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DOE OSTI2020

Active Learning A Neural Network Model For Gold Clusters & Bulk From Sparse First Principles Training Data

Small metal clusters are of fundamental scientific interest and of tremendous significance in catalysis. These nanoscale clusters display diverse geometries and structural motifs depending on the cluster size; a knowledge of this size-dependent structural motifs and their dynamical evolution has been of longstanding interest. Given the high computational cost of first-principles calculations, molecular modeling and atomistic simulations such as molecular dynamics (MD) has proven to be an important complementary tool to aid this understanding. Classical MD typically employ predefined functional forms which limits their ability to capture such complex size-dependent structural and dynamical transformation. Neural Network (NN) based potentials represent flexible alternatives and in principle, well-trained NN potentials can provide high level of flexibility, transferability and accuracy on-par with the reference model used for training. A major challenge, however, is that NN models are interpolative and requires large quantities (similar to 10 4 or greater) of training data to ensure that the model adequately samples the energy landscape both near and far-from-equilibrium. A highly desirable goal is minimize the number of training data, especially if the underlying reference model is first-principles based and hence expensive. In this work, we introduce an active learning (AL) scheme that trains a NN model on-the-fly with minimal amount of first-principles based training data. Our AL workflow is initiated with a sparse training dataset (similar to 1 to 5 data points) and is updated on-the-fly via a Nested Ensemble Monte Carlo scheme that iteratively queries the energy landscape in regions of failure and updates the training pool to improve the network performance. Using a representative system of gold clusters, we demonstrate that our AL workflow can train a NN with similar to 500 total reference calculations. Using an extensive DFT test set of similar to 1100 configurations, we show that our AL-NN is able to accurately predict both the DFT energies and the forces for clusters of a myriad of different sizes. Our NN predictions are within 30 meV/atom and 40 meV/angstrom of the reference DFT calculations. Moreover, our AL-NN model also adequately captures the various size-dependent structural and dynamical properties of gold clusters in excellent agreement with DFT calculations and available experiments. We finally show that our AL-NN model also captures bulk properties reasonably well, even though they were not included in the training data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Nonconvex regularization for sparse neural networks

Convex ℓ 1 regularization using an infinite dictionary of neurons has been suggested for constructing neural networks with desired approximation guarantees, but can be affected by an arbitrary amount of over-parametrization. This can lead to a loss of sparsity and result in networks with too many active neurons for the given data, in particular if the number of data samples is large. As a remedy, in this paper, a nonconvex regularization method is investigated in the context of shallow ReLU networks: We prove that in contrast to the convex approach, any resulting (locally optimal) network is finite even in the presence of infinite data (i.e., if the data distribution is known and the limiting case of infinite samples is considered). Moreover, here we show that approximation guarantees and existing bounds on the network size for finite data are maintained.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Machine learning-based surrogate modeling for data-driven optimization: a comparison of subset selection for regression techniques

Optimization of simulation-based or data-driven systems is a challenging task, which has attracted significant attention in the recent literature. A very efficient approach for optimizing systems without analytical expressions is through fitting surrogate models. Due to their increased flexibility, nonlinear interpolating functions, such as radial basis functions and Kriging, have been predominantly used as surrogates for data-driven optimization; however, these methods lead to complex nonconvex formulations. Alternatively, commonly used regression-based surrogates lead to simpler formulations, but they are less flexible and inaccurate if the form is not known a priori. In this work, we investigate the efficiency of subset selection regression techniques for developing surrogate functions that balance both accuracy and complexity. Subset selection creates sparse regression models by selecting only a subset of original features, which are linearly combined to generate a diverse set of surrogate models. Five different subset selection techniques are compared with commonly used nonlinear interpolating surrogate functions with respect to optimization solution accuracy, computation time, sampling requirements, and model sparsity. Furthermore, our results indicate that subset selection-based regression functions exhibit promising performance when the dimensionality is low, while interpolation performs better for higher dimensional problems.

42 ENGINEERING↗

DOE OSTI2013

Reweighted ℓ{sub 1} minimization method for stochastic elliptic differential equations

We consider elliptic stochastic partial differential equations (SPDEs) with random coefficients and solve them by expanding the solution using generalized polynomial chaos (gPC). Under some mild conditions on the coefficients, the solution is “sparse” in the random space, i.e., only a small number of gPC basis makes considerable contribution to the solution. To exploit this sparsity, we employ reweighted l{sub 1} minimization to recover the coefficients of the gPC expansion. We also combine this method with random sampling points based on the Chebyshev probability measure to further increase the accuracy of the recovery of the gPC coefficients. We first present a one-dimensional test to demonstrate the main idea, and then we consider 14 and 40 dimensional elliptic SPDEs to demonstrate the significant improvement of this method over the standard l{sub 1} minimization method. For moderately high dimensional (∼10) problems, the combination of Chebyshev measure with reweighted l{sub 1} minimization performs well while for higher dimensional problems, reweighted l{sub 1} only is sufficient. The proposed approach is especially suitable for problems for which the deterministic solver is very expensive since it reuses the sampling results and exploits all the information available from limited sources.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ 1 regularization

Over the last decade or so, reconstruction methods using ℓ 1 regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The most popular ℓ 1 regularization approach within electron tomography has been total variation (TV) regularization. In addition to reducing unwanted noise, TV regularization encourages a piecewise constant solution with sparse boundary regions. In this paper we propose an alternative ℓ 1 regularization approach for electron tomography based on higher order total variation (HOTV). Like TV, the HOTV approach promotes solutions with sparse boundary regions. In smooth regions however, the solution is not limited to piecewise constant behavior. We demonstrate that this allows for more accurate reconstruction of a broader class of images – even those for which TV was designed for – particularly when dealing with pragmatic tomographic sampling patterns and very fine image features. In conclusion, we develop results for an electron tomography data set as well as a phantom example, and we also make comparisons with discrete tomography approaches.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Enhanced detection of paramagnetic fluorine-19 magnetic resonance imaging agents using zero echo time sequence and compressed sensing

Fluorine-19 ( 19 F) magnetic resonance imaging (MRI) is an emerging technique offering specific detection of labeled cells in vivo. Lengthy acquisition times and modest signal-to-noise ratio (SNR) makes three-dimensional spin-density–weighted 19 F imaging challenging. Recent advances in tracer paramagnetic metallo-perfluorocarbon (MPFC) nanoemulsion probes have shown multifold SNR improvements due to an accelerated 19 F T 1 relaxation rate and a commensurate gain in imaging speed and averages. However, 19 F T 2 -reduction and increased linewidth limit the amount of metal additive in MPFC probes, thus constraining the ultimate SNR. To overcome these barriers, we describe a compressed sampling (CS) scheme, implemented using a “zero” echo time (ZTE) sequence, with data reconstructed via a sparsity-promoting algorithm. Our CS-ZTE scheme acquires k-space data using an undersampled spherical radial pattern and signal averaging. Image reconstruction employs off-the-shelf sparse solvers to solve a joint total variation and -norm regularized least square problem. To evaluate CS-ZTE, we performed simulations and acquired 19 F MRI data at 11.7 T in phantoms and mice receiving MPFC-labeled dendritic cells. For MPFC-labeled cells in vivo, we show SNR gains of ~6.3 × with 8-fold undersampling. We show that this enhancement is due to three mechanisms including undersampling and commensurate increase in signal averaging in a fixed scan time, denoising attributes from the CS algorithm, and paramagnetic reduction of T 1 . Importantly, 19 F image intensity analyses yield accurate estimates of absolute quantification of 19 F spins. Overall, the CS-ZTE method using MPFC probes achieves ultrafast imaging, a substantial boost in detection sensitivity, accurate 19 F spin quantification, and minimal image artifacts.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2017

Uncertainty and Sensitivity Analysis of TREAT Transient Test #15

The U.S. Department of Energy (DOE) is preparing for the resumption of transient testing using the Transient Reactor Test Facility (TREAT) located at the Idaho National Laboratory (INL). In order to support the analysis of TREAT operation and experiment planning, the MAMMOTH reactor physics team has recently begun development of uncertainty and sensitivity analysis for the TREAT core simulated via MAMMOTH. MAMMOTH is a high-fidelity three-dimensional transient multi-physics code developed at INL under the DOE-NE Advanced Modeling and Simulation program (NEAMS) [1]. This research is part of the development presenting some initial uncertainty and sensitivity analysis of TREAT Transient Test #15 [2]. In this summary, we employ the Sobol sampling strategy implemented in RAVEN [3] to efficiently perform the sensitivity and uncertainty analysis. The idea is using Sobol functional decomposition with generalized polynomial chaos (gPC) expansions to estimate the responses of interest [4]. The gPC coefficients are then computed via the spectral projection method with sparse grid approach. In addition, this strategy includes evaluation of the second or higher order sensitivity indices, allowing the study of interactions between several input variables. The principal focus of this analysis is to quantify the uncertainties in the total power and maximum fuel temperatures with respect to uncertainties in the initial transient conditions, such as rated power, fuel temperature, graphite fuel density and control rod boron concentration. In addition, both the first order and second order time-dependent sensitivity indices are computed and analyzed. The results show that the interactions between initial control rod boron concentration and the rated power will contribute at most 1% to the total uncertainty of the power peak.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Machine learning-based inversion for acoustic impedance with large synthetic training data: Workflow and data characterization

Where wells are sparse or training data are difficult to label with high-quality wireline-derived impedance logs, machine learning (ML)-based inversion of acoustic impedance typically depends on small training data sets, leading to biased prediction. We have advanced a novel workflow that applies large synthetic seismic training data to reduce facies-related bias. Using a geologically realistic model as the truth model, we randomly select sparse seed wells to perform sequential Gaussian simulation (SGS) for impedance models of the same geometry and simulate facies variability. We implement random forest regression on 30 features extracted from the synthetic volume. We observe that more seed wells tend to reduce facies-induced bias by sampling more types of facies, resulting in a better prediction. We then focus on the responses of SGS models to facies changes, the number of seed wells necessary for a useful synthetic model, and how much a synthetic model can help ML-based inversion. Here, we observe that the SGS synthetic training model outperforms well-direct training in general. For modeled clastic shore-zone systems in Miocene Gulf of Mexico, two or more seed wells are necessary for a significant reduction of root-mean-square error and outliners, and improvement of facies imaging. In a field-data test, we apply a similar workflow to quantitatively predict acoustic impedance, which is then converted to a sand-volume map at a high-frequency sequence (10–100 m), revealing detailed facies and sandstone patterns. Such results are valuable in many geologic and engineering applications, such as hydrocarbon and CO 2 reservoir prospecting, reserve estimation, simulation, etc.

3D seismic↗

DOE OSTI2016

Reducing Computation and Communication in Scientific Computing: Connecting Theory to Practice.

This report summarizes the work produced as part of a Truman Fellowship appointment and its associated LDRD project. The overall goal of the project was to develop better algorithms and implementations for key computational kernels within the field of scientific computing by designing them to be communication efficient, moving as little data as possible. The primary problem of interest was dense matrix multiplication; other computations that were addressed include sparse matrix-matrix multiplication, QR factorization, solving symmetric linear systems, and the symmetric eigendecomposition. The project also involved the study of computations at the intersection of scientific computing and data analysis, including nonnegative matrix factorization for discovering latent factors, Tucker tensor decomposition for data compression, and sampling methods for similarity search.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

Small-Footprint Lidar Estimations of Sagebrush Canopy Characteristics

Separating lidar returns for use in determining canopy height and shape in low-height vegetation is difficult because the vegetation canopy return is often close to the ground return in time and space. In addition, height underestimation is likely exacerbated in sparsely vegetated shrub ecosystems. This study compares lidar point-cloud data to sagebrush canopy characteristics measured in the field. It was determined that cumulative prediction error could account for as much as 35.6% of the average height and 37.4% of the average canopy area of shrubs sampled. When scaling from the individual shrub scale to coarser scales, prediction error averaged over a number of shrubs decreases as observation numbers increase. High density (in this case an average of 9.46 returns per m2), small footprint lidar (in this case a footprint diameter of 18 cm at nadir) may provide sufficient accuracy for characterizing sagebrush structure and cover and estimating biomass across landscapes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2016

Imaging electronic trap states in perovskite thin films with combined fluorescence and femtosecond transient absorption microscopy

Charge carrier trapping degrades the performance of organometallic halide perovskite solar cells. To characterize the locations of electronic trap states in a heterogeneous photoactive layer, a spatially resolved approach is essential. Here, we report a comparative study on methylammonium lead tri-iodide perovskite thin films subject to different thermal annealing times using a combined photoluminescence (PL) and femtosecond transient absorption microscopy (TAM) approach to spatially map trap states. This approach coregisters the initially populated electronic excited states with the regions that recombine radiatively. Although the TAM images are relatively homogeneous for both samples, the corresponding PL images are highly structured. The remarkable variation in the PL intensities as compared to transient absorption signal amplitude suggests spatially dependent PL quantum efficiency, indicative of trapping events. Furthermore, detailed analysis enables identification of two trapping regimes: a densely packed trapping region and a sparse trapping area that appear as unique spatial features in scaled PL maps.

36 MATERIALS SCIENCE↗

DOE OSTI2022

All-purpose, all-sky photometric redshifts for the Legacy Imaging Surveys Data Release 8

ABSTRACT In this paper, we present photometric redshift (photo-z) estimates for the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys, currently the most sensitive optical survey covering the majority of the extragalactic sky. Our photo-z methodology is based on a machine-learning approach, using sparse Gaussian processes augmented with Gaussian mixture models (GMMs) that allow regions of parameter space to be identified and trained separately in a purely data-driven way. The same GMMs are also used to calculate cost-sensitive learning weights that mitigate biases in the spectroscopic training sample. By design, this approach aims to produce reliable and unbiased predictions for all parts of the parameter space present in wide area surveys. Compared to previous literature estimates using the same underlying photometry, our photo-zs are significantly less biased and more accurate at z > 1, with negligible loss in precision or reliability for resolved galaxies at z < 1. Our photo-z estimates offer accurate predictions for rare high-value populations within the parent sample, including optically selected quasars at the highest redshifts (z > 6), as well as X-ray or radio continuum selected populations across a broad range of flux (densities) and redshift. Deriving photo-z estimates for the full Legacy Imaging Surveys Data Release 8, the catalogues provided in this work offer photo-z estimates predicted to be of high quality for ≳9 × 108 galaxies over ${\sim}19\, 400\, \text{deg}^{2}$ and spanning 0 < z ≲ 7, offering one of the most extensive samples of redshift estimates ever produced.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

Continuous distribution model for the investigation of complex molecular architectures near interfaces with scattering techniques

Biological membranes are composed of a thermally disordered lipid matrix and therefore require non-crystallographic scattering approaches for structural characterization with x-rays or neutrons. Here we develop a continuous distribution (CD) model to refine neutron or x-ray reflectivity data from complex architectures of organic molecules. The new model is a flexible implementation of the composition-space refinement of interfacial structures to constrain the resulting scattering length density profiles. We show this model increases the precision with which molecular components may be localized within a sample, with a minimal use of free model parameters. We validate the new model by parameterizing all-atom molecular dynamics (MD) simulations of bilayers and by evaluating the neutron reflectivity of a phospholipid bilayer physisorbed to a solid support. The determination of the structural arrangement of a sparsely-tethered bilayer lipid membrane (stBLM) comprised of a multi-component phospholipid bilayer anchored to a gold substrate by a thiolated oligo(ethylene oxide) linker is also demonstrated. From the model we extract the bilayer composition and density of tether points, information which was previously inaccessible for stBLM systems. The new modeling strategy has been implemented into the ga lowbar refl reflectivity data evaluation suite, available through the National Institute of Standards and Technology (NIST) Center for Neutron Research (NCNR).

60 APPLIED LIFE SCIENCES↗

DOE OSTI2018

Characterization of different forms of Zr-2.5Nb samples before and after neutron irradiation

Deleterious effects of hydride precipitation on the mechanical properties of Zr-based alloy systems have been studied for many years. Most of these studies have been conducted at high-temperature irradiation conditions that are compatible with those in commercial reactor systems, such as light water and pressurized water reactors. Evaluations of hydride effects on the mechanical properties of welded Zr-2.5Nb are sparse among these reported studies. Research on the mechanical properties of Zr-based alloys neutron irradiated at low temperatures (<100 °C) is also very rare in the literature. Since some companies are interested in using Zr-based alloys as structural materials and in other parts such as pressure tubes in small reactor systems, low-temperature irradiation studies of these materials are important. The current work presents an evaluation of the tensile properties of Zr-2.5Nb welded using tungsten inert gas and electron beam welding as a function of hydrogen charging and neutron irradiation at low temperatures (60–100 °C).

36 MATERIALS SCIENCE↗

DOE OSTI2024

Annotation of DOM metabolomes with an ultrahigh resolution mass spectrometry molecular formula library

Current approaches to analyzing metabolomic data often rely on matching MS/MS fragmentation data to sparse libraries or databases. This approach results in limited identification of features, often with less than 10% of the dataset being annotated. A complementary approach is to assign molecular formula to features based on accurate mass measurements, but the platforms commonly used for metabolomics do not have the needed accuracy or resolving power to do this robustly, particularly for larger molecules. Using our newly modified analysis tool, CoreMS, we generated a library of molecular formula from pooled samples analyzed with LC-21T FT-ICR MS. This library successfully annotated approximately 53.2% of features identified from the exometabolome of marine diatom Phaeodactylum tricornutum – a nearly ten-fold increase over the 5.9% annotation rate achieved using a conventional MS/MS library matching approach. Using this FT-ICR MS library approach, we were able to differentiate differences in the exometabolome of P. tricornutum in iron replete and iron limited conditions, with 668 metabolites being differentially expressed (p < 0.05, 2 x intensity difference) under these conditions. The traditional MS/MS fragmentation-based annotation approach only annotated 61 of these metabolites, while our novel pipeline annotated 450 metabolites and revealed 12 metabolites that were significantly more abundant under low iron conditions. Our results demonstrate the utility of ultrahigh resolution mass spectrometry for generating more comprehensive and confident molecular annotations.

21T-FTICR-MS, CoreMS↗

DOE OSTI2014

Multicolor photometry of the merging galaxy cluster A2319: Dynamics and star formation properties

Asymmetric X-ray emission and a powerful cluster-scale radio halo indicate that A2319 is a merging cluster of galaxies. This paper presents our multicolor photometry for A2319 with 15 optical intermediate filters in the Beijing-Arizona-Taiwan-Connecticut (BATC) system. There are 142 galaxies with known spectroscopic redshifts within the viewing field of 58' × 58' centered on this rich cluster, including 128 member galaxies (called sample I). A large velocity dispersion in the rest frame, 1622{sub −70}{sup +91} km s{sup –1}, suggests merger dynamics in A2319. The contour map of projected density and localized velocity structure confirm the so-called A2319B substructure, at ∼10' northwest to the main concentration A2319A. The spectral energy distributions (SEDs) of more than 30,000 sources are obtained in our BATC photometry down to V ∼ 20 mag. A u-band (∼3551 Å) image with better seeing and spatial resolution, obtained with the Bok 2.3 m telescope at Kitt Peak, is taken to make star-galaxy separation and distinguish the overlapping contamination in the BATC aperture photometry. With color-color diagrams and photometric redshift technique, 233 galaxies brighter than h {sub BATC} = 19.0 are newly selected as member candidates after an exclusion of false candidates with contaminated BATC SEDs by eyeball-checking the u-band Bok image. The early-type galaxies are found to follow a tight color-magnitude correlation. Based on sample I and the enlarged sample of member galaxies (called sample II), subcluster A2319B is confirmed. The star formation properties of cluster galaxies are derived with the evolutionary synthesis model, PEGASE, assuming a Salpeter initial mass function and an exponentially decreasing star formation rate (SFR). A strong environmental effect on star formation histories is found in the manner that galaxies in the sparse regions have various star formation histories, while galaxies in the dense regions are found to have shorter SFR time scales, older stellar ages, and higher interstellar medium metallicities. For the merging cluster A2319, local surface density is a better environmental indicator rather than the cluster-centric distance. Compared with the well-relaxed cluster A2589, a higher fraction of star-forming galaxies is found in A2319, indicating that the galaxy-scale turbulence stimulated by the subcluster merger might have played a role in triggering the star formation activity.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

Multi-View Budgeted Learning under Label and Feature Constraints Using Label-Guided Graph-Based Regularization

Budgeted learning under constraints on both the amount of labeled information and the availability of features at test time pertains to a large number of real world problems. Ideas from multi-view learning, semi-supervised learning, and even active learning have applicability, but a common framework whose assumptions fit these problem spaces is non-trivial to construct. We leverage ideas from these fields based on graph regularizers to construct a robust framework for learning from labeled and unlabeled samples in multiple views that are non-independent and include features that are inaccessible at the time the model would need to be applied. We describe examples of applications that fit this scenario, and we provide experimental results to demonstrate the effectiveness of knowledge carryover from training-only views. As learning algorithms are applied to more complex applications, relevant information can be found in a wider variety of forms, and the relationships between these information sources are often quite complex. The assumptions that underlie most learning algorithms do not readily or realistically permit the incorporation of many of the data sources that are available, despite an implicit understanding that useful information exists in these sources. When multiple information sources are available, they are often partially redundant, highly interdependent, and contain noise as well as other information that is irrelevant to the problem under study. In this paper, we are focused on a framework whose assumptions match this reality, as well as the reality that labeled information is usually sparse. Most significantly, we are interested in a framework that can also leverage information in scenarios where many features that would be useful for learning a model are not available when the resulting model will be applied. As with constraints on labels, there are many practical limitations on the acquisition of potentially useful features. A key difference in the case of feature acquisition is that the same constraints often don't pertain to the training samples. This difference provides an opportunity to allow features that are impractical in an applied setting to nevertheless add value during the model-building process. Unfortunately, there are few machine learning frameworks built on assumptions that allow effective utilization of features that are only available at training time. In this paper we formulate a knowledge carryover framework for the budgeted learning scenario with constraints on features and labels. The approach is based on multi-view and semi-supervised learning methods that use graph-encoded regularization. Our main contributions are the following: (1) we propose and provide justification for a methodology for ensuring that changes in the graph regularizer using alternate views are performed in a manner that is target-concept specific, allowing value to be obtained from noisy views; and (2) we demonstrate how this general set-up can be used to effectively improve models by leveraging features unavailable at test time. The rest of the paper is structured as follows. In Section 2, we outline real-world problems to motivate the approach and describe relevant prior work. Section 3 describes the graph construction process and the learning methodologies that are employed. Section 4 provides preliminary discussion regarding theoretical motivation for the method. In Section 5, effectiveness of the approach is demonstrated in a series of experiments employing modified versions of two well-known semi-supervised learning algorithms. Section 6 concludes the paper.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2021

Connect the Dots: In Situ 4-D Seismic Monitoring of CO 2 Storage With Spatio-Temporal CNNs

4-D seismic imaging has been widely used in CO 2 sequestration projects to monitor the fluid flow in the volumetric subsurface region that is not sampled by wells. Ideally, real-time monitoring and near-future forecasting would provide site operators with great insights to understand the dynamics of the subsurface reservoir and assess any potential risks. However, due to obstacles such as high deployment cost, availability of acquisition equipment, exclusion zones around surface structures, only very sparse seismic imaging data can be obtained during monitoring. That leads to an unavoidable and growing knowledge gap over time. The operator needs to understand the fluid flow throughout the project lifetime and the seismic data are only available at a limited number of times. This is insufficient for understanding reservoir behavior. To overcome those challenges, we have developed spatio-temporal neural-network-based models that can produce high-fidelity interpolated or extrapolated images effectively and efficiently. Specifically, our models are built on an autoencoder, and incorporate the long short-term memory (LSTM) structure with a new loss function regularized by optical flow. We validate the performance of our models using real 4-D post-stack seismic imaging data acquired at the Sleipner CO 2 sequestration field. We employ two different strategies in evaluating our models. Numerically, we compare our models with different baseline approaches using classic pixel-based metrics. We also conduct a blind survey and collect a total of 20 responses from domain experts to evaluate the quality of data generated by our models. Finally, via both numerical and expert evaluation, we conclude that our models can produce high-quality 2-D/3-D seismic imaging data at a reasonable cost, offering the possibility of real-time monitoring or even near-future forecasting of the CO 2 storage reservoir.

4-D seismic imaging↗