Reduced Order Modeling (ROM)

Many physical systems, from turbulent flows to the atmosphere and ocean, are governed by equations whose numerical solution requires millions of degrees of freedom. Yet their essential dynamics are often organized by a much smaller number of coherent structures. Reduced order modeling (ROM) exploits this observation: from data generated by a high-fidelity simulation, it extracts a low-dimensional basis, such as proper orthogonal decomposition (POD) modes, and projects the governing equations onto it. The result is a small system of equations that can be solved orders of magnitude faster than the original model, making repeated tasks such as prediction, control, data assimilation, and uncertainty quantification computationally feasible.

The price of reduction is that the discarded scales still act on the resolved ones. Modeling this interaction, the ROM closure problem, is a central theme of my work. I develop closure models that combine physical principles, such as the variational multiscale framework and energy conservation, with data-driven and stochastic modeling, so that reduced models remain accurate, stable, and physically consistent over long time horizons.