Combining probabilistic and trajectory-based learning for reduced-order modeling

Learning efficient and accurate reduced-order models is a primary aim of the fluid dynamics community. Recently, data-driven techniques have achieved impressive results in extracting models from data measurements. These techniques usually aim to match the predicted trajectory of the learned model with data measurements. However, the chaotic systems frequently encountered in fluid dynamics are highly sensitive to their parameters, which can prevent data-driven methods from converging accurately. To ameliorate this issue, we suggest a reduced-order modeling framework that blends trajectory-based learning with probability density function matching. Specifically, we optimize our model by using adjoint methods to evaluate the sensitivity of the Kullback–Leibler divergence of the learned model with respect to the measured data. We explore our approach on a range of fluid mechanics problems.