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DOE OSTI2024

Efficient mapping between void shapes and stress fields using Deep Convolutional Neural Networks with sparse data

Establishing fast and accurate structure-to-property relationships is an important component in the design and discovery of advanced materials. Physics-based simulation models like the finite element method (FEM) are often used to predict deformation, stress, and strain fields as a function of material microstructure in material and structural systems. Such models may be computationally expensive and time intensive if the underlying physics of the system is complex. This limits their application to solve inverse design problems and identify structures that maximize performance. In such scenarios, surrogate models are employed to make the forward mapping computationally efficient to evaluate. However, the high dimensionality of the input microstructure and the output field of interest often renders such surrogate models inefficient, especially when dealing with sparse data. Deep convolutional neural network (CNN) based surrogate models have shown great promise in handling such high-dimensional problems. In this paper, a single ellipsoidal void structure under a uniaxial tensile load represented by a linear elastic, high-dimensional and expensive-to-query, FEM model. We consider two deep CNN architectures, a modified convolutional autoencoder framework with a fully connected bottleneck and a UNet CNN, and compare their accuracy in predicting the von Mises stress field for any given input void shape in the FEM model. Additionally, a sensitivity analysis study is performed using the two approaches, where the variation in the prediction accuracy on unseen test data is studied through numerical experiments by varying the number of training samples from 20 to 100.

surrogate modeling; convolutional neural networks;↗

DOE OSTI2023

hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty

Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex forward models described by partial differential equations (PDEs) remains prohibitive with black-box Markov chain Monte Carlo (MCMC) methods. We present hIPPYlib-MUQ, an extensible and scalable software framework that contains implementations of state-of-the art algorithms aimed to overcome the challenges of high-dimensional, PDE-constrained Bayesian inverse problems. These algorithms accelerate MCMC sampling by exploiting the geometry and intrinsic low-dimensionality of parameter space via derivative information and low rank approximation. The software integrates two complementary open-source software packages, hIPPYlib and MUQ. hIPPYlib solves PDE-constrained inverse problems using automatically-generated adjoint-based derivatives, but it lacks full Bayesian capabilities. MUQ provides a spectrum of powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients and Hessians to permit large-scale solution. By combining these two complementary libraries, we created a robust, scalable, and efficient software framework that realizes the benefits of each and allows us to tackle complex large-scale Bayesian inverse problems across a broad spectrum of scientific and engineering disciplines. To illustrate the capabilities of hIPPYlib-MUQ, we present a comparison of a number of MCMC methods available in the integrated software on several high-dimensional Bayesian inverse problems. These include problems characterized by both linear and nonlinear PDEs, various noise models, and different parameter dimensions. The results demonstrate that large (~ 50×) speedups over conventional black box and gradient-based MCMC algorithms can be obtained by exploiting Hessian information (from the log-posterior), underscoring the power of the integrated hIPPYlib-MUQ framework.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Diffusion Probabilistic Modeling for Video Generation

Denoising diffusion probabilistic models are a promising new class of generative models that mark a milestone in high-quality image generation. This paper showcases their ability to sequentially generate video, surpassing prior methods in perceptual and probabilistic forecasting metrics. We propose an autoregressive, end-to-end optimized video diffusion model inspired by recent advances in neural video compression. The model successively generates future frames by correcting a deterministic next-frame prediction using a stochastic residual generated by an inverse diffusion process. We compare this approach against six baselines on four datasets involving natural and simulation-based videos. We find significant improvements in terms of perceptual quality and probabilistic frame forecasting ability for all datasets.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Improving Subsurface Stress Characterization for Carbon Dioxide Storage Projects by Incorporating Machine Learning Techniques

The overall objective of this project is to develop a framework for reliable characterization and prediction of the state of stress in the overburden and underburden (including the basement) in CO 2 storage reservoirs using machine learning and integrated geomechanics and geophysical methods. Specifically, we propose to develop workflow encompassing of technologies and/or methods to predict stress and pressure changes due to CO 2 injection in an active tertiary recovery site and their impacts on subtle fault activation, fractures and occurrence of microseismic events and compare responses to field observations. In this project, we anticipate using dataset from the Farnsworth field Unit (FWU) which is operated by Purdure Petroleum. A novel elastic-waveform VSP inversion technique will be used to estimate high-resolution spatial and temporal changes of elastic moduli in CO 2 storage reservoirs, which will be combined with velocity-stress relationship derived from laboratory tests to obtain subsurface pressure and stress. Clustered microseismic data will be jointly inverted for improved focal mechanisms. Least-squares reverse-time migration of microseismic waveform data will be performed to directly image fracture/fault zones. Additionally, a deep neural network machine learning technique with convolutional and recurrent layers will be used for learning the spectro-temporal structures in microseismic waveforms. The results of this geotechnical data analysis will be integrated to develop a high-resolution 3D mechanical earth model extending from the overburden sealing formations to the underburden including the basement. Mechanical properties will be derived through integration of mechanical logs, tests, available results from chemo-mechanical laboratory tests, and elastic inversion of seismic data using a combination of Bayesian and stochastic methods as well as machine learning technique. Failure features (faults/fractures) will be represented and/or modeled based on seismic and core data analysis. A transient hydrodynamic-geomechanical model will be developed through coupling with the calibrated FWU reservoir simulation model. The full physics coupled model will be used to train a reduced order proxy model using machine learning algorithm for estimating stress which will then be used with appropriate constitutive relationships and forward seismological models to simulate pressure changes and induced microseismicity. An advanced optimization framework will be developed to perform a history match to minimize error between field observations and simulated. The history matched proxy model will be verified against the full-physics equivalent. The field observations that will be used in the coupled model calibration process include pressure/stress inverted from VSP, moment magnitude from microseismic analysis, real time downhole pressure measurements, production and injection data. Parameter sensitivity and uncertainty analysis will be performed to characterize the impact of model parameter uncertainty on stress estimates. The proposed project will have significant impact on future field implementation of the proposed technology. Because the project field site is an ongoing CO 2 EOR development, the value of the new technology will be demonstrated in an operational context and evaluated as a viable risk mitigation strategy. Cost/benefit will be evaluated together with the various commercial incentives for CO 2 sequestration available to oil and gas operators. The extensive available dataset and ongoing data acquisition under the SWP Phase III work plan provides flexibility for investigation of multiple approaches and reduces technical risk.

58 GEOSCIENCES↗

DOE OSTI2025

Emulation of the calculations of final r -process abundance patterns with a neural network

This work explores the construction of a fast emulator for the calculation of the final pattern of nucleosynthesis in the rapid neutron capture process (the r-process). An emulator is built using a feed-forward artificial neural network (ANN). We train the ANN with nuclear data and relative abundance patterns. We take as input the β-decay half-lives and the one-neutron separation energy of the nuclei in the rare-earth region. The output is the final isotopic abundance pattern. In this work, we focus on the nuclear data and abundance patterns in the rare-earth region to reduce the dimension of the input and output space. We show that the ANN can capture the effect of the changes in the nuclear physics inputs on the final r-process abundance pattern in the adopted astrophysical conditions. We employ the deep ensemble method to quantify the prediction uncertainty of the neural network emulator. The emulator achieves a speed-up by a factor of about 20 000 in obtaining a final abundance pattern in the rare-earth region. The emulator may be utilized in statistical analyses such as uncertainty quantification, inverse problems, and sensitivity analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Optimizing shift selection in multilevel Monte Carlo for disconnected diagrams in lattice QCD

The calculation of disconnected diagram contributions to physical signals is a computationally expensive task in Lattice QCD. To extract the physical signal, the trace of the inverse Lattice Dirac operator, a large sparse matrix, must be stochastically estimated. Because the variance of the stochastic estimator is typically large, variance reduction techniques must be employed. Multilevel Monte Carlo (MLMC) methods reduce the variance of the trace estimator by utilizing a telescoping sequence of estimators. Frequency Splitting is one such method that uses a sequence of inverses of shifted operators to estimate the trace of the inverse lattice Dirac operator, however there is no a priori way to select the shifts that minimize the cost of the multilevel trace estimation. Here we present a sampling and interpolation scheme that is able to predict the variances associated with Frequency Splitting under displacements of the underlying space time lattice. The interpolation scheme is able to predict the variances to high accuracy and therefore chooses shifts that correspond to an approximate minimum of the cost for the trace estimation. We show that Frequency Splitting with the chosen shifts displays significant speedups over multigrid deflation, and that these shifts can be used for multiple configurations within the same ensemble with no penalty to performance.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

ML-based Dimension Reduction Strategies

Deep learning (DL)--based surrogate models have achieved success in various applications in carbon capture and storage (CCS). However, the model training on high-dimensional spaces is computationally expensive and impractical for large-scale and complex geological models, because the models usually contain hundreds of thousands to millions of grid cells, each with a set of parameters. Furthermore, the high cost of generating training data with sufficient variation is another limitation of model training on high-dimensional spaces, which may result in overfitting and reduce the model efficiency and prediction performance. We proposed the workflow incorporating dimension reduction methods and deep learning models, which aim to extract the latent variables of input parameters and output state variables, and then build the mapping function at the latent spaces. The proposed workflow can significantly reduce the computational complexity in solving both forward and inverse problems compared to models trained on high-dimensional spaces. Dimensionality reduction models showed great potential in workflows for fast reservoir simulation, history matching, prior model generation, visualization, and more, ultimately enhancing DL model performance in related SMART Work Packages.

Hosseini, Seyyed↗

DOE OSTI2022

Interpolation as a means of shift selection for multilevel Monte Carlo with lattice displacements

The calculation of disconnected diagram contributions to physical signals is a computationally expensive task in Lattice QCD. To extract the physical signal, the trace of the inverse Lattice Dirac operator, a large sparse matrix, must be stochastically estimated. Because the variance of the stochastic estimator is typically large, variance reduction techniques must be employed. Multilevel Monte Carlo (MLMC) methods reduce the variance of the trace estimator by utilizing a telescoping sequence of estimators. Frequency Splitting is one such method that uses a sequence of inverses of shifted operators to estimate the trace of the inverse of the lattice Dirac operator, however there is no a priori way to select the shifts that minimize the cost of the multilevel trace estimation. We present a sampling and interpolation scheme that is able to predict the variances associated with Frequency Splitting under displacements of the underlying space time lattice. The interpolation scheme is able to predict the variances to high accuracy and therefore choose shifts that correspond to an approximate minimum of the cost for the trace estimation. We show that Frequency Splitting with the chosen shifts displays significant speedups over multigrid deflation

Whyte, Travis↗

DOE OSTI2025

Machine Learning-Driven Conservative-to-Primitive Conversion in Hybrid Piecewise Polytropic and Tabulated Equations of State

We present a novel machine learning (ML)-based method to accelerate conservative-to-primitive inversion, focusing on hybrid piecewise polytropic and tabulated equations of state. Traditional root-finding techniques are computationally expensive, particularly for large-scale relativistic hydrodynamics simulations. To address this, we employ feedforward neural networks (NNC2PS and NNC2PL), trained in PyTorch (2.0+) and optimized for GPU inference using NVIDIA TensorRT (8.4.1), achieving significant speedups with minimal accuracy loss. The NNC2PS model achieves 𝐿 1 and 𝐿 ∞ errors of 4.54 × 10 −7 and 3.44 × 10−6, respectively, while the NNC2PL model exhibits even lower error values. TensorRT optimization with mixed-precision deployment substantially accelerates performance compared to traditional root-finding methods. Specifically, the mixed-precision TensorRT engine for NNC2PS achieves inference speeds approximately 400 times faster than a traditional single-threaded CPU implementation for a dataset size of 1,000,000 points. Ideal parallelization across an entire compute node in the Delta supercomputer (dual AMD 64-core 2.45 GHz Milan processors and 8 NVIDIA A100 GPUs with 40 GB HBM2 RAM and NVLink) predicts a 25-fold speedup for TensorRT over an optimally parallelized numerical method when processing 8 million data points. Moreover, the ML method exhibits sub-linear scaling with increasing dataset sizes. We release the scientific software developed, enabling further validation and extension of our findings. By exploiting the underlying symmetries within the equation of state, these findings highlight the potential of ML, combined with GPU optimization and model quantization, to accelerate conservative-to-primitive inversion in relativistic hydrodynamics simulations.

conservative-to-primitive conversion↗

DOE OSTI2025

Resummation for lattice QCD calculation of generalized parton distributions at nonzero skewness

Large-momentum effective theory (LaMET) provides an approach to directly calculate the x-dependence of generalized parton distributions (GPDs) on a Euclidean lattice through power expansion and a perturbative matching. When a parton’s momentum becomes soft, the corresponding logarithms in the matching kernel become non-negligible at higher orders of perturbation theory, which requires a resummation. But the resummation for the off-forward matrix elements at nonzero skewness ξ is difficult due to their multi-scale nature. In this work, we demonstrate that these logarithms are important only in the threshold limit, and derive the threshold factorization formula for the quasi-GPDs in LaMET. We then propose an approach to resum all the large logarithms based on the threshold factorization, which is implemented on a GPD model. We demonstrate that the LaMET prediction is reliable for [−1 + x 0 , −ξ − x 0 ] ∪ [−ξ + x 0 , ξ − x 0 ] ∪ [ξ + x 0 , 1 − x 0 ], where x 0 is a cutoff depending on hard parton momenta. Through our numerical tests with the GPD model, we demonstrate that our method is self-consistent and that the inverse matching does not spread the nonperturbative effects or power corrections to the perturbatively calculable regions.

hadronic spectroscopy↗

DOE OSTI2024

Reactor antineutrino flux and anomaly

Reactor antineutrinos have played a significant role in establishing the standard model of particle physics and the theory of neutrino oscillations. In this article, we review the reactor antineutrino flux and in particular the reactor antineutrino anomaly (RAA) coined over a decade ago. RAA refers to a deficit of the measured antineutrino inverse beta decay rates at very short-baseline reactor experiments compared to the theoretically improved predictions (i.e. the Huber–Mueller model). Since the resolution of several previous experimental anomalies have led to the discovery of non-zero neutrino mass and mixing, many efforts have been invested to study the origin of RAA both experimentally and theoretically. The progress includes the observation of discrepancies in antineutrino energy spectrum between data and the Huber–Mueller model, the re-evaluation of the Huber–Mueller model uncertainties, the potential isotope-dependent rate deficits, and the better agreement between data and new model predictions using the improved summation method. Importantly, these developments disfavor the hypothesis of a light sterile neutrino as the explanation of RAA and supports the deficiencies of Huber–Mueller model as the origin. Looking forward, more effort from both the theoretical and experimental sides is needed to fully understand the root of RAA and to make accurate predictions of reactor antineutrino flux and energy spectrum for future discoveries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Artificial Intelligence for Conjugated Polymers

Conjugated polymers have garnered significant attention due to their diverse applications in electronics, photonics, and energy storage. However, realizing their full potential poses a formidable challenge, as their design has historically relied on iterative adjustments and continuous inspiration from researchers. Traditional methods often struggle to efficiently navigate their vast chemical landscape. In this work, the application of artificial intelligence (AI), specifically machine learning (ML), needs to be discussed in the realm of conjugated polymers. Our paper emphasizes the importance of understanding the structure–property relationships of these polymers and how ML can facilitate property prediction and inverse-design. We delve into various chemical fingerprints, structural descriptors, and ML algorithms, showcasing their utility across a spectrum of applications, including simulations, glass transition temperature determination, photovoltaics, reorganization energy for charge transport, photocatalysts, and sensors. Finally, we give some outlooks in this filed and propose unexplored areas within the field that hold the potential to benefit from ML techniques.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Predicting Dynamic-to-Static Correction Factor from Petrophysical Data and Chemostratigraphy using Unsupervised Machine Learning

Estimating static mechanical properties of stratigraphic layers is critical for optimizing subsurface engineering applications. To estimate dynamic-to-static correction factor F ds (static-to-dynamic Young’s modulus ratio) across the Caney shale interval in Oklahoma, USA, we integrated triaxial test measurements and petrophysical data, including well logs and X-ray fluorescence (XRF) using unsupervised machine learning (ML). We used a novel workflow that includes principal component analysis (PCA) to reduce data set dimensionality of well logs and XRF data sets—both separately and combined—creating three scenarios, and later applied inverse distance weighting (IDW) to derive F ds profiles for these scenarios. Furthermore, we applied K-means clustering on each scenario to predict depositional facies, and built a stiffness zonation profile through chemostratigraphic analysis of the terrigenous elements to validate the predicted F ds . The predicted F ds profile from each scenario using the PCA-IDW method was compared with the constant F ds approach from our previous study by calculating the root mean square error (RMSE). The combined data sets scenario yielded the lowest RMSE value of 0.113, while the RMSE values for the well logs and XRF scenarios were 0.131 and 0.129, respectively. In addition, the predicted F ds from the XRF scenario well-matched the stiffness zonation from the chemostratigraphic analysis that was built using the optimized K-means clustering of nine clusters for that scenario. These methods and findings offer a valuable tool for refining lithological classification and improving the F ds profile, potentially enhancing drilling and stimulation strategies for subsurface energy engineering applications.

clastic rock↗

DOE OSTI2023

Integration of seismic-pressure-petrophysics inversion of continuous active-seismic monitoring data for monitoring and quantifying CO 2 plume (Final Report)

The overall objective of this project is to develop and validate an integrated package of joint seismic-pressure-petrophysics inversion (jSPPI) of continuous active-source seismic monitoring dataset capable of providing real-time monitoring of CO 2 plume during geologic carbon sequestration (GCS). The three specific developments include: (a) the methodologies for fast seismic full waveform inversion of continuous active source seismic monitoring, (CASSM) datasets for simultaneously estimating velocity and attenuation, and with data assimilation; (b) joint Bayesian petrophysical inversion of seismic models and pressure data for providing and updating CO 2 saturation models; (c) the methods using multiple datasets including (Crainfield and Frio-II borehole) synthetic, laboratory, and field CASSM datasets. The outcomes of jSPPI include (a) a workflow for processing CASSM data, (b) Bayesian inversion algorithms using CASSM data and pressure response data, and (c) integration with data assimilation algorithms for continuously updating site-specific models used for prediction and reservoir management. The validation of joint FWI will be conducted using synthetic models based on the Cranfield and Frio experiments as well as field CASSM datasets collected as part of the Frio-II pilot injection. To quantify and map the mass and distribution of CO 2 (saturation), we will jointly invert velocity and attenuation measurements from the FWI with a Bayesian approach using a rock physics model for attenuation (e.g., White’s attenuation model with two selected patch sizes (White, 1976; Dutta and Seriff, 1979)). The Bayesian inversion will be applied to each time step in the CASSM survey in an updating scheme, which integrates with an ensemble of reservoir simulations at each step. A more complete experimental validation dataset will be collected as part of a mesoscale (2-3 m) gas-CO 2 injection experiment utilizing a higher frequency version of the CASSM system developed for laboratory studies; the integrated inversion will be demonstrated using this dataset which will provide both a dense geometry as well as more precise secondary confirmation measurements (e.g. saturation) typically not available in the field. The resulting real-time map of CO 2 saturation is able to provide a deeper scientific understanding of the complex, time-varying dynamics of subsurface fluid flow migration path as well as the rapid detection of CO 2 leakage hazards.

25 ENERGY STORAGE↗

DOE OSTI2024

Modeling hydrogen markets: Energy system model development status and decarbonization scenario results

Hydrogen can be used as an energy carrier and chemical feedstock to reduce greenhouse gas emissions, especially in difficult-to-decarbonize markets such as medium- and heavy-duty vehicles, aviation and maritime, iron and steel, and the production of fuels and chemicals. Significant literature has been accumulated on engineering-based assessments of various hydrogen technologies, and real-world projects are validating technology performance at larger scales and for low-carbon supply chains. While energy system models continue to be updated to track this progress, many are currently limited in their representation of hydrogen, and as a group they tend to generate highly variable results under decarbonization constraints. Here, the present work provides insights into the development status and decarbonization scenario results of 15 energy system models participating in study 37 of the Stanford Energy Modeling Forum (EMF37), focusing on the U.S. energy system. The models and scenario results vary widely in multiple respects: hydrogen technology representation, scope and type of hydrogen end-use markets, relative optimism of hydrogen technology input assumptions, and market uptake results reported for 2050 under various decarbonization assumptions. Most models report hydrogen market uptake increasing with decarbonization constraints, though some models report high carbon prices being required to achieve these increases and some find hydrogen does not compete well when assuming optimistic assumptions for all advanced decarbonization technologies. Across various scenarios, hydrogen market success tends to have an inverse relationship to success with direct air capture (DAC) and carbon capture and storage (CCS) technologies. While most model-scenario combinations predict modest hydrogen uptake by 2050 – <10 million metric tons (MMT) – aggregating the top 10 % of market uptake results across sectors suggests an upper range demand potential of 42–223 MMT. The high degree of variability across both modeling methods and market uptake results suggests that increased harmonization of both input assumptions and subsector competition scope would lead to more consistent results across energy system models. The wide variability in results indicates strongly divergent conclusions on the role of hydrogen in a decarbonized energy future.

08 HYDROGEN↗

DOE OSTI2022

Inferring topological transitions in pattern-forming processes with self-supervised learning

Abstract The identification of transitions in pattern-forming processes are critical to understand and fabricate microstructurally precise materials in many application domains. While supervised methods can be useful to identify transition regimes, they need labels, which require prior knowledge of order parameters or relevant microstructures describing these transitions. Instead, we develop a self-supervised, neural-network-based approach that does not require predefined labels about microstructure classes to predict process parameters from observed microstructures. We show that assessing the difficulty of solving this inverse problem can be used to uncover microstructural transitions. We demonstrate our approach by automatically discovering microstructural transitions in two distinct pattern-forming processes: the spinodal decomposition of a two-phase mixture and the formation of binary-alloy microstructures during physical vapor deposition of thin films. This approach opens a path forward for discovering unseen or hard-to-discern transitions and ultimately controlling complex pattern-forming processes.

Abram, Marcin↗

DOE OSTI2026

Multi-Modal Bayesian Neural Network Surrogates with Conjugate Last-Layer Estimation

As data collection and simulation capabilities advance, multi-modal learning, the task of learning from multiple modalities and sources of data, is becoming an increasingly important area of research. Surrogate models that learn from data of multiple auxiliary modalities to support the modeling of a highly expensive quantity of interest have the potential to aid outer loop applications such as optimization, inverse problems, or sensitivity analyses when multi-modal data are available. We develop two multi-modal Bayesian neural network surrogate models and leverage conditionally conjugate distributions in the last layer to estimate model parameters using stochastic variational inference (SVI). We provide a method to perform this conjugate SVI estimation in the presence of partially missing observations. Here, we demonstrate improved prediction accuracy and uncertainty quantification compared to unimodal surrogate models for both scalar and time series data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Modeling the viscoplastic behavior of a semicrystalline polymer

In this study, a complex constitutive relation is identified using inverse modeling with the nominal mechanical response as sole experimental input. The methodology is illustrated for a semicrystalline thermoplastic in the presence of strain localization at finite deformations. The experimental database includes cylindrical tensile bars, compression pins and round notched bars loaded at strain rates spanning up to five decades and temperatures below and above T g . The data is organized into a calibration set and a validation set. The response of tensile specimens is determined using finite element analyses and a two-phase constitutive relation for semicrystalline polymers that accounts for temperature- and rate-sensitive plastic flow, pressure-sensitivity, small-strain softening and large-strain orientational hardening of the amorphous phase, along with the evolution of crystallinity. The large number of constitutive parameters is identified using an optimization tool coupled with the finite element solver and the calibration set from experiments. The methodology is shown to be successful in predicting the response of round notched bars and replicating the effects of temperature and strain rate on the severity of necking in tensile bars. The proposed model identification strategy is both simple and effective in comparison with other elaborate methods that attempt to access intrinsic behavior directly from high-fidelity experimental measurements.

36 MATERIALS SCIENCE↗