Paolo Guida

Paolo Guida, Didier Barradas-Bautista

Multiphase flows frequently occur naturally and in manufactured devices. Controlling such phenomena is extremely challenging due to the strongly non-linear dynamics, rapid phase transitions, and the limited spatial and temporal resolution of available sensors, which can lead to significant inaccuracies in predicting and managing these flows. In most cases, numerical models are the only way to access high spatial and temporal resolution data to an extent that allows for fine control. While embedding numerical models in control algorithms could enable fine control of multiphase processes, the significant computational burden currently limits their practical application. This work proposes a surrogate-assisted model predictive control (MPC) framework for regulating multiphase processes using learned operators. A Fourier Neural Operator (FNO) is trained to forecast the spatiotemporal evolution of a phase-indicator field (the volume fraction) over a finite horizon from a short history of recent states and a candidate actuation signal. The neural operator surrogate is then iteratively called during the optimisation process to identify the optimal control variable. To illustrate the approach, we solve an optimal control problem (OCP) on a two-phase Eulerian bubble column. Here, the controller tracks piecewise-constant liquid level setpoints by adjusting the gas flow rate introduced into the system. The results we obtained indicate that field-level forecasting with FNOs are well suited for closed-loop optimization since they have relatively low evaluation cost. The latter provide a practical route toward MPC for fast multiphase unit operations and a foundation for future extensions to partial observability and physics-informed operator learning.

Paolo Guida, William L. Roberts

Recent progress in AI has established neural operators as powerful tools that can predict the evolution of partial differential equations, such as the Navier-Stokes equations. Some complex problems rely on sophisticated algorithms to deal with strong discontinuities in the computational domain. For example, liquid-vapour multiphase flows are a challenging problem in many configurations, particularly those involving large density gradients or phase change. The complexity mentioned above has not allowed for fine control of fast industrial processes or applications because computational fluid dynamics (CFD) models do not have a quick enough forecasting ability. This work demonstrates that the time scale of neural operators-based predictions is comparable to the time scale of multi-phase applications, thus proving they can be used to control processes that require fast response. Neural Operators can be trained using experimental data, simulations or a combination. In the following, neural operators were trained in volume of fluid simulations, and the resulting predictions showed very high accuracy, particularly in predicting the evolution of the liquid-vapour interface, one of the most critical tasks in a multi-phase process controller.