Progressive Reduced Order Modeling: From Single-Phase Flow to Coupled Multiphysics Processes
Authors: Kadeethum Teeratorn , Chang Kyung Won , Jakeman John D. , Yoon Hongkyu 
Published: August 2024

ABSTRACT:
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.

1 INTRODUCTION
The integration of underground energy production with the geological sequestration of greenhouse gases emerges as a pivotal strategy for achieving sustainable development and net-zero emissions, as highlighted by Masood et al. (2022). Navigating the intricate and variable dynamics of subsurface physics and geology poses formidable challenges, impeding our comprehensive understanding of these systems (Hu and Chugunova, 2008; Yoon et al., 2013; Chang et al., 2018). While empirical studies through laboratory and field works provide valuable insights, their scalability, cost, and controllability limitations necessitate the adoption of high-fidelity computational modeling. This approach is indispensable for elucidating the complex interplay between fluid dynamics and solid mechanics under diverse conditions, albeit at a high computational expense (Hesthaven et al., 2016; Cho and Jun, 2021; Kadeethum et al., 2022).
Machine learning (ML)-based reduced order modeling (ROM) offers a promising avenue for addressing these complex spatiotemporal challenges. It efficiently facilitates large-scale modeling, optimization, and uncertainty quantification, although it demands extensive training data (Choi et al., 2020; Kadeethum et al., 2021, 2023a; Silva et al., 2023). Transfer learning, as a method to alleviate data scarcity, repurposes pre-trained models for new tasks by employing strategies such as fine-tuning and layer augmentation, leveraging pre-existing knowledge to bolster model efficacy (Weiss et al., 2016; Zhuang et al., 2020). However, it is hampered by limitations, including restricted direct knowledge transfer and the peril of catastrophic forgetting, underscoring the imperative for advanced learning strategies that enable selective knowledge retention and application across diverse models (Rusu et al., 2016; Fayek et al., 2020).