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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Simulating Atmospheric Processes in Earth System Models and Quantifying Uncertainties With Deep Learning Multi‐Member and Stochastic Parameterizations

Abstract Deep learning is a powerful tool to represent subgrid processes in climate models, but many application cases have so far used idealized settings and deterministic approaches. Here, we develop stochastic parameterizations with calibrated uncertainty quantification to learn subgrid convective and turbulent processes and surface radiative fluxes of a superparameterization embedded in an Earth System Model (ESM). We explore three methods to construct stochastic parameterizations: (a) a single Deep Neural Network (DNN) with Monte Carlo Dropout; (b) a multi‐member parameterization; and (c) a Variational Encoder Decoder with latent space perturbation. We show that the multi‐member parameterization improves the representation of convective processes, especially in the planetary boundary layer, compared to individual DNNs. The respective uncertainty quantification illustrates that methods (b) and (c) are advantageous compared to a dropout‐based DNN parameterization regarding the spread of convective processes. Hybrid simulations with our best‐performing multi‐member parameterizations remained challenging and crash within the first days. Therefore, we develop a pragmatic partial coupling strategy relying on the superparameterization for condensate emulation. Partial coupling reduces the computational efficiency of hybrid Earth‐like simulations but enables model stability over 5 months with our multi‐member parameterizations. However, our hybrid simulations exhibit biases in thermodynamic fields and differences in precipitation patterns. Despite this, the multi‐member parameterizations enable improvements in reproducing tropical extreme precipitation compared to a traditional convection parameterization. Despite these challenges, our results indicate the potential of a new generation of multi‐member machine learning parameterizations leveraging uncertainty quantification to improve the representation of stochasticity of subgrid effects.

Behrens, Gunnar [Deutsches Zentrum für Luft‐ und R↗
DOE OSTI2020

Quantifying Uncertainties of Microscopic Nuclear Theories

The goal of this project was to produce modernized nuclear data libraries of light ion fusion reactions and actinide fission product yields. Such libraries are essential input in both stockpile science but also fundamental science (nucleosynthesis, superheavy nuclei). When such libraries are used to model complex processes involving exotic, very short-lived nuclei that have not been measured experimentally, the underlying nuclear data come from theoretical models, the predictive power of which needs to be quantified, together with its uncertainties. By teaming up nuclear theorists and statisticians, we built comprehensive theoretical frameworks based on the most fundamental theories of fusion and fission that we coupled for the first time with a Bayesian framework with machine learning techniques for uncertainty quantification. Our results include: (1) statistical emulators for neutron-alpha scattering, and the fission product mass yields of neutron-induced fission of 239 Pu, which will enable developers to generate random realizations of the corresponding data for uncertainty quantification (UQ) in applications; (2) the first complete and most accurate ab initio prediction of the S-factor for proton capture on 7 Be, which – combined with UQ – may become the recommended value at solar energies in the next review of solar fusion cross sections; (3) statistical emulators for fission mass yields in the neutron-induced fission of 239 Pu; (4) the first quantification of how uncertainties in nuclear forces impact fission properties that are relevant in nucleosynthesis simulations to explain how heavy elements are formed in the Cosmos.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Machine learning materials properties with accurate predictions, uncertainty estimates, domain guidance, and persistent online accessibility

One compelling vision of the future of materials discovery and design involves the use of machine learning (ML) models to predict materials properties and then rapidly find materials tailored for specific applications. However, realizing this vision requires both providing detailed uncertainty quantification (model prediction errors and domain of applicability) and making models readily usable. At present, it is common practice in the community to assess ML model performance only in terms of prediction accuracy (e.g. mean absolute error), while neglecting detailed uncertainty quantification and robust model accessibility and usability. Here, we demonstrate a practical method for realizing both uncertainty and accessibility features with a large set of models. We develop random forest ML models for 33 materials properties spanning an array of data sources (computational and experimental) and property types (electrical, mechanical, thermodynamic, etc). All models have calibrated ensemble error bars to quantify prediction uncertainty and domain of applicability guidance enabled by kernel-density-estimate-based feature distance measures. All data and models are publicly hosted on the Garden-AI infrastructure, which provides an easy-to-use, persistent interface for model dissemination that permits models to be invoked with only a few lines of Python code. We demonstrate the power of this approach by using our models to conduct a fully ML-based materials discovery exercise to search for new stable, highly active perovskite oxide catalyst materials.

domain of applicability↗
DOE OSTI2021

From Machine Learning to Nuclear Digital Twins

This presentation provides multiple case studies of Machine Learning, Uncertainty Quantification, Reduced Order Modeling, to achieve digital transformation and provide the components for nuclear digital twinning. The presentation is for an international virtual event titled: Consultancy Meeting on Applications of AI and Pattern Recognition Techniques for Uncertainty Quantification in Nuclear Power Modelling and Simulation held Oct 21-22, 2021.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Initial Efforts Organizing WPNCS SG-8: Preservation of Expert Knowledge and Judgement Applied to Criticality Benchmarks

The Working Party on Nuclear Criticality Safety (WPNCS) under the guidance of the Organization for Economic Co-operation and Development (OECD) Nuclear Energy Agency (NEA) has over 20 years of experience addressing concerns related to static and transient configurations encountered within the nuclear fuel cycle: fuel fabrication, transportation, reprocessing, storage, and geological disposal. One of the cornerstone activities of the WPNCS is the International Criticality Safety Benchmark Evaluation Project (ICSBEP), which was established to identify a comprehensive set of criticality benchmark data, evaluate the data, including quantification of overall uncertainties; compile the data into a standardized format, perform sample calculations utilizing modern nuclear data sets and codes utilized in nuclear criticality safety, and formally document the work into a single source of verified benchmark data. Annually, members of the ICSBEP Technical Review Group (TRG) contribute evaluated benchmark data that undergoes comprehensive technical review prior to publication in the ICSBEP Handbook. In the years since the ICSBEP was established, there has been much work to prepare benchmark data to support validation activities in nuclear criticality safety. The 2020 edition of the ICSBEP Handbook contains acceptable benchmark specifications for 5,053 critical, subcritical, or near-critical configurations in 582 benchmark evaluations. Modern benchmark development benefits from decades of experienced international participants, a well-established handbook format, supplementary guides to deal with uncertainty quantification, and a comprehensive review process based upon independent reviews from international experts. The ICSBEP Handbook also contains 838 configurations deemed unacceptable to support criticality safety efforts. They are recorded, with the reasoning for their rejection, to preserve the experimental data, prevent reevaluation of data that are incomplete or contain known errors, and/or to potentially allow future reevaluation of the experiment pending the identification of sufficient data to resolve identified inconsistencies and errors. Users of the ICSBEP Handbook today might notice that the rigor and quality of modern criticality safety benchmarks is much greater than those prepared within the initial decade of the project. Benchmarks with 1s uncertainties in k eff greater than 1% were traditionally rejected unless they were identified as unique experiment types that encompassed materials, fuels, or designs not available from other benchmark experiments. However, benchmarks developed using modern experimental techniques and practices typically have uncertainties on the order of a few tenths of a percent. There have been ongoing efforts to improve the overall quality of previously published benchmark evaluations. Seventy-eight evaluations, containing approximately 600 configurations, have been revised just within the past decade. An additional eleven benchmarks are under revision for updated release in the 2020 edition of the ICSBEP Handbook. If some of the historic benchmarks were resubmitted in their current form to the TRG today, they would be rejected due to lack of data, missing components in the uncertainty analysis, or incomplete benchmark model development. The use of historic criticality safety benchmarks that underestimate the total uncertainty, lack properly quantified biases, or provide inadequate benchmark specifications do not sufficiently support modern criticality safety and nuclear data efforts. Although the ICSBEP Handbook is recognized by regulating bodies to support criticality safety, users are required to justify their reasons to ignore historic benchmark data and include additional safety margins within their designs. Discussions were held at the WPNCS 23rd Annual Meeting in September 2019 regarding the aforementioned issues. The resultant decision was to establish Subgroup 8 (SG-8): Preservation of Expert Knowledge and Judgement Applied to Criticality Benchmarks. The current activities of SG-8 are discussed herein.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

GPR_calculator: An on-the-fly surrogate model to accelerate massive nudged elastic band calculations

We present GPR_calculator, a package based on Python and C++ programming languages to build an on-the-fly surrogate model using Gaussian Process Regression (GPR) to approximate computationally expensive electronic structure calculations. The key idea is to dynamically train a GPR model during the simulation that can accurately predict energies and forces with uncertainty quantification. When the uncertainty is high, the costly electronic structure calculation is performed to obtain the ground truth data, which is then used to update the GPR model. To illustrate the effectiveness of GPR_calculator, we demonstrate its application in Nudged Elastic Band (NEB) simulations of surface diffusion and reactions, achieving 3-10 times acceleration compared to pure ab initio calculations. The source code is available at https://github.com/MaterSim/GPR_calculator.

Gaussian process regression↗
DOE OSTI2023

Complete quantification of parametric uncertainties in ( d , p ) transfer reactions

Deuteron-induced transfer reactions are a popular probe in nuclear structure and nuclear astro physics studies. The interpretation of these transfer measurements relies on reaction theory that takes as input effective interactions between the nucleons and the target nucleus. Previous work quantified the uncertainty associated with the optical potentials between the nucleons and the target. In this study, we extend that work by also including the parameters of the mean field associated with the overlap function of the final bound state, thus obtaining the full parametric uncertainty on transfer observables. We use Bayesian Markov Chain Monte Carlo simulations to obtain parameter posterior distributions. We use elastic-scattering cross sections to constrain the optical potential parameters and use the asymptotic normalization coefficient of the final state to constrain the bound state interaction. We then propagate these posteriors to the transfer angular distributions and obtain confidence intervals for this observable. We study (d,p) reactions on 14 C, 16 O, and 48 Ca at energies in the range $E$ $d$ = 7 - 24 MeV. Our results show a strong reduction in uncertainty by using the asymptotic normalization coefficient as a constraint, particularly for those reactions most sensitive to ambiguities in the mean field. For those reactions, the importance of constraining the bound state interaction is equal to that of constraining the optical potentials. Furthermore, the case of 14 C is an outlier because the cross section is less sensitive to the nuclear interior. When minimal constraints are used on the parameters of the nucleon-target interaction, the 1σ uncertainties on the differential cross sections are large (~ 500-100%). However, if elastic-scattering data and the asymptotic normalization coefficient are used in the analysis, with an error of 10% (5%), this uncertainty reduces to ~ 30% (~ 15%).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Probabilistic neural networks for improved analyses with phenomenological R -matrix

Here we present a method for measurement analyses based on probabilistic deep neural networks that provide several advantages over conventional analyses with phenomenological models. These include predicting physical quantities directly from data, the rapid generation of statistically robust uncertainties, and the ability to bypass some parameters that may induce ambiguities and complications in data analysis. As deep learning methods make predictions through “black boxes,” the uncertainty quantification is typically challenging. We use a probabilistic framework that provides thorough uncertainty quantification and is straightforward to follow in practice. With the network architecture based on the Transformer, we demonstrate the current method for predicting nuclear resonance parameters from scattering data using the phenomenological R-matrix model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Assessment of coated cladding impact on large-break LOCA with TRACE-DAKOTA

Since 2011, the U.S. Department of Energy has launched new research and development (R&D) programs for developing new accident tolerant fuels (ATFs). These new fuel concepts are expected to bring several advancements in terms of plant safety. However, development, licensing, as well as deployment of ATF require a substantial investment among fuel vendors, operating utilities, and regulatory authorities. For ATF to be economically feasible, credited safety benefits may be necessary to provide an economic incentive for transition of nuclear power plants from Zr/UO2-based fuel technologies to ATFs. As a result, it is essential to evaluate the economic viability of ATF by conducting a comprehensive safety benefits study informed by R&D and demonstration studies. In the present work, based on the best estimate plus uncertainty methodology, sensitivity analysis and uncertainty quantification for key safety quantities under LB-LOCA are performed for the Peach Bottom boiling water reactor (BWR) with GE14 nuclear fuel design adopting the ATF concepts. A coupled TRACE-DAKOTA analysis framework is adopted to perform the uncertainty quantification. Based on the computational results and obtained statistics, the coping time increase, fuel performance improvement as well as the most dominating phenomena during the accident for Cr-coated cladding are investigated in detail. Overall, the results obtained are useful for subsequent plant PRA study and support a move to more modernized performance-based regulatory requirements to realize plant economic benefits.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Initial development of a generic fluoride salt-cooled reactor model

Fluoride high-temperature reactors (FHRs) are high-temperature, low-pressure reactor concepts that use tri-structural isotropic (TRISO) fuel and molten fluoride salt coolant. These reactors have the potential to provide both electrical power and high-temperature process heat. We used generic FHR parameters for a pebble-bed FHR to develop an initial model with fresh fuel for a generic FHR (gFHR) in MELCOR and SCALE (NEWT and KENO). In this paper, we present the development of our gFHR models, which will serve as the baseline for a sensitivity and uncertainty analysis to quantify the range of possible source terms for FHRs in severe accidents. We present MELCOR results for fuel and coolant temperatures through the core, a nodalization study for the steady-state thermal hydraulic model, and development of reactor physics models in SCALE. As this work progresses, these models will be used to calculate source terms for a loss-of-forced-flow accident and to conduct a sensitivity study on this accident to establish a range of possible source terms. SCALE will provide reactor physics parameters like isotopic inventory, decay heat generation, and temperature coefficients of reactivity. Using the uncertainty quantification tools within SCALE, we will generate distributions for those parameters and will use the uncertainty quantification code RAVEN or DAKOTA to sample those distributions in MELCOR to quantify the impact of reactor physics and thermal hydraulic uncertainties on FHR source terms. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Predicting Flow in Fracture Networks With Quantum Algorithms

Uncertainty quantification plays a crucial role in the modeling of subsurface flow. For instance, uncertainties in the properties of geologic fracture networks significantly impact flow, requiring numerous simulations to accurately estimate quantities of interest. However, each simulation is computationally expensive because it requires solving a large linear system to capture features that involve both small and large fractures. An example is in percolation, where the interaction of many small fractures (which cumulatively can have a large surface area) with the rock matrix must be modeled precisely. Quantum computing is an emerging tool with the potential to address this issue. Quantum algorithms offer a significant speedup in solving linear systems, achieving efficiencies that are challenging to match with classical approaches. These classical approaches include direct solvers, such as LU decomposition, and iterative methods, notably preconditioned conjugate gradient, commonly used in subsurface modeling to solve large sparse systems. However, applying quantum algorithms to geologic fracture flow requires careful attention to algorithmic and problem-specific constraints to fully realize this quantum advantage. In this work we describe a quantum algorithm for generalized Monte Carlo applications with a quadratic speedup over the classical approaches which can be combined with the quantum speedup, currently under investigation, for solving quantum linear systems for subsurface flow. We show that for quantum algorithms the computational cost of estimating a quantity of interest for a statistical ensemble of networks is roughly the same as that of a single realization, essentially implying that one can get uncertainty quantification for free.

58 GEOSCIENCES↗
DOE OSTI2024

Bayesian Analysis of TRISO Fuel: Quantifying Model Inadequacy, Incorporating Lower-Length-Scale Effects, and Developing Parallel Active Learning Capabilities

The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel-cycle systems. This program has been providing engineering-scale support for the continued development of BISON, a high-fidelity, high-resolution fuel performance tool. Fuel behavior in nuclear reactors is governed by a complex network of mechanisms that interact with various other physics aspects in the reactor system. Any model developed to represent fuel behavior will likely be idealized, resulting in uncertainties when comparing their predictions against the observed data. In Fiscal Year (FY)-23, we initiated the Uncertainty Quantification (UQ) work by using Bayesian methods to establish a level of model trustworthiness and further improve it, with a particular emphasis on TRI-Structural isOtropic (TRISO) nuclear fuel. This year, we further expanded on that UQ work by investigating an approach to quantifying model inadequacy and accounting for lower-length scale (LLS) effects in TRISO silver (Ag) release modeling. Furthermore, we are implementing parallel active learning capabilities to reduce the computational cost (i.e., required computational resources and elapsed time) of performing UQ. Specifically, we utilized The Kennedy O’Hagan framework for Bayesian uncertainty quantification (KOH) to account for model inadequacy in TRISO Ag release predictions made by BISON. The KOH framework represents an improvement over the standard Bayesian framework used in FY-23. Explicitly accounting for model inadequacy in the Bayesian framework helps establish the level of experimental noise uncertainty in the Advanced Gas Reactor (AGR) data. We compared the inverse UQ results obtained from both the standard Bayesian and KOH frameworks in light of the AGR-2/3/4 data, and also compared the predictive UQ results obtained from these two frameworks in light of the AGR-1 data. Next, we investigated the impact of considering LLS effects in the Ag release simulations. We developed an expanded database of LLS simulated effective diffusivities for Ag, covering a wide range of microstructures and temperatures. Using this database, we developed a framework for incorporating LLS effects into the engineering-scale Ag release UQ. We developed both parametric and non-parametric approaches for bridging the length scales. We then investigated the inverse UQ results in light of the AGR-2/3/4 data and the predictive UQ results in light of the AGR-1 data, and compared the LLS-informed approach and the Arrhenius equation, which does not include microstructure information. Finally, we discussed implementing parallel active learning capabilities in the Multiphysics Object Oriented Simulation Environment (MOOSE)/BISON to reduce the computational cost (i.e., computational resources and elapsed time) of Bayesian UQ. For verification purposes, we first tested these new capabil ities on a species interaction problem. We then demonstrated them on the TRISO Ag release application, showing that parallel active learning capabilities can enhance the accuracy of UQ while also substantially reducing the computational cost in comparison to the reference methods developed in FY-23.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Machine learning enhanced predictions of ICRF heating: Overcoming numerical limitations via data curation

In this work, we present the development of robust surrogate models for Ion Cyclotron Range of Frequencies (ICRF) and High-Harmonic Fast Wave (HHFW) heating predictions in fusion plasmas. Building upon our previous efforts to achieve real-time capable models, we identify the cause of the outliers found using TORIC in certain HHFW heating scenarios. The outliers are observed to be spurious ion Bernstein wave (IBW)-like modes caused by a wavelength control algorithm designed to address challenging scenarios with high perpendicular wavenumbers. The effect arises from the modulation in the perpendicular susceptibility, which can induce sign reversal and IBW-like propagation for scenarios featuring normalized ion Larmor radius λ i ≫ 1. We use TORIC with this algorithm disabled to generate a novel HHFW-NSTX database that is free of outliers. Surrogate models trained on this database, including Random Forest Regressor (RFR), Multi-Layer Perceptrons, and Gaussian Process Regressors (GPR), demonstrate the ability to accurately predict HHFW heating profiles, with regression scores of R 2 ∈[0.93−0.99]. Additionally we demonstrate that it is possible to generalize predictions beyond training data by the use of both RFR and GPR models, enabling the prediction of scenarios previously limited to the original model. GPR models also provide uncertainty quantification, offering insights into model confidence. This work introduces a comprehensive Verification, Validation, and Uncertainty Quantification methodology for surrogate modeling, applicable not only to ICRF heating but also to other RF heating challenges and fusion physics problems. Beyond accelerated inference, these models show effective extrapolation capabilities, providing an alternative for addressing numerical challenges.

Artificial neural networks↗
DOE OSTI2026

Discovery of Probabilistic Dirichlet-to-Neumann Maps on Graphs

Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning Dirichlet-to-Neumann maps on graphs using Gaussian processes, specifically for problems where the data obey a conservation law arising from an underlying partial differential equation. Our approach combines discrete exterior calculus and nonlinear optimal recovery to infer relationships between vertex and edge values. This framework yields data-driven predictions with uncertainty quantification across the entire graph, even when observations are limited to a subset of vertices and edges. By minimizing the reproducing kernel Hilbert space norm while penalizing kernel complexity through maximum likelihood estimation, our method ensures that the resulting surrogate strictly enforces conservation laws without overfitting. We demonstrate our method on two representative applications: subsurface flow in fracture networks and arterial blood flow. Finally, the results demonstrate that the method maintains high accuracy and well-calibrated uncertainty estimates even under severe data scarcity, highlighting its potential for scientific applications where limited data and reliable uncertainty quantification are critical.

Dirichlet-to-Neumann map↗
DOE OSTI2020

Effects of Photovoltaic Module Materials and Design on Module Deformation Under Load

Quasi-static structural finite-element models of an aluminum-framed crystalline silicon photovoltaic module and a glass-glass thin-film module were constructed and validated against experimental measurements of deflection under uniform pressure loading. Specific practices in the computational representation of module assembly were identified as influential to matching experimental deflection observations. Additionally, parametric analyses using Latin hypercube sampling were performed to propagate input uncertainties related to module materials, dimensions, and tolerances into uncertainties in simulated deflection. Sensitivity analyses were performed on the uncertainty quantification datasets using linear correlation coefficients and variance-based sensitivity indices to elucidate key parameters influencing module deformation. Results identified edge tape and adhesive material properties as being strongly correlated to module deflection, suggesting that optimization of these materials could yield module stiffness gains at par with the conventionally structural parameters, such as glass thickness. This exercise verifies the applicability of finite-element models for accurately predicting mechanical behavior of solar modules and demonstrates a workflow for model-based parametric uncertainty quantification and sensitivity analysis. Finally, applications of this capability include the assessment of field environment loads, derivation of representative loading conditions for reduced-scale testing, and module design optimization, among others.

42 ENGINEERING↗
DOE OSTI2022

Estimation of process steady state with autoregressive models and Bayesian inference

To improve efficiency, separations engineers will typically design process circuits containing recirculating streams, which mix one or more of the process outputs with the feed material. Doing so can improve efficiency, but will cause a delay in the system reaching steady state conditions until the recirculating load mass flows stabilize. In testing separation circuits, engineers will often test a variety of factors and complete an analysis from sample results. Knowledge of if a process is at steady state, as well as the steady state conditions of a process, is essential for a valid techno-economic analysis. However, the definition of process steady state is often poorly defined, or does not include uncertainty quantification. If the performance of a process operating under two different sets of conditions are compared, an engineer who does not test for steady state or quantify steady state conditions risks producing a faulty analysis. In this work, a Bayesian statistical method for testing if all streams are at steady state is further motivated and then derived. Then after testing for steady state, the same model is used with a prior distribution that enforces a steady state assumption to estimate steady state conditions. Further, these methods were validated in a solvent extraction pilot plant where steady state conditions for all outflows were inferred with uncertainty quantification. Analysis is completed with functions available to the reader as part of the BayesMassBal (V 1.1.0) software package written in R.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2020

Solving Stochastic Inverse Problems for Property–Structure Linkages Using Data-Consistent Inversion and Machine Learning

Determining process–structure–property linkages is one of the key objectives in material science, and uncertainty quantification plays a critical role in understanding both process–structure and structure–property linkages. In this work, we seek to learn a distribution of microstructure parameters that are consistent in the sense that the forward propagation of this distribution through a crystal plasticity finite element model matches a target distribution on materials properties. This stochastic inversion formulation infers a distribution of acceptable/consistent microstructures, as opposed to a deterministic solution, which expands the range of feasible designs in a probabilistic manner. Furthermore, to solve this stochastic inverse problem, we employ a recently developed uncertainty quantification framework based on push-forward probability measures, which combines techniques from measure theory and Bayes’ rule to define a unique and numerically stable solution. This approach requires making an initial prediction using an initial guess for the distribution on model inputs and solving a stochastic forward problem. To reduce the computational burden in solving both stochastic forward and stochastic inverse problems, we combine this approach with a machine learning Bayesian regression model based on Gaussian processes and demonstrate the proposed methodology on two representative case studies in structure–property linkages.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A novel conditional generative model for efficient ensemble forecasts of state variables in large-scale geological carbon storage

Integrating monitoring data to efficiently update reservoir pressure and CO 2 plume distribution forecasts presents a significant challenge in geological carbon storage (GCS) applications. Inverse modeling techniques are commonly used to fuse observational data and refine reservoir model parameters, thereby improving state variable forecasts. However, these techniques often rely on linear or Gaussian assumptions, which can limit their effectiveness in accurately predicting state variables. Moreover, simulating large-scale three-dimensional (3D) GCS problems is computationally expensive, making iterative runs in inverse problems prohibitive. To address these challenges, we propose a conditional generative model utilizing the score-based diffusion method for real-time 3D pressure and saturation field distribution predictions. Our approach involves solving the score function with a mini-batch-based Monte Carlo estimator to generate labeled data. This data is subsequently employed to train a fully connected neural network, enabling it to learn the conditional sample generator within a supervised learning framework. This method enables the rapid generation of a large ensemble of predictions, facilitating comprehensive uncertainty quantification of state variables. Here we applied our method to forecast the dynamic 3D distributions of pressure and saturation fields over a 30-year injection period. The statistical assessment with low root mean square error (RMSE) values demonstrates that our method can accurately predict the spatiotemporal distributions of both pressure and saturation fields. Moreover, the developed conditional generative model shows high computational efficiency by generating 100 ensemble forecasts of 3D state variables in less than 10 min. The consistency between ensemble averages and ground truth values further illustrates the model’s capability to capture state variable dynamics during the CO 2 plume injection process. Notably, the ground truth values fall within the ensemble forecasts, indicating that our uncertainty quantification effectively captures variability and potential noise in the observations. Thus, the developed conditional generative model proves to be a more efficient, accurate, and practical tool for GCS applications, facilitating timely risk analysis and informed decision-making.

58 GEOSCIENCES↗