Accurate reconstruction and prediction of complex flow fields from sparse measurements remain a critical challenge in chemical engineering, particularly for nonlinear and multiphase systems. Classical linear reduced-order models, such as dynamic mode decomposition (DMD), often fail to capture strongly unsteady and nonlinear flow dynamics, while high-fidelity computational fluid dynamics (CFD) simulations are computationally prohibitive for real-time analysis and large-scale parametric studies. In this work, we evaluate a time-evolving neural operator (TENO) framework that learns the continuous spatiotemporal evolution of flow fields directly from practically limited and irregularly distributed observations. The performance of TENO is systematically evaluated on benchmark problems, from single-phase flows to an industrially relevant bubble column, where it consistently outperforms DMD in reconstruction and prediction accuracy. Compared with CFD simulations, TENO achieves relative errors on the order of 10−1 in a challenging three-dimensional bubble column benchmark, while significantly reducing computational cost and maintaining robustness under sparse/fixed-plane and noisy measurements.
Zhang et al. (2026) studied this question.