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DOE OSTI2024

Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces

Learning operators between infinitely dimensional spaces is an important learning task arising in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric estimation of Lipschitz operators using deep neural networks. Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class. Under the assumption that the target operator exhibits a low dimensional structure, our error bounds decay as the training sample size increases, with an attractive fast rate depending on the intrinsic dimension in our estimation. Our assumptions cover most scenarios in real applications and our results give rise to fast rates by exploiting low dimensional structures of data in operator estimation. We also investigate the influence of network structures (e.g., network width, depth, and sparsity) on the generalization error of the neural network estimator and propose a general suggestion on the choice of network structures to maximize the learning efficiency quantitatively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Comparative Assessment of U-Net-Based Deep Learning Models for Segmenting Microfractures and Pore Spaces in Digital Rocks

Segmentation of high-resolution X-ray microcomputed tomography (µCT) images is crucial in digital rock physics (DRP), affecting the characterization and analysis of microscale phenomena in the porous media. The complexity of geological structures and nonideal scanning conditions pose significant challenges to conventional image segmentation approaches. Motivated by the recent increasing popularity of deep learning (DL) techniques in image processing, this work undertakes a comparative study of DL models, specifically U-Net and its variants, for segmenting multiple targets with distinguished features in digital rocks, including discrete fracture networks (DFNs), pore spaces, and solid rock. Particularly, DFNs have a smaller volumetric fraction over others, bringing in a substantial challenge of imbalanced segmentation. The primary focus is to evaluate the architecture and feature enhancement strategies of various DL models, including U-Net, attention U-Net, residual U-Net, U-Net++, and residual U-Net++. The models were designed as 2.5D, utilizing a central 2D image and its two adjacent upper and lower 2D images as input to provide a pseudo-3D context. In addition, because the ground truth of segmentation was unknown for real-world digital rocks, we created a benchmark data set following the inverse operations of segmentation. The data synthesis started from the label images (i.e., solid rock, pore spaces, and DFNs), followed by simulating partial volume blurring, adding random background noise, and introducing ring artifacts to mimic real raw X-ray µCT images. The data set, which included various rock types (i.e., sandstone and artificial data), scanning resolution, and magnitudes of noise and artifacts, was divided into training and testing data sets with a 90% and 10% ratio, respectively. Moreover, in addition to the conventional pixel-wise evaluation metrics, the physics-based metric of the lattice-Boltzmann method (LBM) simulated permeability provided more comprehensive assessments. The results demonstrated that the residual connections, nested architectures, and redesigned skip connections contribute to the model performance and give the residual U-Net++ the highest accuracy. The improvements were mainly on the boundaries and small targets, especially the DFNs, which dominate the interconnectivity and therefore affect the permeability greatly. This study also rigorously evaluated the efficiency and generalization of each model, demonstrating that the sophisticated architectures achieved excellent practicability and maintained robust performance on completely unseen data, ensuring their suitability for diverse and challenging DRP applications.

58 GEOSCIENCES↗
DOE OSTI2026

Using Gravitational Lensing to Probe for Candidate Quintessential Galaxies in the Epoch of Reionization

Abstract Understanding the properties of the first generation of galaxies is an ongoing challenge in observational astrophysics. James Webb Space Telescope deep-field observations have led to the identification of large numbers of galaxies within the Epoch of Reionization (EoR); however, it remains observationally challenging to study the detailed properties of the most numerous, faint high- z galaxies without strong gravitational lensing. To this end, we present five m AB ≃ 24 galaxies, all projected behind the cores of massive clusters where high lensing magnifications significantly (≳1.5 mag) boost their observed brightness. These galaxies are each characterized by a drop-off in their spectra between the near-IR and optical wavelengths, suggesting the presence of a Lyman break at z > 6. The bright sources enable precise dropout color constraints. We combine the dropout data with follow-up imaging to constrain continuum slopes redward of their breaks. Using the open-source spectral energy distribution modeling software Prospector , we characterize two of these galaxies as probable high- z ( z ∼ 6.5–7) and three as probable low- z ( z ∼ 2) sources, demonstrating that for very bright ( m AB < 24) dropout candidates even limited photometric data have good power to distinguish between high- z galaxies and red or dusty low- z galaxies. The two candidate high- z dropouts are comparably bright to the brightest galaxies identified at such redshifts in deep fields, but due to lensing magnifications are intrinsically fainter by at least 1.5 mag. If confirmed, these galaxies represent exciting laboratories for performing detailed follow-up studies of galaxy properties within the EoR.

Roberson, Joshua [University of Cincinnati] (ORCID↗
DOE OSTI2025

Leveraging interpolation models and error bounds for verifiable scientific machine learning

Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and methods involved. Error bounds for classical interpolation techniques can provide mathematically rigorous estimates of accuracy, but often are difficult or impractical to determine computationally. Here, in this work, we present a best-of-both-worlds approach to verifiable scientific machine learning by demonstrating that (1) multiple standard interpolation techniques have informative error bounds that can be computed or estimated efficiently; (2) comparative performance among distinct interpolants can aid in validation goals; (3) deploying interpolation methods on latent spaces generated by deep learning techniques enables some interpretability for black-box models. We present a detailed case study of our approach for predicting lift-drag ratios from airfoil images. Code developed for this work is available in a public Github repository.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Sheaves as a Framework for Understanding and Interpreting Model Fit

As data grows in size and complexity, finding frameworks which aid in interpretation and analysis has become critical. This is particularly true when data comes from complex systems where extensive structure is available, but must be drawn from peripheral sources. In this paper we argue that in such situations, sheaves can provide a natural framework to analyze how well a statistical model fits at the local level (that is, on subsets of related datapoints) vs the global level (on all the data). The sheaf-based approach that we propose is suitably general enough to be useful in a range of applications, from analyzing sensor networks to understanding the feature space of a deep learning model.

Kvinge, Henry J.↗
DOE OSTI2026

Make the Fastest Faster: Importance Mask Synthesis for Interactive Volume Visualization using Reconstruction Neural Networks

Visualizing a large-scale volumetric dataset with high resolution is challenging due to the substantial computational time and space complexity. Recent deep learning-based image inpainting methods significantly improve rendering latency by reconstructing a high-resolution image for visualization in constant time on GPU from a partially rendered image where only a portion of pixels go through the expensive rendering pipeline. However, existing solutions need to render every pixel of either a predefined regular sampling pattern or an irregular sample pattern predicted from a low-resolution image rendering. Both methods require a significant amount of expensive pixel-level rendering. In this work, we provide Importance Mask Learning (IML) and Synthesis (IMS) networks, which are the first attempts to directly synthesize important regions of the regular sampling pattern from the user’s view parameters, to further minimize the number of pixels to render by jointly considering the dataset, user behavior, and the downstream reconstruction neural network. Our solution is a unified framework to handle various types of inpainting methods through the proposed differentiable compaction/decompaction layers. Experiments show our method can further improve the overall rendering latency of state-of-the-art volume visualization methods using reconstruction neural network for free when rendering scientific volumetric datasets. Our method can also directly optimize the off-the-shelf pre-trained reconstruction neural networks without elongated retraining.

Large-scale data↗
DOE OSTI2022

Data-driven wind turbine wake modeling via probabilistic machine learning

Wind farm design primarily depends on the variability of the wind turbine wake flows to the atmospheric wind conditions and the interaction between wakes. Physics-based models that capture the wake flow field with high-fidelity are computationally very expensive to perform layout optimization of wind farms, and, thus, data-driven reduced-order models can represent an efficient alternative for simulating wind farms. In this work, we use real-world light detection and ranging (LiDAR) measurements of wind-turbine wakes to construct predictive surrogate models using machine learning. Specifically, we first demonstrate the use of deep autoencoders to find a low-dimensional latent space that gives a computationally tractable approximation of the wake LiDAR measurements. Then, we learn the mapping between the parameter space and the (latent space) wake flow fields using a deep neural network. Additionally, we also demonstrate the use of a probabilistic machine learning technique, namely, Gaussian process modeling, to learn the parameter-space-latent-space mapping in addition to the epistemic and aleatoric uncertainty in the data. Finally, to cope with training large datasets, we demonstrate the use of variational Gaussian process models that provide a tractable alternative to the conventional Gaussian process models for large datasets. Furthermore, we introduce the use of active learning to adaptively build and improve a conventional Gaussian process model predictive capability. Overall, we find that our approach provides accurate approximations of the wind-turbine wake flow field that can be queried at an orders-of-magnitude cheaper cost than those generated with high-fidelity physics-based simulations.

Deep neural networks↗
DOE OSTI2020

A Spitzer survey of Deep Drilling Fields to be targeted by the Vera C. Rubin Observatory Legacy Survey of Space and Time

The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will observe several Deep Drilling Fields (DDFs) to a greater depth and with a more rapid cadence than the main survey. In this paper, we describe the ‘DeepDrill’ survey, which used the Spitzer Space Telescope Infrared Array Camera (IRAC) to observe three of the four currently defined DDFs in two bands, centred on 3.6 and 4.5 μm. Furthermore, these observations expand the area that was covered by an earlier set of observations in these three fields by the Spitzer Extragalactic Representative Volume Survey (SERVS). The combined DeepDrill and SERVS data cover the footprints of the LSST DDFs in the Extended Chandra Deep Field–South (ECDFS) field, the ELAIS-S1 field (ES1), and the XMM-Large-Scale Structure Survey field (XMM-LSS). The observations reach an approximate 5σ point-source depth of 2 μJy (corresponding to an AB magnitude of 23.1; sufficient to detect a 10$^{11} \, \mathrm{M}_{\odot}$ galaxy out to z ≈ 5) in each of the two bands over a total area of $\approx 29\,$ deg2. The dual-band catalogues contain a total of 2.35 million sources. In this paper, we describe the observations and data products from the survey, and an overview of the properties of galaxies in the survey. We compare the source counts to predictions from the Shark semi-analytic model of galaxy formation. We also identify a population of sources with extremely red ([3.6]-[4.5] >1.2) colours which we show mostly consists of highly obscured active galactic nuclei.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Reduced‐Order Modeling of Energetic Materials Using Physics‐Aware Recurrent Convolutional Neural Networks in a Latent Space (LatentPARC)

Physics-aware deep learning (PADL) has gained popularity for use in spatiotemporal dynamics simulations, such as those in computational modeling of energetic materials (EM). We show that the challenge PADL methods face while learning complex field evolution problems can be simplified and accelerated by decoupling it into two tasks: learning complex geometric features in evolving fields and modeling dynamics over these features in a lower-dimensional feature space. We build upon our previous work on physics-aware recurrent convolutional neural networks (PARC). PARC embeds knowledge of underlying physics into its neural network architecture for more robust and accurate prediction of evolving physical fields. PARC was shown to effectively learn complex nonlinear features such as the formation of hotspots and coupled shock fronts in various initiation scenarios of EMs, as a function of microstructures, serving effectively as a microstructure-aware burn model. Here, we further accelerate PARC and reduce its computational cost by projecting the original dynamics onto a lower-dimensional invariant manifold, or “latent space.” The projected latent representation encodes the complex geometry of evolving fields (e.g., temperature and pressure) in a set of data-driven features. The reduced dimension of this latent space allows us to learn the dynamics during the initiation of EM with a lighter and more efficient model. We observe a significant decrease in training and inference time while maintaining results comparable to PARC at inference. This work takes steps towards enabling rapid prediction of EM thermomechanics at larger scales and characterization of EM structure–property–performance linkages at a full application scale.

Mathematics and Computing↗
DOE OSTI2025

OpenUniverse2024: a shared, simulated view of the sky for the next generation of cosmological surveys

The OpenUniverse2024 simulation suite is a cross-collaboration effort to produce matched simulated imaging for multiple surveys as they would observe a common simulated sky. Both the simulated data and associated tools used to produce it are intended to uniquely enable a wide range of studies to maximize the science potential of the next generation of cosmological surveys. We have produced simulated imaging for approximately 70 deg 2 of the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) Wide-Fast-Deep survey and the Nancy Grace Roman Space Telescope High-Latitude Wide-Area Survey, as well as overlapping versions of the ELAIS-S1 Deep-Drilling Field for LSST and the High-Latitude Time-Domain Survey for Roman. OpenUniverse2024 includes (i) an early version of the updated extragalactic model called Diffsky, which substantially improves the realism of optical and infrared photometry of objects, compared to previous versions of these models; (ii) updated transient models that extend through the wavelength range probed by Roman and Rubin; and (iii) improved survey, telescope, and instrument realism based on up-to-date survey plans and known properties of the instruments. It is built on a new and updated suite of simulation tools that improves the ease of consistently simulating multiple observatories viewing the same sky. The approximately 400 TB of synthetic survey imaging and simulated universe catalogs are publicly available, and we preview some scientific uses of the simulations.

large-scale structure of Universe↗
DOE OSTI2024

A Deep Learning-Driven Sampling Technique to Explore the Phase Space of an RNA Stem-Loop

The folding and unfolding of RNA stem-loops are critical biological processes; however, their computational studies are often hampered by the ruggedness of their folding landscape, necessitating long simulation times at the atomistic scale. Here, we adapted DeepDriveMD (DDMD), an advanced deep learning-driven sampling technique originally developed for protein folding, to address the challenges of RNA stem-loop folding. Although tempering- and order parameter-based techniques are commonly used for similar rare-event problems, the computational costs or the need for a priori knowledge about the system often present a challenge in their effective use. DDMD overcomes these challenges by adaptively learning from an ensemble of running MD simulations using generic contact maps as the raw input. DeepDriveMD enables on-the-fly learning of a low-dimensional latent representation and guides the simulation toward the undersampled regions while optimizing the resources to explore the relevant parts of the phase space. We showed that DDMD estimates the free energy landscape of the RNA stem-loop reasonably well at room temperature. Our simulation framework runs at a constant temperature without external biasing potential, hence preserving the information on transition rates, with a computational cost much lower than that of the simulations performed with external biasing potentials. Here, we also introduced a reweighting strategy for obtaining unbiased free energy surfaces and presented a qualitative analysis of the latent space. This analysis showed that the latent space captures the relevant slow degrees of freedom for the RNA folding problem of interest. Finally, throughout the manuscript, we outlined how different parameters are selected and optimized to adapt DDMD for this system. We believe this compendium of decision-making processes will help new users adapt this technique for the rare-event sampling problems of their interest.

Gupta, Ayush↗
DOE OSTI2023

Data-driven prediction of α IIb β 3 integrin activation paths using manifold learning and deep generative modeling

The integrin heterodimer is a transmembrane protein critical for driving cellular process and is a therapeutic target in the treatment of multiple diseases linked to its malfunction. Activation of integrin involves conformational transitions between bent and extended states. Some of the conformations that are intermediate between bent and extended states of the heterodimer have been experimentally characterized, but the full activation pathways remain unresolved both experimentally due to their transient nature and computationally due to the challenges in simulating rare barrier crossing events in these large molecular systems. An understanding of the activation pathways can provide new fundamental understanding of the biophysical processes associated with the dynamic interconversions between bent and extended states and unveil new putative therapeutic targets. In this work, we apply nonlinear manifold learning to coarse-grained molecular dynamics simulations of bent, extended, and two intermediate states of αI I b β3 integrin to learn a low-dimensional embedding of the configurational phase space. We then train deep generative models to learn an inverse mapping between the low-dimensional embedding and high-dimensional molecular space and use these models to interpolate the molecular configurations constituting the activation pathways between the experimentally characterized states. Furthermore, this work furnishes plausible predictions of integrin activation pathways and reports a generic and transferable multi-scale technique to predict transition pathways for biomolecular systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Type Ia supernova observations combining data from the Euclid mission and the Vera C. Rubin Observatory

ABSTRACT The Euclid mission will provide first-of-its-kind coverage in the near-infrared over deep (three fields, ∼10–20 square degrees each) and wide (∼10 000 square degrees) fields. While the survey is not designed to discover transients, the deep fields will have repeated observations over a two-week span, followed by a gap of roughly six months. In this analysis, we explore how useful the deep field observations will be for measuring properties of Type Ia supernovae (SNe Ia). Using simulations that include Euclid’s planned depth, area, and cadence in the deep fields, we calculate that more than 3700 SNe between 0.0 < $z$ < 1.5 will have at least five Euclid detections around peak with signal-to-noise ratio larger than 3. While on their own, Euclid light curves are not good enough to directly constrain distances, when combined with legacy survey of space and time (LSST) deep field observations, we find that uncertainties on SN distances are reduced by 20–30 per cent for $z$ < 0.8 and by 40–50 per cent for $z$ > 0.8. Furthermore, we predict how well additional Euclid mock data can be used to constrain a key systematic in SN Ia studies – the size of the luminosity ‘step’ found between SNe hosted in high-mass (>1010 M⊙) and low-mass (<1010 M⊙) galaxies. This measurement has unique information in the rest-frame near-infrared (NIR). We predict that if the step is caused by dust, we will be able to measure its reduction in the NIR compared to optical at the 4σ level. We highlight that the LSST and Euclid observing strategies used in this work are still provisional and some level of joint processing is required. Still, these first results are promising, and assuming that Euclid begins observations well before the Nancy Roman Space Telescope (Roman), we expect this data set to be extremely helpful for preparation for Roman itself.

Astronomy & Astrophysics↗
DOE OSTI2024

Measurement and calibration of non-linear shear terms in galaxy cluster fields

Introduction Galaxy cluster lensing is a powerful tool for measuring the mass of galaxy clusters, but accurate shear measurement and calibration are critical to obtaining reliable results. This study focuses on the measurement and calibration of weak lensing shears to improve mass estimates in cluster lensing. To deal with the problem, we first developed an image simulation pipeline, jedisim, which utilizes galaxy images extracted from the Hubble Space Telescope (HST) Ultra Deep Field (UDF) and the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS). Methods The simulations represent realistic galaxy distributions and morphologies as input sources. The foreground halo with a Navarro–Frenk–White (NFW) profile is constructed such that the lensing signals of background galaxies can be measured by the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST) Science Pipelines. By comparing the measured reduced shear g meas and the true reduced shear g true , we observe non-linearity up to g ≲ 0.6 . We fit polynomials to the data with quadratic correction adequate to g ≲ 0.4 . Meanwhile, we conduct mass estimates using the pzmassfitter code on four different clusters. Results The mass estimate results are significantly improved after applying the shear calibration derived from the present work—from 4.954 ± 0.504 × 1 0 14 M ⊙ to 10.507 ± 0.498 × 1 0 14 M ⊙ after calibration for a simulated cluster with the mass of 10 × 1 0 14 M ⊙ . In multiple cases of validation, the estimated results are all consistent with true cluster mass. Discussion This study yields the first relationship between reality and shape measurement of the LSST Science Pipelines and serves as the first step toward the overall goal of mass calibration in cluster lensing. By addressing the challenges in shear measurement and calibration, we aim to enhance the accuracy and reliability of mass estimates in galaxy cluster lensing studies.

Astronomy & Astrophysics↗
DOE OSTI2022

Deep Generative Modeling of Periodic Variable Stars Using Physical Parameters

The ability to generate physically plausible ensembles of variable sources is critical to the optimization of time domain survey cadences and the training of classification models on data sets with few to no labels. Traditional data augmentation techniques expand training sets by reenvisioning observed exemplars, seeking to simulate observations of specific training sources under different (exogenous) conditions. Unlike fully theory-driven models, these approaches do not typically allow principled interpolation nor extrapolation. Moreover, the principal drawback of theory-driven models lies in the prohibitive computational cost of simulating source observables from ab initio parameters. In this work, we propose a computationally tractable machine learning approach to generate realistic light curves of periodic variables capable of integrating physical parameters and variability classes as inputs. Our deep generative model, inspired by the transparent latent space generative adversarial networks, uses a variational autoencoder (VAE) architecture with temporal convolutional network layers, trained using the OGLE-III optical light curves and physical characteristics (e.g., effective temperature and absolute magnitude) from Gaia DR2. A test using the temperature–shape relationship of RR Lyrae demonstrates the efficacy of our generative “physics-enhanced latent space VAE” (PELS-VAE) model. Such deep generative models, serving as nonlinear nonparametric emulators, present a novel tool for astronomers to create synthetic time series over arbitrary cadences.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

GAMA/DEVILS: constraining the cosmic star formation history from improved measurements of the 0.3–2.2 μm extragalactic background light

We present a revised measurement of the optical extragalactic background light (EBL), based on the contribution of resolved galaxies to the integrated galaxy light (IGL). The cosmic optical background radiation (COB), encodes the light generated by star formation, and provides a wealth of information about the cosmic star formation history (CSFH). We combine wide and deep galaxy number counts from the Galaxy And Mass Assembly survey (GAMA) and Deep Extragalactic VIsible Legacy Survey (DEVILS), along with the Hubble Space Telescope (HST) archive and other deep survey data sets, in nine multiwavelength filters to measure the COB in the range from 0.35 μm to 2.2 μm. We derive the luminosity density in each band independently and show good agreement with recent and complementary estimates of the optical-EBL from very high-energy (VHE) experiments. Our error analysis suggests that the IGL and γ-ray measurements are now fully consistent to within $\sim 10{{\ \rm per\ cent}}$, suggesting little need for any additional source of diffuse light beyond the known galaxy population. We use our revised IGL measurements to constrain the CSFH, and place amplitude constraints on a number of recent estimates. As a consistency check, we can now demonstrate convincingly, that the CSFH, stellar mass growth, and the optical-EBL provide a fully consistent picture of galaxy evolution. Here, we conclude that the peak of star formation rate lies in the range 0.066–0.076 M ⊙ yr -1 Mpc -3 at a lookback time of 9.1 to 10.9 Gyr.

79 ASTRONOMY AND ASTROPHYSICS↗