Latent State Space Learning with Physics Constraints for Gas Liquid Hydraulics and Safety Critical Diagnostics

Abstract

Gas--liquid two-phase flow appears throughout energy and process systems, including wellbores, risers, and pipelines, where operating decisions depend on interpreting sparse and noisy measurements. In drilling and managed-pressure operations, the same surface signals that drive routine control can also contain early indications of regime transitions and hazardous transients, yet the mapping from measurements to downhole states is typically non-unique and closure-dependent. This paper proposes a physics-constrained latent state-space learning framework that targets real-time inference of distributed two-phase hydraulics while providing calibrated uncertainty for safety-relevant decisions. The approach embeds a reduced-order two-fluid/drift-flux backbone inside a differentiable probabilistic state-space model whose latent variables represent coupled hydraulic states and regime-related structure without requiring a fixed, hand-crafted regime map. Training combines simulation-consistent objectives with weak supervision when available, enforcing conservation-consistent residuals and stability regularization across a wide envelope of flow rates, fluid properties, and geometries. Online inference is performed with a hybrid variational--sequential Monte Carlo scheme that yields posterior distributions over pressure, holdup, mixture velocity, and anomaly indicators under sensor latency and changing operating conditions. The resulting estimator supports regime-agnostic diagnostics, change-point detection, and risk-aware control interfaces while remaining computationally compatible with edge deployment. Numerical studies spanning synthetic high-fidelity rollouts and loop-inspired scenarios demonstrate improved generalization under distribution shift and tighter calibration compared with purely discriminative baselines, enabling earlier detection of hazardous transients at controlled false-alarm rates.