Stiven Massala’s thesis defence

A hybrid twin is a physics-based simulation model continuously informed by measurements from sensors probing the real system. It relies on learning what the model fails to capture, namely the bias inherited from simplifying assumptions and unmodelled phenomena, in order to quantify the discrepancy between the simulation’s prediction and the measured reality. This deviation is then fed back into the physical model to re-estimate its parameters in real time and refine its predictions. To this end, this thesis presents a methodology for the construction of hybrid twins, enabling fast and accurate simulations of complex physical systems. The thesis builds on the Parameterized-Background Data-Weak (PBDW) formulation, naturally bias-aware since it enriches the reduced model built offine with a correction component orthogonal to it, estimated directly from the measurements and designed to absorb the gap between the modelled physics and reality; around this formulation, three complementary contributions are developed.

First, a Deep Operator Network (DeepONet) is integrated into the PBDW framework to learn the unmodelled physics from observed states; an orthogonality constraint between the subspace already spanned by the reduced model and the one learned by the network is enforced, ensuring that the neural network captures only what escapes the physics-based model and avoiding any redundancy between the two components. Second, in the time-dependent setting where measurements arrive sequentially, the PBDW correction fields are exploited in two complementary ways: a classifier performs real-time bias identification by recognising, at each acquisition step, the dominant category of model error (e.g. erroneous boundary conditions or erroneous constitutive law), while a Joint Embedding Predictive Architecture (JEPA) performs prediction by estimating the next correction field in a latent space before the next measurement arrives, thereby giving the twin the ability to anticipate. Third, the overall framework is embedded into an online control loop built around three components: a PBDW correction layer providing bias-aware state reconstruction, a dual Kalman filter that identifies the physical parameters online from the corrected state, and a Model Predictive Control (MPC) scheme that leverages the updated model in real time to control the system. The three contributions are validated on a Helmholtz problem, a transient heat-conduction problem, and a drone trajectory-tracking problem, respectively.

Membres du jury :

• Gianluigi Rozza (SISSA, Italie), Professeur, Rapporteur
• Elias Cueto (Univ. Zaragoza, Espagne), Professeur, Rapporteur
• Tommaso Taddei (Univ. Sapienza Rome, Italie), Associate Professor, Examinateur
• Lock Yue Chew (NTU, Singapour), Professeur, Examinateur
• Guillaume Puel (CentraleSupélec, France), Professeur, Examinateur