Publications

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This project helped address the growing need for efficient and scalable models to support geological carbon and energy storage, which are crucial for achieving net-zero emissions. Traditionally accurate high-fidelity numerical models have been used to simulate relevant storage processes under a handful of processes, however such models are computationally demanding, making uncertainty quantification impractical. Consequently, we first developed a machine learning framework, based on Graph Neural Operators (GNOs), to improving the accuracy of model predictions for a fixed computational budget. We then developed an Ensemble of Improved Neural Operators (ENO), which uses bagging and Monte Carlo dropout techniques, to further improve prediction accuracy. Lastly, we developed the way to explain progressive transfer learning methods to reduce the amount of training data and computational cost of training (i.e., reduce trainable parameters) when using our models for multiple storage sites. Our numerical investigation, which used real-world case studies, demonstrated that our framework can significantly improve the safety and efficiency of geological storage operations, with potential applications in other domains such as geothermal reservoirs and climate modeling.

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This study introduces the Progressive Improved Neural Operator (p-INO) framework, aimed at advancing machine-learning-based reduced-order models within geomechanics for underground resource optimization and carbon sequestration applications.The p-INO method transcends traditional transfer learning limitations through progressive learning, enhancing the capability of transferring knowledge from many sources.Through numerical experiments, the performance of p-INO is benchmarked against standard Improved Neural Operators (INO) in scenarios varying by data availability (different number of training samples).The research utilizes simulation data reflecting scenarios like single-phase, two-phase, and two-phase flow with mechanics inspired by the Illinois Basin Decatur Project.Results reveal that p-INO significantly surpasses conventional INO models in accuracy, particularly in data-constrained environments.Besides, adding more priori information (more trained models used by p-INO) can further enhance the process.This experiment demonstrates p-INO's robustness in leveraging sparse datasets for precise predictions across complex subsurface physics scenarios.The findings underscore the potential of p-INO to revolutionize predictive modeling in geomechanics, presenting a substantial improvement in computational efficiency and accuracy for large-scale subsurface simulations.

This study introduces the Progressive Improved Neural Operator (p-INO) framework, aimed at advancing machine-learning-based reduced-order models within geomechanics for underground resource optimization and carbon sequestration applications.The p-INO method transcends traditional transfer learning limitations through progressive learning, enhancing the capability of transferring knowledge from many sources.Through numerical experiments, the performance of p-INO is benchmarked against standard Improved Neural Operators (INO) in scenarios varying by data availability (different number of training samples).The research utilizes simulation data reflecting scenarios like single-phase, two-phase, and two-phase flow with mechanics inspired by the Illinois Basin Decatur Project.Results reveal that p-INO significantly surpasses conventional INO models in accuracy, particularly in data-constrained environments.Besides, adding more priori information (more trained models used by p-INO) can further enhance the process.This experiment demonstrates p-INO's robustness in leveraging sparse datasets for precise predictions across complex subsurface physics scenarios.The findings underscore the potential of p-INO to revolutionize predictive modeling in geomechanics, presenting a substantial improvement in computational efficiency and accuracy for large-scale subsurface simulations.

Fast and reliable estimation of engineered fracture geometries is a key factor in controlling undesirable fractures and enhancing stimulation design. Measuring the surface deformation gradient (tilt) for engineered fractures in shallow depths (<1000 m) has been proven a reliable source of data to infer fracture geometry, thanks to the impressive resolution of tiltmeter units (in the order of nano-radians). However, solving the inverse problem requires reliable and fast forward models. In this study, we present a fast and reliable machine-learned surrogate model to estimate the ground surface tilt induced by pressurised fractures. The proposed surrogate model, based on Conditional Generative Adversarial Networks (cGAN), receives a fracture aperture map in XY and XZ planes as input and predicts the corresponding surface tilts (in X and Y directions). The surrogate model with Wasserstein loss and gradient penalty has been trained using 11,000 samples and tested for a range of input parameters such as depth, dip angles, elastic properties, fluid pressures and fracture shapes. The testing results show excellent performance of the surrogate model compared with the forward finite element model for both single and multiple pressurised fractures, while running hundreds to potentially thousands of times faster.

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This study presents a method for constructing machine learning-based reduced order models (ROMs) that accurately simulate nonlinear contact problems while quantifying epistemic uncertainty. These purely non-intrusive ROMs significantly lower computational costs compared to traditional full order models (FOMs). The technique utilizes adversarial training combined with an ensemble of Barlow twins reduced order models (BT-ROMs) to maximize the information content of the nonlinear reduced manifolds. These lower-dimensional manifolds are equipped with Gaussian error estimates, allowing for quantifying epistemic uncertainty in the ROM predictions. The effectiveness of these ROMs, referred to as UQ-BT-ROMs, is demonstrated in the context of contact between a rigid indenter and a hyperelastic substrate under finite deformations. The ensemble of BT-ROMs improves accuracy and computational efficiency compared to existing alternatives. The relative error between the UQ-BT-ROM and FOM solutions ranges from approximately 3% to 8% across all benchmarks. Remarkably, this high level of accuracy is achieved at a significantly reduced computational cost compared to FOMs. For instance, the online phase of the UQ-BT-ROM takes only 0.001 seconds, while a single FOM evaluation requires 63 seconds. Furthermore, the error estimate produced by the UQ-BT-ROMs reasonably captures the errors in the ROMs, with increasing accuracy as training data increases. The ensemble approach improves accuracy and computational efficiency compared to existing alternatives. The UQ-BT-ROMs provide a cost-effective solution with significantly reduced computational times while maintaining a high level of accuracy.

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