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DOE OSTI2024

Unifying Quantum Materials Modeling and Experiments: The Role of Machine Learning Interatomic Potentials

Computational experiments have emerged as a powerful complement to traditional experiments in the design of new materials. The development of machine learning (ML) and deep learning techniques, combined with database construction and data mining, has significantly enhanced traditional quantum mechanical methods. This synergy enables the rapid development of structure-property relationships. In this talk, I will discuss our recent efforts in applying Machine Learning Interatomic Potentials (MLIAPs) to accelerate materials modeling across various material classes and challenging applications where traditional methods fall short. First, I will highlight the success of MLIAPs in accurately modeling the melting behavior of complex materials. Our results demonstrate high fidelity with experimental observations and also with calculated reference melting temperatures. In the second application, I will discuss how MLIAPs are trained and applied to elucidate the interplay between segregation tendencies and surface reconstructions in CuNi alloys under oxidizing conditions. A key factor in the success of these MLIAP applications is the design of minimalistic yet flexible datasets along with a computational framework for training MLIAPs.

Saidi, Wissam↗

DOE OSTI2025

Low‐dimensional manifold learning for uncertainty quantification in complex multi‐scale stochastic systems

Broadly speaking, the goals of the project are to develop techniques to use manifold learning to develop reduced‐order and surrogate models for "hyper‐reduction" of very high‐dimensional complex multi‐scale systems. This is being achieved by employing a newly proposed form of manifold projection and learning that leverages recent advancements in computational geometry and data‐driven modeling. In particular, we are applying a manifold projection technique to project the solutions of very high‐dimensional systems onto the so‐called Grassmannmanifold, a Reimannian manifold comprised of orthonormal matrices. We then apply data‐driven machine learning techniques to classify the solutions on the manifold (e.g. clustering techniques) according to their proximity on the manifold and leverage a further nonlinear dimension reduction to organize the structured data on the manifold. Finally, we are developing novel techniques that enable us to directly interpolate the hyper‐reduced data such that we can predict the solution of the complex, high‐ dimensional system without need to call the full expensive computational model. Given their adherence to the underlying structure of the solution of the physical system, it is expected that these approximate solutions will be sufficiently constrained so as to (approximately) adhere to physical principles.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Embracing the unknown: Why uncertainty matters in deep learning

Most cutting-edge deep learning models are focused on only one thing: improving prediction accuracy. But in the real world, especially in high-stakes domains like science, medicine, and safety (e.g. self-driving cars), knowing what your model doesn't know can be just as important. My goal for this talk is to convince you that uncertainty quantification (UQ) is essential in deep learning. We’ll explore how existing UQ methods work, what they still get wrong, and how ideas from disciplines like astrophysics and environmental science are key to driving the development of better (more trustworthy) deep learning methods.

Nevin, Becky [Fermilab]↗

DOE OSTI2025

An Advanced Machine Learning and Artificial Intelligence System for Demonstrating Radiation Regulatory Compliance in DOE Accelerator Facilities

In this Phase II proposal, Applied Research LLC (ARLLC), Thomas Jefferson National Accelerator Facility (Jefferson Lab), and Old Dominion University (ODU) propose the combination of domain knowledge (beam characteristics, fixed structural shielding, earthen burden (the soil and foliage added to the dome of the experimental halls as additional shielding), etc.), machine learning (ML) and/or artificial intelligence (AI) to correlate a variety of multi-modal onsite signals and the radiation fields seen in accessible areas of the accelerator site and the site boundary. The ML/AI will consider the complex influence of environmental parameters affecting the radon contribution of the measurements, focusing on actual data obtained from Jefferson Lab. In Phase I, the coded beam and location data were fed into a deep learning model to predict doses at several designated locations in Jefferson Lab’s facility. Moreover, a dense radiation map was generated using only a sparse collection of the samples in a facility. In Phase II, we will develop a software prototype containing a radiation prediction algorithm, dense radiation map algorithms, and background noise prediction algorithms, with actual data used to evaluate the prototype. This work will provide a framework for evaluation of radiation measurement results around the site based on learned responses. In addition, the proposed approach allows more granular mapping of radiation levels. Better understanding and communication of these levels is related to the overall approach in keeping doses to personnel ALARA.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Machine Learning for Automated Weld Quality Monitoring and Control

Resistance Spot Welding (RSW) is a critical process in the automotive industry, valued for its cost-effectiveness, short cycle time, and robustness. However, achieving consistent high-quality joints remains challenging due to the complex interplay of various factors, like materials, processes, and manufacturing uncertainties, etc. Under the collaborative project between Oak Ridge National Laboratory (ORNL) and General Motors (GM), we have developed a robust and expansible machine learning (ML) framework aimed at enhancing quality control in RSW. By harnessing the power of machine learning, we have developed the ability to ensure every aspect of the welding process, from the initial process design stage to the final weld joint quality. The framework operates by analyzing a variety of data streams, including in-line process signals, process parameters, materials, and postprocessed weld joint data. Through this analysis, the models have been trained to detect deviations from optimal quality standards, leveraging their ability to identify signature data patterns and anomalies within in-line signals and construct complex correlations between these signals and weld quality parameters. Meanwhile, the machine learning framework is designed to adapt to a variety of materials, including high strength steels and aluminum alloys, etc. Its flexible architecture facilitates the incorporation of diverse data sources and features, enabling precise modeling and prediction across a broad range of material properties and weld quality variables. The expansible ML frameworks represent a promising transformation in weld quality monitoring and control, empowering industry to achieve high levels of efficiency, consistency, and reliability in manufacturing.

42 ENGINEERING↗

DOE OSTI2025

Non-destructive structural characterization of graphite components using mechanical resonance and deep learning

As compared to conventional nuclear reactors, microreactors have the potential to significantly reduce construction timelines and capital costs, decreasing the barriers for advanced nuclear reactor technologies. However, the lower power output of these microreactors (typically < 20 MWe) creates challenging economics if operation and maintenance costs cannot be sufficiently reduced. The compact size of these designs presents an opportunity for comprehensive in-situ structural health monitoring to provide real-time feedback in order to reduce operational costs associated with maintenance and downtime. Many microreactor concepts use graphite for both in-core neutron moderation and as a structural material, which has typically required some form of periodic and laborious inspection. This report provides a description and assessment of recent work with graphite to couple acoustic-based experimental measurements and characterization with machine learning models to mature structural health monitoring capabilities and generate benefits for the nuclear microreactor industry. With resilient embedded sensors in development in other programs funded by the US Department of Energy’s Office of Nuclear Energy and elsewhere, the work described herein builds upon previously funded efforts to mature non-destructive testing technology that relates measured vibrational signatures to structural changes, using a combination of new experimental measurements and machine learning processing. Building on past successful demonstrations of predictive workflows to identify structural changes in a hexagonal stainless steel test article with excellent acoustic propagation, we first performed baseline characterization on graphite samples with canonical geometries to ensure compatibility and confidence in the applied techniques for a material with distinctly different mechanical properties. In contrast to efforts in previous years, we worked exclusively with unidirectional vibration data that is more comparable to those expected from the existing embedded sensor technologies which are suitable for deployment in a reactor setting. Established acoustic and modern machine-learning-based characterization approaches were applied to the resulting datasets from these simple geometries. Both approaches were found to be highly capable of detecting even small geometric irregularities amongst nominally identical samples. As such, we then moved to testing these approaches for detection of artificial local stress perturbations introduced into a more complex geometry: a hexagonal block with drilled holes. A main outcome of this work is that a generalizable ML workflow can be used to detect and predict the characteristics of small artificial anomalies in a graphite component with a relevant geometry. While this work was performed using surficial vibration data, we expect the approach to be flexible and viable for other monitoring scenarios, such as those with different arrangements or types of sensor arrays. As compared to previously funded efforts, an existing ML workflow based on neural networks was enhanced through the addition of recently developed Fourier neural operators. As applied to previously collected and new vibration datasets, prediction accuracies of anomaly characterizations were greatly improved with minimal added computational cost. As trained on small durations of vibration data (tens of seconds) collected over a realistic number of locations, the model was able to reliably determine the presence of a subtle stress anomaly and begin to provide location estimates. Such an approach is likely to be viable for more relevant reactor damage scenarios for graphite components, such as progressive crack growth or creep.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Characterization and Quantification of Radiation-Induced Clusters/Precipitates in RPV Steels Using STEM-EDS and Machine Learning

Over the operational lifespan of a nuclear reactor, reactor pressure vessel (RPV) steels are subjected to significant neutron irradiation, resulting in complex microstructural changes and the consequent degradation of mechanical properties. Various physically motivated correlation models have been developed to predict neutron irradiation-induced embrittlement of RPVs under different irradiation conditions. However, the efficient and accurate characterizations and quantification of radiation-induced clusters in RPVs are still challenging, which will affect the precision of the predictive models for embrittlement of RPV components. In the DOE Visiting Faculty Program (VFP) research work at Oak Ridge National Lab (ORNL), I integrate machine learning to aid Scanning Transmission Electron Microscopy – Energy Dispersive X-ray Spectroscopy (STEM-EDS) analyses, which improve the characterization and quantification of radiation-induced clusters in RPV steels, thereby enabling more accurate predictions of material behavior under irradiation. The surveillance base- and welded- RPV steels were annealed at various temperatures of 340 °C, 450 °C and 500 °C for up to 168 hours, respectively. Afterwards, I have characterized radiation-induced clusters using advanced STEM-EDS techniques and subsequently applying machine learning algorithms to analyze and refine STEM-EDS datasets, enhancing the quantification of clusters compositions and distributions. In the end, an efficient workflow for integrating STEM-EDS data analysis with machine learning to address challenges including noise reduction has been developed. The completion of this VFP work will support bridge critical gaps in the accurate quantification of radiation-induced clusters in RPV steels using STEM-EDS and support the development of more precise models for predicting RPV embrittlement in the Light Water Reactor Sustainability program supported by Department of Energy and enhancing the collaboration between ORNL and Alred University. The outcome of the VFP project will leverage a few research papers submission to peer-reviewed journals in the relevant scientific field and a few oral presentations at national and international conferences.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Reliable and Efficient Machine Learning (Final Technical Report)

Modern scientific experiments generate massive amounts of data at a pace much faster than humans can manually analyze. While machine learning has revolutionized commercial data analysis (such as recommending movies or recognizing faces), applying these tools to complex scientific discovery is challenging because scientific answers must be precise, interpretable, and adhere to physical laws. The research under this project aims to develop new mathematical tools and computer algorithms specifically designed for scientific applications. Major progress has been made in automatically cleaning and deconstructing messy experimental data, analyzing the visual information of physical phenomena, determining the underlying physical variables, and providing rig orous mathematical analysis of interesting algorithms and concepts widely used in machine learning. This project addressed the critical gap between our ability to generate massive scientific data and our ability to extract interpretable information from it. We established mathematical foundations for Scientific Machine Learning (SciML) aimed at effective data analytics and automated discovery. Our work focused on three core objectives: (1) developing reliable feature extraction methods for dynamic high-dimensional data, (2) establishing mathematical foundations for discovering dynamics via neural networks, and (3) creating rigorous optimization techniques for these models. Key outcomes come from two fronts. On the practical side, they include the development of algorithms that significantly enhance the extraction of signals from field data, as well as the capability to handle situations that exhibit smooth variations or physical stretching due to temperature changes. They also include the creation of an automated framework for discovering fundamental state variables from raw experimental data, demonstrating the ability to identify intrinsic physical dimensions without prior knowledge of the governing laws. On the theoretical front, the research results in theoretical advances in Optimal Transport, a widely used notion in SciML, specifically regarding functions with fixed-size nodal sets, provide sharp bounds relevant to uncertainty quantification. Meanwhile, the outcomes also include the establishment of convergence theories for nonlocal gradient descent methods, enabling robust optimization with noisy data in high-dimensional settings commonly encountered in scientific modeling. The project also helps creating opportunities to train the next generation of researchers, equipping them with the necessary technical skills for today’s workplace and preparing them for future advances.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Deep Learning for Fish Identification from Sonar Data (CRADA 481 Final Report)

In eastern regions of the United States, the American eel is a species of management and regulatory concern because of significant population declines, despite the species’ previous abundance in all tributaries of rivers flowing into the Atlantic Ocean. The American eel is also a candidate for listing under the U.S. Endangered Species Act. While hydropower construction and operation are only one of several factors contributing to this population decline, such a listing could impose additional regulatory challenges for a large number of hydropower projects. In this CRADA project, we improved technologies for identifying migrating eels with the goal of reducing the cost and time required for future American eel hydropower impact assessment and mitigation studies, while maintaining accuracy. We built on results from a previous FOA project (FOA# DE-FOA-0001662), led by the Electric Power Research Institute (EPRI), which developed a highly accurate, deep-learning method for identifying migrating eels from imaging sonar data. The current study aimed to further optimize this deep-learning model, originally designed for image classification, and to develop an object detection software capable of identifying fish from sonar videos in real time, enabling the detection of events like fish migrations and specific species, such as the American eel, at hydropower dams. The data conversion algorithms were packaged as software with a graphical user interface, and the software is evaluated by external collaborators. We focused on the American eel in this project and explored the transferability of the developed deep learning models to the sea lamprey, given the similar body shape and swimming behavior between the two species.

13 HYDRO ENERGY↗

DOE OSTI2025

Hybrid learning techniques for scientific data reduction with performance guarantees

The research initiatives supported by the U.S. Department of Energy (DOE) Grant DE-SC0022265 are fundamentally aimed at pioneering advanced machine learning (ML) techniques for scientific data compression within high-performance computing (HPC) environments. This comprehensive body of work addresses the critical challenge posed by the exponential growth of data generated by scientific simulations in domains such as fusion energy, climate modeling, and computational fluid dynamics (CFD). A core objective is to develop compression algorithms that achieve substantial data reduction—often by orders of magnitude—while rigorously ensuring the fidelity of both the primary data (PD) and scientifically crucial derived quantities of interest (QoI). The methodologies deployed under this grant integrate sophisticated deep learning architectures, prominently featuring autoencoders, advanced generative models like conditional diffusion, and hybrid learning techniques. Key innovations include the development of Guaranteed Autoencoders (GAE) and the Guaranteed Conditional Diffusion with Tensor Correction (GCDTC) framework, which provide explicit, instance-level error bounds on reconstructed data. Furthermore, specialized strategies such as nonlinear constraint satisfaction are employed to preserve the integrity of QoI, a vital requirement for the trustworthiness of downstream scientific analyses. This research also focuses on the design and implementation of scalable, GPU-accelerated software pipelines that seamlessly integrate into existing HPC workflows, ensuring both computational efficiency and practical applicability. The CAESAR framework, for example, unifies foundation and generative models to create an adaptive and efficient compression solution for spatio-temporal scientific data. Collectively, these efforts represent a significant advancement in mitigating the scientific data deluge, enabling more effective data management, accelerated scientific discovery, and optimized utilization of HPC resources.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Continual Learning for Particle Accelerators

Particle accelerators operate under dynamically changing conditions, which often lead to data distribution drifts. These drifts pose significant challenges for Machine Learning (ML) models, which typically fail to maintain performance when faced with such non-stationary data. In particle accelerators, the primary sources of these data drifts include changes in accelerator settings and non-measured parameters such as machine degradation and environmental factors. Previous research has proposed conditional models to handle multiple beam configurations effectively; however, it is challenging to train the ML models on all possible configuration settings. Additionally, conditional models alone can not address performance degradation caused by drifts due to non-measured factors. These limitations contribute to a significant gap between ML development and its deployment in real-world operational settings. To bridge this gap, in this paper, we identify some of the key areas within particle accelerators where continual learning can help mitigate drift-induced performance degradation. In addition, we present a practical use case where a conditional Auto-Encoder model coupled with memory-based continual learning has been employed to demonstrate stable performance even when underlying data drifts.

Schram, Malachi [Thomas Jefferson National Acceler↗

DOE OSTI2026

Augmenting Molecular Graphs with Geometries via Machine Learning Interatomic Potentials

Accurate molecular property predictions require 3D geometries, which are typically obtained using expensive methods such as density functional theory (DFT). Here, we attempt to obtain molecular geometries by relying solely on machine learning interatomic potential (MLIP) models. To this end, we first curate a large-scale molecular relaxation dataset comprising 3.5 million molecules and 300 million snapshots. Then MLIP pre-trained models are trained with supervised learning to predict energy and forces given 3D molecular structures. Once trained, we show that the pre-trained models can be used in different ways to obtain geometries either explicitly or implicitly. First, it can be used to obtain approximate low-energy 3D geometries via geometry optimization. While these geometries do not consistently reach DFT-level chemical accuracy or convergence, they can still improve downstream performance compared to non-relaxed structures. To mitigate potential biases and enhance downstream predictions, we introduce geometry fine-tuning based on the relaxed 3D geometries. Second, the pre-trained models can be directly fine-tuned for property prediction when ground truth 3D geometries are available. Our results demonstrate that MLIP pre-trained models trained on relaxation data can learn transferable molecular representations to improve downstream molecular property prediction and can provide practically valuable but approximate molecular geometries that benefit property predictions. Our code is publicly available at: https://github.com/divelab/AIRS/.

Fu, Cong [Texas A & M Univ., College Station, TX (↗

DOE OSTI2026

Improving Detector Systematic Uncertainties Through Data-Driven Machine Learning

Detector simulation in liquid argon time projection chambers (LArTPCs) is a constant challenge. In particular the modeling of electrons response on wires is highly nontrivial. However, new machine learning techniques exist which can be leveraged to ameliorate these concerns. We present a novel methodology to attempt to learn from cosmic muon data in the ICARUS detector how reconstructed wire signals are influenced by features of the hits such as location, particle direction, angle relative to the wire plane, etc. A model can then be generated which can apply the learned mapping to Monte Carlo events to create a more data-like simulation sample. By creating such a sample we expect to reduce the systematic uncertainties at ICARUS due to our detector modeling.

Hausner, Harry [Fermilab] (ORCID:0000000188932280)↗

DOE OSTI2026

Improving Detector Systematic Uncertainties Through Data-Driven Machine Learning

Hausner, Harry [Fermilab] (ORCID:0000000188932280)↗

DOE OSTI2025

Applying Transfer Learning for Street-Scale Nuisance Flood Forecasting in Coastal-Urban Cities

An important challenge with Machine Learning (ML) is its transferability; that is, whether a ML model trained on one set of data can be applied to a second set of data without requiring a full re-training of the model. Transfer Learning (TL) addresses this challenge by transferring knowledge learned in the source domain (the data it was trained on) to the target domain (a second set of data that is statistically different but related, which the model was not trained on). This study investigates the use of TL for street-scale nuisance flood forecasting by exploring whether a ML model trained on data collected for one set of streets can effectively forecast flooding for another set of streets in the same city using TL. The envisioned use case is a city deploying a new flood depth monitoring sensor on a street and using TL to apply a ML model, trained on sensor data from an existing flood depth sensor network, to this new street. Eventually, the new flood depth sensor will have a sufficient dataset for training its own ML model, but TL can be used to fill the gap in time while this new dataset is being generated. This method is explored using a Long Short-Term Memory (LSTM) model trained on data for the flood-prone streets of Norfolk City, Virginia. The data used for training includes environmental time series (rainfall, tide), topographic features (Digital Elevation Model (DEM), Topographic Wetness Index (TWI), Depth To Water (DTW)), and street-scale flood depth time series obtained from a high-fidelity physics-based model, acting as a synthetic street-scale stream depth sensor dataset since actual stream depth sensor data is generally unavailable for most cities. A set of 180 flood-prone streets was used to train a base model, while another set of 180 flood-prone streets was used to re-train that model using different TL strategies. The results show that full-weight re-training proved most effective and minimal re-training of only the output layer was insufficient. The advantage of TL was most pronounced when target data was limited, meaning data collected at the new water depth sensor location included generally less than 18 flood events. As target data increased beyond 18 flood events, the benefit of TL diminished relative to training a ML model directly on the local flood events. These findings can assist cities as they implement street-scale flood sensing systems to create accurate forecasts for new sensing locations that do not yet have sufficient data records to train a local ML model.

Roy, Binata [Univ. of Virginia, Charlottesville, V↗

DOE OSTI2025

Datasets for Custom-trained Machine-learning Interatomic Potentials: Nitric Acid Aqueous Solution

This dataset was generated using an iterative active learning strategy with the ArcaNN software package (https://github.com/arcann-chem/arcann_training) to train machine-learning interatomic potentials (MLIPs) for aqueous nitric acid. Each active-learning cycle consisted of three stages: (1) training, (2) exploration, and (3) labeling. The initial training set comprised approximately 800 randomly selected configurations from a previous study by Lewis et al. (https://doi.org/10.1021/jp205510q), which investigated nitric acid solutions at 2, 3, 4, and 5 mol/L. For all configurations, single-point calculations of atomic forces and total energies were performed at the quantum density functional theory BLYP-D2 and PBE-D3 levels of theory using the CP2K Quickstep module. Valence electrons were treated explicitly, while core electrons on all atoms were represented by norm-conserving Goedecker–Teter–Hutter (GTH) pseudopotentials. Long-range dispersion interactions were accounted for using Grimme dispersion corrections. Wave functions were expanded in a mixed Gaussian-and-plane-wave scheme using TZV2P-MOLOPT basis sets for all elements and an 800 Ry auxiliary plane-wave cutoff for the electron density. Self-consistent field convergence was accelerated using orbital transformation and Direct Inversion in the Iterative Subspace, with a convergence threshold of 10^{-6}. All single-point calculations were carried out in periodic orthorhombic cells whose dimensions match those of the molecular configurations sampled from earlier trajectories. The CELL_REF keyword in CP2K was used to define a fixed reference cell, ensuring consistency in the reference data used for MLIP training, particularly when cell fluctuations are present in NpT simulations. The resulting high-fidelity energies and forces constitute the ground-truth labels used to train the MLIPs contained in this dataset.

Dinpajooh, Mohammadhasan [Pacific Northwest Nation↗

DOE OSTI2025

Protein-ligand binding affinity prediction using multi-instance learning with docking structures

Recent advances in 3D structure-based deep learning approaches demonstrate improved accuracy in predicting protein-ligand binding affinity in drug discovery. These methods complement physics-based computational modeling such as molecular docking for virtual high-throughput screening. Despite recent advances and improved predictive performance, most methods in this category primarily rely on utilizing co-crystal complex structures and experimentally measured binding affinities as both input and output data for model training. Nevertheless, co-crystal complex structures are not readily available and the inaccurate predicted structures from molecular docking can degrade the accuracy of the machine learning methods. We introduce a novel structure-based inference method utilizing multiple molecular docking poses for each complex entity. Our proposed method employs multi-instance learning with an attention network to predict binding affinity from a collection of docking poses. We validate our method using multiple datasets, including PDBbind and compounds targeting the main protease of SARS-CoV-2. The results demonstrate that our method leveraging docking poses is competitive with other state-of-the-art inference models that depend on co-crystal structures. This method offers binding affinity prediction without requiring co-crystal structures, thereby increasing its applicability to protein targets lacking such data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Machine Learning-Driven Quantification of CO2 Plume Dynamics at Illinois Basin Decatur Project Sites Using Microseismic Data

This study utilizes machine learning to quantify CO2 plume extents by analyzing microseismic data from the Illinois Basin Decatur Project (IBDP). Leveraging a unique dataset of well logs, microseismic records, and CO2 injection metrics, this work aims to predict the temporal evolution of subsurface CO2 saturation plumes. The findings illustrate that machine learning can predict plume dynamics, revealing vertical clustering of microseismic events over distinct time periods within certain proximities to the injection well, consistent with an invasion percolation model. The buoyant CO2 plume partially trapped within sandstone intervals periodically breaches localized barriers or baffles, which act as leaky seals and impede vertical migration until buoyancy overcomes gravity and capillary forces, leading to breakthroughs along vertical zones of weakness. Between different unsupervised clustering techniques, K-Means and DBSCAN were applied and analyzed in detail, where K-means outperformed DBSCAN in this specific study by indicating the combination of the highest Silhouette Score and the lowest Davies–Bouldin Index. The predictive capability of machine learning models in quantifying CO2 saturation plume extension is significant for real-time monitoring and management of CO2 sequestration sites. The models exhibit high accuracy, validated against physical models and injection data from the IBDP, reinforcing the viability of CO2 geological sequestration as a climate change mitigation strategy and enhancing advanced tools for safe management of these operations.

Iyegbekedo, Ikponmwosa↗