Brownian Bridge Augmented Surrogate Simulation and Injection Planning for Geological CO$_2$ Storage

Geological CO2 storage (GCS) involves injecting captured CO2 into deep subsurface formations to support climate goals. The effective management of GCS relies on adaptive injection planning to dynamically control injection rates and well pressures to balance both storage safety and efficiency. Prior literature, including numerical optimization methods and surrogate-optimization methods, is limited by real-world GCS requirements of smooth state transitions and goal-directed planning within limited time. To address these limitations, we propose a Brownian Bridge-augmented framework for surrogate simulation and injection planning in GCS and develop two insights: (i) Brownian bridge as a smooth state regularizer for better surrogate simulation; (ii) Brownian bridge as goal-time-conditioned planning guidance for improved injection planning. Our method has three stages: (i) learning deep Brownian bridge representations with contrastive and reconstructive losses from historical reservoir and utility trajectories, (ii) incorporating Brownian bridge-based next state interpolation for simulator regularization, and (iii) guiding injection planning with Brownian utility-conditioned trajectories to generate high-quality injection plans. Experimental results across multiple datasets collected from diverse GCS settings demonstrate that our framework consistently improves simulation fidelity and planning effectiveness while maintaining low computational overhead.