Passivity-Constrained Hybrid Learning for Two-Phase Flow Networks: Port-Hamiltonian Modeling and Risk-Sensitive State Estimation

Abstract

Gas--liquid two-phase flow is a recurring challenge in energy and process systems because the macroscopic variables that operators measure and control are shaped by strongly nonlinear interfacial dynamics. In field practice, sparse telemetry and uncertain closures make it difficult to maintain stable pressure and flow delivery when operating conditions change rapidly. This paper develops a digital-twin methodology that is explicitly designed for online decision support in two-phase flow networks, emphasizing stability guarantees rather than solely predictive accuracy. The main contribution is a passivity-constrained hybrid model that combines a port-Hamiltonian network representation of two-phase transport with learned dissipative and interfacial closure terms. The network model exposes power ports at boundaries and junctions, enabling a consistent treatment of pumps, chokes, compressors, and valves as energy-shaping elements. Learning is restricted by inequality constraints that preserve passivity and prevent nonphysical energy generation, which is critical for robust rollout during transients. To assimilate telemetry, we derive a risk-sensitive smoothing formulation that jointly estimates hidden states and closure multipliers while penalizing underestimation of tail risk in pressure and holdup. The resulting estimator outputs calibrated predictive bands that can be propagated through a safety-aware controller. A constrained receding-horizon policy uses the twin to enforce probabilistic pressure and flow limits under regime ambiguity and sensor bias. Computational experiments demonstrate improved stability under aggressive actuation and improved reliability under sensor dropout compared to unconstrained learning baselines, while maintaining competitive point-forecast error.