Bayesian Port–Hamiltonian Surrogate for Three-Phase Reservoir Flow Simulation

Abstract We present a learned structure-preserving surrogate operator in the form of a Hamiltonian Network that reproduces full-physics three-phase slightly-compressible flow simulations at roughly 10× lower computational cost while retaining fundamental conservation laws. We express the reservoir dynamics as a finite-volume port–Hamiltonian (pH) dynamic system and to progressively learn the Hamiltonian through its dynamic vector field with Bayesian optimization, and using a scalable mixture-of-Gaussian-process (MoGP) prior. The pH scaffold enforces mass balance, passivity, and Lyapunov stability by construction; the Bayesian GP treatment supplies calibrated epistemic uncertainty that propagates through the surrogate estimation state process and can be used to quantify forecast uncertainty in closed-loop reservoir management. Unlike previously published neural-operator and reduced-order surrogates, our method guarantees conservation without ad-hoc penalties and delivers analytic gradients for adjoint-free history matching.