Abstract
Gas--liquid two-phase flows in annular geometries exhibit interfacial waves spanning broad temporal and spatial scales, which couple to pressure losses, heat transfer, and operational constraints in networked systems. In many deployments, sensing is sparse and strongly filtered, yet the most consequential variability is carried by coherent wave packets and regime-dependent slip fluctuations rather than by slowly varying mean quantities alone. This paper develops a spectral-entropy reduced modeling framework that targets the evolution of interfacial wave energy and its projection onto measurable pressure and temperature signals while enforcing physical admissibility. The approach begins from a two-fluid balance formulation and derives a wave-amplitude representation about a time-varying annular base state, yielding a low-dimensional stochastic dynamics for complex Fourier amplitudes driven by shear-induced production and damped by viscosity and wall friction. A central contribution is an entropy-bounded spectral closure that replaces unresolved nonlinear mode coupling by a constrained dissipation operator in spectral space, with a differentiable projection that guarantees nonnegative film thickness, bounded void fraction, and a discrete entropy inequality for the reconstructed physical state. On top of this reduced dynamics, a Koopman-consistent identification procedure learns a linear propagator for dominant wave modes across operating envelopes without requiring regime switching logic, and a probabilistic inference layer estimates spectral state from boundary pressure and differential measurements through frequency-domain transfer operators. Computational studies demonstrate calibrated uncertainty and stable long-horizon predictions of pressure-drop spectra under regime transitions and parameter drift. The resulting framework is intended for fast prediction and diagnosis of wave-driven variability in annular two-phase networks