Beyond training horizons: A physics-informed U-Net transformer for time-dependent CO₂ storage simulation in environmental applications

Abstract

CO₂ geological storage is a key strategy for reducing greenhouse gas emissions, requiring accurate modeling of subsurface CO₂ migration is essential for effective storage planning and risk assessment. Conventional numerical simulations, which solve time-dependent nonlinear partial differential equations, provide detailed physical insights but are computationally demanding, especially for large-scale or long-term scenarios. To improve computational efficiency, surrogate models based on machine learning have been increasingly investigated. Methods such as deep learning and physics-Informed neural networks aim to approximate the behavior of physical systems, offering potential reductions in simulation time. However, these approaches often require extensive case-specific datasets and are typically limited to fixed time horizons defined during training, which can restrict their generalizability and practical application. This study presents a time-aware surrogate modeling framework that combines convolutional neural networks with self-attention mechanisms to address these limitations. Drawing inspiration from autoregressive forecasting used in sequential learning models, the proposed approach captures temporal dependencies through iterative prediction of system states.The framework requires only a short-term numerical simulation to initialize the physical system, after which it can generate predictions for arbitrarily extended time horizons without the need for retraining. By enabling long-term forecasting, the method improves efficiency and supports repeated scenario evaluations, such as site screening and well placement optimization. Such predictive capabilities are particularly valuable in addressing environmental sustainability goals, where rapid and scalable simulations are essential for managing long-term subsurface processes under climate-related constraints.