POD-CNF: reduced order modeling of parametrized stochastic PDEs via normalizing flows and proper orthogonal decomposition

Andrea Violante, Nicola Rares Franco, Andrea Manzoni

Reduced-order models (ROMs) learned from trusted numerical simulations enable the real-time simulation of complex physical systems, making computationally prohibitive tasks-such as uncertainty quantification and optimal control-tractable. In particular, data-driven ROMs are opening the opportunity to learn from both numerical simulations and experimental data. However, integrating these sources of information is far from straightforward. Real-world measurements often involve multiple sources of uncertainty, including non-Gaussian noise, latent heterogeneities, unknown or hidden system parameters, and multiscale phenomena occurring below the resolution of the data. Consequently, real-world data are better described by parametrized stochastic partial differential equations, for which the development of effective ROMs remains relatively unexplored. In this work, we introduce POD-CNF, a data-driven generative ROM for efficient uncertainty quantification of parametrized high-dimensional systems. The approach combines projection-based model reduction and deep generative modeling. First, Proper Orthogonal Decomposition (POD) is employed to obtain a low-dimensional representation of the…