The role of surrogate models in applied problems: bread leavening and fluid dynamics

Laura Rinaldi, CNR-IMATI

Abstract: The demand for efficient surrogate models has become central to addressing complex problems across scientific and technological domains, including inverse problems, data assimilation, and real‑time monitoring. In this seminar, I will discuss the role of surrogate models in different applied contexts, focusing in particular on Variationally Mimetic Operator Networks (VarMiON) for predicting the solutions of PDEs governing each case study. This approach leverages the underlying physical–mathematical model—specifically its weak space‑time formulation—to define the network architecture and thus construct physics‑informed surrogates.

The first application concerns the development of a digital twin for bread leavening. A digital twin is an integrated multiphysics simulation that mirrors the evolution of a real system. Incorporating a surrogate model enables real‑time monitoring and interaction with the physical process through indirect measurements.

The second case study addresses surrogate modeling in fluid dynamics. I will illustrate the surrogate’s performance in predicting solutions to the Navier–Stokes equations at low Reynolds numbers, considering paradigmatic configurations such as cavity flow, flow past a cylinder, and contraction flow.

Finally, I will conclude by outlining my future work during my stay at CNR-IMATI, particularly the use of surrogate models in cancer‑on‑chip systems, where the underlying dynamic is governed by Keller–Segel–type equations.