Reduced‐Order Modeling of Parameterized Visco‐Plastic Shallow Flows

ABSTRACT We propose a nonintrusive reduced‐order modeling framework for parametrized visco‐plastic free‐surface flows governed by a shallow‐water formulation of Herschel–Bulkley fluids. These flows exhibit strong nonlinearities, non‐smooth rheology, moving fronts, and yield surfaces, making efficient surrogate modeling particularly challenging. To address this challenge, we employ a tensor‐based approach in which the solution manifold is approximated using a low‐rank representation obtained via higher‐order singular value decomposition of snapshot data over a structured parameter space. The resulting tensorial reduced‐order model (TROM) enables rapid online evaluation by directly reconstructing solution trajectories from the compressed representation, thereby avoiding the need to perform time integration of a reduced dynamical system. The proposed nonintrusive framework can be interpreted as an encoder–decoder architecture with a compressed latent representation and efficient multilinear decoding. Numerical experiments demonstrate that the proposed approach accurately captures key flow features, including front propagation, plug and shear regions, and near‐stopping dynamics, while achieving substantial computational speedups relative to full‐order simulations.