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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Solving high-dimensional partial integral differential equations: The finite expression method

Partial integro-differential equations (PIDEs) have broad applications in the sciences, from electro-magnetism to options pricing. Here, in this paper, we introduce a new finite expression method (FEX) to solve PIDEs. This approach builds upon the original FEX and its inherent advantages with new advances: 1) A novel method of parameter grouping is proposed to reduce the number of coefficients in high-dimensional function approximation; 2) A Taylor series approximation method is implemented to significantly improve the computational efficiency and accuracy of the evaluation of the integral terms of PIDEs. The new FEX based method, denoted FEX-PG to indicate the addition of the parameter grouping (PG) step to the algorithm, provides both high accuracy and interpretable numerical solutions, with the outcome being an explicit equation that facilitates intuitive understanding of the underlying solution structures. These features are often absent in traditional methods, such as finite element methods (FEM) and finite difference methods, as well as in deep learning-based approaches. To benchmark our method against recent advances, we apply the new FEX-PG to solve benchmark PIDEs in the literature. In high-dimensional settings, FEX-PG exhibits strong and robust performance, achieving relative errors on the order of single precision machine epsilon, significantly outperforming existing approaches based on neural networks.

Combinatorial optimization↗
DOE OSTI2023

A Workflow for Accelerating Multimodal Data Collection for Electrodeposited Films

Abstract Future machine learning strategies for materials process optimization will likely replace human capital-intensive artisan research with autonomous and/or accelerated approaches. Such automation enables accelerated multimodal characterization that simultaneously minimizes human errors, lowers costs, enhances statistical sampling, and allows scientists to allocate their time to critical thinking instead of repetitive manual tasks. Previous acceleration efforts to synthesize and evaluate materials have often employed elaborate robotic self-driving laboratories or used specialized strategies that are difficult to generalize. Herein we describe an implemented workflow for accelerating the multimodal characterization of a combinatorial set of 915 electroplated Ni and Ni–Fe thin films resulting in a data cube with over 160,000 individual data files. Our acceleration strategies do not require manufacturing-scale resources and are thus amenable to typical materials research facilities in academic, government, or commercial laboratories. The workflow demonstrated the acceleration of six characterization modalities: optical microscopy, laser profilometry, X-ray diffraction, X-ray fluorescence, nanoindentation, and tribological (friction and wear) testing, each with speedup factors ranging from 13–46x. In addition, automated data upload to a repository using FAIR data principles was accelerated by 64x.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A machine learning approach for clinker quality prediction and nonlinear model predictive control design for a rotary cement kiln

Abstract Cement manufacturing is energy‐intensive (5Gj/t) and comprises a significant portion of the energy footprint of concrete systems. Incorporating modern monitoring, simulation and control systems will allow lower energy use, lower environmental impact, and lower costs of this widely used construction material. One of the goals of the CESMII roadmap project on the Smart Manufacturing of Cement included developing an analytical process model for clinker quality that includes the chemistry of the kiln feed and accounts for critical process variables. This predictive model will be used in nonlinear model predictive control system designed to significantly reduce process energy use while maintaining or improving product quality. In the cement manufacturing plant used in this study, the kiln feed (meal) is tested every 12 h and used to estimate the mineral composition of the cement kiln output (clinker) using the stoichiometry‐based Bogue's model and the expertise of the plant operators. During kiln operation, kiln output (clinker) is sampled and tested every 2 h to measure its chemical and mineral composition. The predicted and measured values of the clinker composition are used by the plant operators to adjust the kiln input stream and the production process characteristics to maintain stable operation and uniform product quality. However, the time delay between prediction and testing, along with inaccuracies inherent in the Bogue's model have made any process changes designed to minimize energy use problematic, especially in‐light of potential clinker quality issues that process changes often pose. A new analytical model that integrates quality information and process operation information has been developed from data collected from 2 years of production from an operating cement facility. To make the model fuel‐type‐independent, consumed heat energy was computed in the model instead of fuel type and amount. A Feedforward Network was trained and tailored from collected data. Many data‐based simulations were conducted to quantitatively evaluate the proposed model and the 5‐fold cross‐validation procedure was used to test the models. The resulting predictive model was shown to have a low root mean square error (MSE) with respect to the estimated clinker mineral composition compared to that using the industry standard “Bogue’ model”. The end goal of this work was to develop a single machine learning tool that allows the use of quality control data and process control variables to improve energy efficiency of the process in a continuous fashion. The proposed nonlinear model predictive control system (NMPC) can generate predicted kiln production characteristics based on manipulated variables in manner that accurately follows the target product quality values. Simulation results also show that the proposed model produced accurate predictions of kiln outputs that fell within the required constraints, while manipulating control variables within typical operational ranges.

Ali, Asem M.↗
DOE OSTI2024

Data-driven closure modeling for hypersonic turbulent flows

The Reynolds-averaged Navier–Stokes (RANS) equations remain a workhorse technology for simulating compressible fluid flows of practical interest. Due to model-form errors, however, RANS models can yield erroneous predictions that preclude their use on mission-critical problems. This report summarizes work performed from FY22-FY24 focused on improving RANS models for hypersonic flows using data-driven modeling and scientific machine learning. In this work we: 1. Investigate the current capabilities of RANS models in Sandia’s parallel aerodynamics and re-entry code (SPARC) for hypersonic flows with a focus on shock boundary layer interactions (SBLIs), 2. Assess several established corrections that exist in the literature aimed at improving predictions for SBLIs, 3. Develop improved models for the Reynolds stress tensor using tensor-basis neural networks, 4. Develop a neural-network-based variable turbulent Prandtl number model to reduce errors in wall heating in SBLIs. 5. Begin future investigations including employing the LIFE framework to improve wall heating predictions in SBLIs as well as the ensemble Kalman filter. We find that current RANS models in SPARC are deficient for complex SBLI flows. In particular, no current model jointly predicts wall heat flux, wall shear stress, and wall pressure with reasonable accuracy. Existing corrections help, but do not alleviate this issue altogether. The development of improved models for the Reynolds stress tensor via tensor-basis neural networks results in more predictive RANS models across a suite of low-speed and high-speed cases. For hypersonic boundary layers, the inclusion of the wall-normal Reynolds stress via TBNNs has an appreciable impact on the wall-normal momentum balance and wall quantities. However, we find that improvements to the Reynolds stress tensor do not address the over-prediction in wall heat flux in SBLIs. We find that a neural-network-based variable turbulent Prandtl number model systematically and substantially improves wall heating predictions for a range of SBLI cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Nuclear microreactor transient and load-following control with deep reinforcement learning

The economic feasibility of nuclear microreactors will depend on minimizing operating costs through advancements in autonomous control, especially when these microreactors are operating alongside other types of energy systems (e.g., renewable energy). This study explores the application of deep reinforcement learning (RL) for real-time drum control in microreactors, exploring performance in regard to load-following scenarios. By leveraging a point kinetics model with thermal and xenon feedback, we first establish a baseline using a single-output RL agent, then compare it against a traditional proportional–integral–derivative (PID) controller. This study demonstrates that RL controllers, including both single- and multi-agent RL (MARL) frameworks, can achieve similar or even superior load-following performance as traditional PID control across a range of load-following scenarios. In short transients, the RL agent was able to reduce the tracking error rate in comparison to PID by one half to one third. Over extended 300-minute load-following scenarios in which xenon feedback becomes a dominant factor, PID maintained better accuracy, but RL still remained within a 1% error margin despite being trained only on short-duration scenarios. This highlights RL’s strong ability to generalize and extrapolate to longer, more complex transients, affording substantial reductions in training costs and reduced overfitting. Furthermore, when control was extended to multiple drums, MARL enabled independent drum control as well as maintained reactor symmetry constraints without sacrificing performance---an objective that standard single-agent RL could not learn. We also found that, as increasing levels of Gaussian noise were added to the power measurements, the RL controllers were able to maintain lower error rates than PID, and to do so with at least 10% and upwards of 150% less control effort. These findings illustrate RL's potential for autonomous nuclear reactor control, laying the groundwork for future integration into high-fidelity simulations and experimental validation efforts.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Building thermal dynamics modeling with deep transfer learning using a large residential smart thermostat dataset

Understanding thermal dynamics and obtaining the computational model of residential buildings enable its scaled application in energy retrofits, control optimization and decarbonization. In this paper, we present a deep learning approach to model building thermal dynamics with smart thermostat data collected from residential buildings, with the goal to investigate model generalizability. In the first stage, we developed and compared different Deep Learning architectures including Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM) models and CNN-LSTM to predict indoor air temperature in a multi-step time horizon. In the second stage, we implemented a Transfer Learning (TL) process, which aims to improve the prediction performance on a new set of buildings (targets), exploiting the knowledge of related or similar buildings (sources). Different TL strategies and source model identification methods were investigated. The study showed that the CNN-LSTM performed the best among the architectures compared, with an average Mean Absolute Error (MAE) of 0.26 °C for one-hour-ahead (twelve 5-min future steps) predictions. Furthermore, the results showed that freezing the LSTM layer and fine-tuning the other layers of the CNN-LSTM achieved the best performance among four TL strategies, which further improved the performance with respect to a machine learning approach by 10%, and proving the effectiveness and generalizability of the proposed approach. A comparison of three different source model identification methods showed that randomly selecting source models constrained by similar building characteristics can provide good TL performance while retaining simplicity comparing with other quantitative source identification methods.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

High-throughput, Ultra-fast Laser Sintering of Ceramics and AI Based Prediction on Processing-Microstructure-Property Relationships

We report high-throughput, ultra-fast laser sintering of alumina sample array and characterization of sample units’ microstructure and hardness, as a fast exploration of laser processing parameters, microstructure, and property. These experimental data were used to train machine-learning (ML) models. Accurate ML predictions were demonstrated for the processing-microstructure-property relationship, specifically in (1) prediction of the microstructure of alumina under arbitrary laser power and (2) prediction of the expected microstructure from the desired hardness. An independent neural network was developed and showed that ML-predicted microstructure had less than 10% error from real ones, in terms of projected hardness. To monitor the microstructure during laser sintering, we demonstrated an ML model that can instantaneously predict ceramic’s microstructure at the laser spot, based on the laser spot brightness. The ML model can generate more than 10 predictions per second, and the error in average grain size was less than 5% from the experimental observations.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Correcting for filter-based aerosol light absorption biases at the Atmospheric Radiation Measurement program's Southern Great Plains site using photoacoustic measurements and machine learning

Abstract. Measurement of light absorption of solar radiation by aerosols is vital for assessing direct aerosol radiative forcing, which affects local and global climate. Low-cost and easy-to-operate filter-based instruments, such as the Particle Soot Absorption Photometer (PSAP), that collect aerosols on a filter and measure light attenuation through the filter are widely used to infer aerosol light absorption. However, filter-based absorption measurements are subject to artifacts that are difficult to quantify. These artifacts are associated with the presence of the filter medium and the complex interactions between the filter fibers and accumulated aerosols. Various correction algorithms have been introduced to correct for the filter-based absorption coefficient measurements toward predicting the particle-phase absorption coefficient (Babs). However, the inability of these algorithms to incorporate into their formulations the complex matrix of influencing parameters such as particle asymmetry parameter, particle size, and particle penetration depth results in prediction of particle-phase absorption coefficients with relatively low accuracy. The analytical forms of corrections also suffer from a lack of universal applicability: different corrections are required for rural and urban sites across the world. In this study, we analyzed and compared 3 months of high-time-resolution ambient aerosol absorption data collected synchronously using a three-wavelength photoacoustic absorption spectrometer (PASS) and PSAP. Both instruments were operated on the same sampling inlet at the Department of Energy's Atmospheric Radiation Measurement program's Southern Great Plains (SGP) user facility in Oklahoma. We implemented the two most commonly used analytical correction algorithms, namely, Virkkula (2010) and the average of Virkkula (2010) and Ogren (2010)–Bond et al. (1999) as well as a random forest regression (RFR) machine learning algorithm to predict Babs values from the PSAP's filter-based measurements. The predicted Babs was compared against the reference Babs measured by the PASS. The RFR algorithm performed the best by yielding the lowest root mean square error of prediction. The algorithm was trained using input datasets from the PSAP (transmission and uncorrected absorption coefficient), a co-located nephelometer (scattering coefficients), and the Aerosol Chemical Speciation Monitor (mass concentration of non-refractory aerosol particles). A revised form of the Virkkula (2010) algorithm suitable for the SGP site has been proposed; however, its performance yields approximately 2-fold errors when compared to the RFR algorithm. To generalize the accuracy and applicability of our proposed RFR algorithm, we trained and tested it on a dataset of laboratory measurements of combustion aerosols. Input variables to the algorithm included the aerosol number size distribution from the Scanning Mobility Particle Sizer, absorption coefficients from the filter-based Tricolor Absorption Photometer, and scattering coefficients from a multiwavelength nephelometer. The RFR algorithm predicted Babs values within 5 % of the reference Babs measured by the multiwavelength PASS during the laboratory experiments. Thus, we show that machine learning approaches offer a promising path to correct for biases in long-term filter-based absorption datasets and accurately quantify their variability and trends needed for robust radiative forcing determination.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

IMPROVING THE ACCURACY OF COMPOSITE METHODS: A G4MP2 METHOD WITH G4-LIKE ACCURACY AND IMPLICATIONS FOR MACHINE LEARNING

G4MP2 theory has proven to be a reliable and accurate quantum chemical composite method for the calculation of molecular energies using an approximation based on second-order perturbation theory to lower computational costs compared to G4 theory. However, it has been found to have significantly increased errors when applied to larger organic molecules with 10 or more nonhydrogen atoms. We report here on an investigation of the cause of the failure of G4MP2 theory for such larger molecules. One source of error is found to be the "higher-level correction (HLC)", which is meant to correct for deficiencies in correlation contributions to the calculated energies. This is because the HLC assumes that the contribution is independent of the element and the type of bonding involved, both of which become more important with larger molecules. We address this problem by adding an atom-specific correction, dependent on atom type but not bond type, to the higher-level correction. We find that a G4MP2 method that incorporates this modification of the higher-level correction, referred to as G4MP2A, becomes as accurate as G4 theory (for computing enthalpies of formation) for a test set of molecules with less than 10 nonhydrogen atoms as well as a set with 10-14 such atoms, the set of molecules considered here, with a much lower computational cost. The G4MP2A method is also found to significantly improve ionization potentials and electron affinities. Finally, we implemented the G4MP2A energies in a machine learning method to predict molecular energies.

Dandu, Naveen↗
DOE OSTI2024

Enriching OpenStreetMap network data for transportation applications: Insights into the impact of urban congestion on accessibility

OpenStreetMap (OSM) data is a valuable open-source resource for various transportation, traffic, and planning applications. However, OSM network data lack operating traffic speed information, which is critical for transport planning and operations. Addressing this shortcoming, this study leverages commercial vendor data (to serve as ground truth) with exogenous, open-source variables characterizing local transport infrastructure, land use, and demographic information to predict average congested traffic speeds on OSM networks. Three machine-learning models were tested and estimated for OSM links with and without speed limit information in the Denver metropolitan region. Among these, XGBoost performed best, with mean absolute errors of 3.27 and 3.62 mph for links with and without speed limits, respectively. The developed models accurately predicted traffic speeds for different hours and days of the week compared to ground truth data. Using these predicted speeds, drive accessibility scores were computed for the Denver region for different time periods using the Mobility Energy Productivity (MEP) metric to understand the impact of congestion on energy-efficient accessibility. Results show that congestion-adjusted drive accessibility can be significantly lower compared to accessibility calculated using free flow speeds. Specifically, weekday evening hours saw a 42 % drop in accessibility due to reduced speeds, particularly around downtown Denver. Across the Denver metro region, approximately half as many opportunities and jobs are accessible in under 20 min by car during the evening peak period relative to free flow conditions. These findings underscore the importance of using congestion-adjusted operating speeds rather than speed limits in accessibility calculations, as reliance on speed limits can substantially overestimate energy-efficient drive accessibility in large, car-centric cities susceptible to significant congestion. In conclusion, the methodology presented here could further enrich OSM network data, making them useful for an even broader range of transportation applications.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2024

A tutorial review of machine learning-based model predictive control methods

Abstract This tutorial review provides a comprehensive overview of machine learning (ML)-based model predictive control (MPC) methods, covering both theoretical and practical aspects. It provides a theoretical analysis of closed-loop stability based on the generalization error of ML models and addresses practical challenges such as data scarcity, data quality, the curse of dimensionality, model uncertainty, computational efficiency, and safety from both modeling and control perspectives. The application of these methods is demonstrated using a nonlinear chemical process example, with open-source code available on GitHub. The paper concludes with a discussion on future research directions in ML-based MPC.

Wu, Zhe [Department of Chemical and Biomolecular E↗
NASA NTRS1989

An improved adaptive control for repetitive motion of robots

An adaptive control algorithm is proposed for a class of nonlinear systems, such as robotic manipulators, which is capable of improving its performance in repetitive motions. When the task is repeated, the error between the desired trajectory and that of the system is guaranteed to decrease. The design is based on the combination of a direct adaptive control and a learning process. This method does not require any knowledge of the dynamic parameters of the system.

Pourboghrat, F.↗
NASA NTRS1992

Sound transmission reduction with intelligent panel systems

Experimental and theoretical investigations are performed of the use of intelligent panel systems to control the sound transmission and radiation. An intelligent structure is defined as a structural system with integrated actuators and sensors under the guidance of an adaptive, learning type controller. The system configuration is based on the Active Structural Acoustic Control (ASAC) concept where control inputs are applied directly to the structure to minimize an error quantity related to the radiated sound field. In this case multiple piezoelectric elements are employed as sensors. The importance of optimal shape and location is demonstrated to be of the same order of influence as increasing the number of channels of control.

Fuller, Chris R.↗
NASA NTRS2011

Adaptive System Modeling for Spacecraft Simulation

This invention introduces a methodology and associated software tools for automatically learning spacecraft system models without any assumptions regarding system behavior. Data stream mining techniques were used to learn models for critical portions of the International Space Station (ISS) Electrical Power System (EPS). Evaluation on historical ISS telemetry data shows that adaptive system modeling reduces simulation error anywhere from 50 to 90 percent over existing approaches. The purpose of the methodology is to outline how someone can create accurate system models from sensor (telemetry) data. The purpose of the software is to support the methodology. The software provides analysis tools to design the adaptive models. The software also provides the algorithms to initially build system models and continuously update them from the latest streaming sensor data. The main strengths are as follows: Creates accurate spacecraft system models without in-depth system knowledge or any assumptions about system behavior. Automatically updates/calibrates system models using the latest streaming sensor data. Creates device specific models that capture the exact behavior of devices of the same type. Adapts to evolving systems. Can reduce computational complexity (faster simulations).

Thomas, Justin↗
NASA NTRS2013

Regression Analysis of Top of Descent Location for Idle-thrust Descents

In this paper, multiple regression analysis is used to model the top of descent (TOD) location of user-preferred descent trajectories computed by the flight management system (FMS) on over 1000 commercial flights into Melbourne, Australia. The independent variables cruise altitude, final altitude, cruise Mach, descent speed, wind, and engine type were also recorded or computed post-operations. Both first-order and second-order models are considered, where cross-validation, hypothesis testing, and additional analysis are used to compare models. This identifies the models that should give the smallest errors if used to predict TOD location for new data in the future. A model that is linear in TOD altitude, final altitude, descent speed, and wind gives an estimated standard deviation of 3.9 nmi for TOD location given the trajec- tory parameters, which means about 80% of predictions would have error less than 5 nmi in absolute value. This accuracy is better than demonstrated by other ground automation predictions using kinetic models. Furthermore, this approach would enable online learning of the model. Additional data or further knowl- edge of algorithms is necessary to conclude definitively that no second-order terms are appropriate. Possible applications of the linear model are described, including enabling arriving aircraft to fly optimized descents computed by the FMS even in congested airspace. In particular, a model for TOD location that is linear in the independent variables would enable decision support tool human-machine interfaces for which a kinetic approach would be computationally too slow.

trajectory prediction↗
DOE OSTI2022

Design of a neutral thermal scattering (NeTS) module for hydrogen in light water

The accurate representation of thermal scattering law (TSL) data is integral to the design and characterization of many modern nuclear systems, particularly those using light water as a moderator/coolant. As a material-dependent distribution over energy-momentum phase space, the TSL may exhibit a variety of unique and relevant conditional (e.g., temperature, pressure) and compositional (e.g., porosity, stoichiometry, radiation damage) dependencies. Currently, there are various approaches to incorporate temperature dependence, which is especially important in coupled neutronic-thermal hydraulic simulations. In each approach, there is an inherent tradeoff between memory consumption and accuracy. Some techniques require tens to hundreds of MBs or more, while others fail to reproduce the underlying data to within 10% error over the considered input domain, despite having a reduced storage burden. This work aims to address both sides of the tradeoff simultaneously by implementing a novel deep learning (DL) approach to TSL representation. The neural thermal scattering (NeTS) concept, which is amenable to an arbitrary number of dependencies, is demonstrated via the inclusion of temperature dependence into a highly compact, highly accurate functional form of the multi- variate TSL (i.e., S(α, β, T)) for hydrogen in light water. Resulting storage requirements are on the order of 100 kB, and median and maximum percent deviations are on the order of 0.1% and 1%, respectively. These measures represent a step improvement over previous techniques. Notably, the developed neural network and feature methodology build on those employed in prior work on beryllium oxide. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Improving deep learning performance for predicting large-scale geological ${{CO}_{2}}$ sequestration modeling through feature coarsening

Physics-based reservoir simulation for fluid flow in porous media is a numerical simulation method to predict the temporal-spatial patterns of state variables (e.g. pressure p) in porous media, and usually requires prohibitively high computational expense due to its non-linearity and the large number of degrees of freedom (DoF). This work describes a deep learning (DL) workflow to predict the pressure evolution as fluid flows in large-scale 3-dimensional(3D) heterogeneous porous media. In particular, we develop an efficient feature coarsening technique to extract the most representative information and perform the training and prediction of DL at the coarse scale, and further recover the resolution at the fine scale by spatial interpolation. We validate the DL approach to predict pressure field against physics-based simulation data for a field-scale 3D geologic CO 2 sequestration reservoir model. We evaluate the impact of feature coarsening on DL performance, and observe that the feature coarsening not only decreases the training time by >74% and reduces the memory consumption by >75%, but also maintains temporal error 0.63% on average. Besides, the DL workflow provides predictive efficiency with 1406 times speedup compared to physics-based numerical simulation. The key findings from this research significantly improve the training and prediction efficiency of deep learning model to deal with large-scale heterogeneous reservoir models, and thus it can also be further applied to accelerate workflows of history matching and reservoir optimization for close-loop reservoir management.

58 GEOSCIENCES↗
DOE OSTI2024

Unveiling the Potential of MeshGraphNets for Predicting Subsurface Evolution in Carbon Storage Projects

This is the conference paper accompanying an oral presentation “Unveiling the Potential of MeshGraphNets for Predicting Subsurface Evolution in Carbon Storage Projects” at the 17th International Conference on Greenhouse Gas Control Technologies GHGT-17 held in Calgary, Canada, October 20-24 , 2024. Carbon capture and storage (CCS) technology is critical for mitigating climate change but requires effective subsurface reservoir management to ensure safe containment of injected CO2. Accurate predictions of reservoir pressure and saturation are essential for assessing long-term CCS performance. Traditional numerical simulations, while effective, are computationally intensive, time-consuming, and constrained by data discretization. Previous work has shown the effectiveness of MeshGraphNets (MGN), a graph-based machine learning framework, as an innovative alternative for predicting reservoir behavior. MGN leverages graph neural networks (GNNs) and mesh representations to model complex geological formations, offering superior adaptability across different discretizations and reservoir configurations. Classic MGN implementations utilize an autoregressive technique to predict future behavior based on current predictions, but this technique is hampered by error accumulation over time. To enhance the model accuracy in time-series predictions, this study implemented a multi-step rollout strategy that integrates autoregressive predictions during training to stabilize prediction of saturation over time. Using the Illinois Basin – Decatur Project (IBDP) dataset, comprising 100 simulations of CO2 injection, pressure, and saturation changes, the framework demonstrated its ability to learn spatial dependencies and temporal dynamics. With inputs including permeabilities, porosities, and injection rates, MGN accurately predicted CO2 plume evolution over time, even with limited training data. Moreover, the addition of a multi-step rollout procedure during training improved the ability of MGN to predict stably over time by ~15%. This research positions MGN, enhanced with multi-step rollout capabilities, as a robust and efficient tool for CCS applications. It advances the field by enabling precise, computationally efficient predictions of reservoir behavior, providing a foundation for the broader adoption of machine learning frameworks in CCS and other geoscience domains.

Holcomb, Paul↗