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In this effort we propose a data-driven learning framework for reduced ordermodeling of fluid dynamics. Designing accurate and efficient reduced ordermodels for nonlinear fluid dynamic problems is challenging for many practicalengineering applications. Classical projection-based model reduction methodsgenerate reduced systems by projecting full-order differential operators intolow-dimensional subspaces. However, these techniques usually lead to severeinstabilities in the presence of highly nonlinear dynamics, which dramaticallydeteriorates the accuracy of the reduced-order models. In contrast, our newframework exploits linear multistep networks, based on implicit Adams-Moultonschemes, to construct the reduced system. The advantage is that the methodoptimally approximates the full order model in the low-dimensional space with agiven supervised learning task. Moreover, our approach is non-intrusive, suchthat it can be applied to other complex nonlinear dynamical systems withsophisticated legacy codes. We demonstrate the performance of our methodthrough the numerical simulation of a two-dimensional flow past a circularcylinder with Reynolds number Re = 100. The results reveal that the newdata-driven model is significantly more accurate than standard projection-basedapproaches.

Non-intrusive inference reduced order model for fluids using linear multistep neural network