Bayesian Stochastic Closure Identification in Multiphase Two-Fluid Networks via Entropy-Stable Residual Operators and Sparse Sensor Calibration

Abstract

 Multiphase thermal-hydraulic systems are routinely modeled with balance laws whose predictive utility is limited by closure relations for interfacial momentum exchange, wall friction, and heat transfer. In practice these closures vary across operating conditions, geometric details, and evolving surface states, while available measurements are sparse and indirect. This paper develops a stochastic closure identification framework that treats uncertain closure contributions as constrained random fields coupled to a two-fluid network model. The central contribution is a Bayesian formulation in which closure uncertainty is decomposed into a low-dimensional latent process capturing global regime-dependent drift and a spatially localized field capturing persistent mismatch, both embedded in an entropy-stable residual operator to preserve physical admissibility. Posterior inference is performed from streaming pressure, temperature, and differential signals using a likelihood defined by conservative residuals and a measurement operator that accounts for sensor bias and time aggregation. To enable real-time posterior updates and uncertainty propagation without sacrificing thermodynamic structure, the approach introduces a differentiable projection enforcing positivity, bounded volume fractions, and a discrete entropy inequality, and it uses amortized residual evaluation to accelerate the repeated solves required by Bayesian filtering and smoothing. The resulting posterior is explicitly used to quantify identifiability limits, to separate epistemic closure uncertainty from aleatoric process noise, and to diagnose when model inadequacy must be expressed as uncertainty rather than forced into overconfident parameter estimates. Computational studies on annular and networked configurations illustrate calibration and robustness under distribution shift.