifies the improvement of the orbital-element estimates and data associations as the detection probability increases. However, standard application of EM requires knowing the number of objects or may fail when a large number of objects are present. To address these issues, this paper employs a multistage version of EM that is applicable when there are a large and possibly unknown number of objects.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Accelerating Scientific Simulations with Bi-Fidelity Weighted Transfer Learning

High-fidelity modeling is an essential design tool for many engineering applications. However, for complex systems, computational cost can be a limiting factor. Analyzing parameter sensitivity, uncertainty quantification, and design optimization require many model evaluations. Surrogate models are often used to develop the relationship between model parameters and quantities of interest. However, in the case of complex systems, surrogate models require several degrees of freedom and, thus, a large number of data points to determine the correct dependencies. For many applications, this may be prohibitively expensive. The reduction of computational requirements can be achieved by leveraging low-fidelity models. Low-fidelity models represent the system at a coarser resolution with the advantage of computational efficiency. Therefore, a bi-fidelity modeling paradigm, which augments the accuracy of a low-fidelity model in a computationally efficient manner by invoking limited runs of a high-fidelity model, can be leveraged to sufficiently balance the accuracy and computational requirements. In this work, a bi-fidelity weighted transfer learning method using neural networks was applied to a computational fluid dynamics heat transfer modeling problem. The transfer learning advantage was investigated as a function of hyperparameters. Our main finding is that the use of a bi-fidelity modeling paradigm achieves accuracy close to that of a high-fidelity Gaussian process model while significantly reducing computational cost. The bi-fidelity model achieves comparable performance with 90 high-fidelity samples-that is, 60% less than the samples needed to achieve similar accuracy without the use of bi-fidelity modeling,

Borowiec, Katarzyna↗
DOE OSTI2023

The DESI One-Percent Survey: exploring a generalized SHAM for multiple tracers with the UNIT simulation

We perform SubHalo Abundance Matching (SHAM) studies on UNIT simulations with {σ, V ceil , v smear }-SHAM and {σ, V ceil , $f$ sat }-SHAM. They are designed to reproduce the clustering on 5–30 h -1 Mpc of luminous red galaxies (LRGs), emission-line galaxies (ELGs), and quasi-stellar objects (QSOs) at 0.4 < z < 3.5 from DESI (Dark Energy Spectroscopic Instrument) One Percent Survey. V ceil is the incompleteness of the massive host (sub)haloes and is the key to the generalized SHAM. v smear models the clustering effect of redshift uncertainties, providing measurements consistent with those from repeat observations. A free satellite fraction $f$ sat is necessary to reproduce the clustering of ELGs. We find ELGs present a more complex galaxy–halo mass relation than LRGs reflected in their weak constraints on σ. LRGs, QSOs, and ELGs show increasing V ceil values, corresponding to the massive galaxy incompleteness of LRGs, the quenched star formation of ELGs and the quenched black hole accretion of QSOs. For LRGs, a Gaussian v smear presents a better profile for subsamples at redshift bins than a Lorentzian profile used for other tracers. The impact of the statistical redshift uncertainty on ELG clustering is negligible. The best-fitting satellite fraction for DESI ELGs is around 4 per cent, lower than previous estimations for ELGs. The mean halo mass log 10 ($\langle$M vir $\rangle$) in h -1 M ⊙ for LRGs, ELGs, and QSOs are 13.16 ± 0.01, 11.90 ± 0.06, and 12.66 ± 0.45, respectively. Our generalized SHAM algorithms facilitate the production of multitracer galaxy mocks for cosmological tests.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Coarse-Grained Density Functional Theory Predictions via Deep Kernel Learning

Scalable electronic predictions are critical for soft materials design. Recently, the Electronic Coarse-Graining (ECG) method was introduced to renormalize all-atom quantum chemical (QC) predictions to coarse-grained (CG) resolutions using deep neural networks (DNNs). While DNNs can learn complex representations that prove challenging for kernel-based methods, they are susceptible to overfitting and the overconfidence of uncertainty estimations. Here, we develop ECG within a GPU-accelerated Deep Kernel Learning (DKL) framework to enable CG QC predictions using range-separated hybrid density functional theory (DFT), obtaining a 107 speedup relative to naive all-atom QC. By treating the predicted electronic properties as random Gaussian Processes, DKL incorporates CG mapping degeneracy by learning the distribution of electronic energies as a function of CG configuration. DKL-ECG accurately reproduces molecular orbital energies from range-separated DFT while facilitating efficient training via active learning using the uncertainties provided by DKL. Further, we show that while active learning algorithms enable efficient sampling of a more diverse configurational space relative to random sampling, all explored query methods exhibit comparable performance for the examined system. We attribute this result to the significant overlap of the feature space and output property distributions across multiple temperatures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Dynamical Complexity of Non-Gaussian Many-Body Systems with Dissipation

We characterize the dynamical state of many-body bosonic and fermionic many-body models with intersite Gaussian couplings, on-site non-Gaussian interactions, and local dissipation comprising incoherent particle loss, particle gain, and dephasing. We first establish that, for fermionic systems, if the dephasing noise is larger than the non-Gaussian interactions, irrespective of the Gaussian coupling strength, the system state is a convex combination of Gaussian states at all times. Furthermore, for bosonic systems, we show that if the particle loss and particle gain rates are larger than the Gaussian intersite couplings, the system remains in a separable state at all times. Building on this characterization, we establish that at noise rates above a threshold, there exists a classical algorithm that can efficiently sample from the system state of both the fermionic and bosonic models. Finally, we show that, unlike fermionic systems, bosonic systems can evolve into states that are not convex Gaussian even when the dissipation is much higher than the on-site non-Gaussianity. Similarly, unlike bosonic systems, fermionic systems can generate entanglement even with noise rates much larger than the intersite couplings.

Computational complexity↗