Abstract
Gas--liquid two-phase flow appears in wells, pipelines, and surface facilities where operators must manage pressure, throughput, and safety margins under rapidly changing conditions. The governing balances are known in principle, yet practical prediction and control remain difficult because closure relations for slip, friction, and interfacial exchange depend on evolving flow structure, geometry, and transient history. This paper proposes an entropy-stable multi-fidelity digital-twin architecture that couples a conservative low-order transport core with a probabilistic closure layer and an information-theoretic sensing policy. The main technical contribution is a closure learning method based on constrained normalizing flows that produces state- and geometry-conditioned distributions over closure coefficients while enforcing thermodynamic admissibility and numerical entropy stability of the host solver. A second contribution is an active sensing formulation that selects measurement configurations and excitation maneuvers to maximize expected information gain about latent holdup and closure parameters under operational constraints. The twin yields calibrated predictive distributions for pressure gradient and holdup profiles, propagates uncertainty through regime transitions without requiring explicit regime labels, and remains stable under long-horizon rollout through an entropy inequality enforced at the discretization level. Computational studies on vertical and horizontal conduits demonstrate reduced overconfidence under sensor dropout, improved extrapolation across geometry shifts, and more reliable risk quantiles compared to deterministic surrogate closures. The framework is intended for real-time integration with drilling and production workflows where decisions must be made from limited telemetry and where conservative stability guarantees are preferable to brittle point forecasts.