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In this paper, we introduce an uplifted reduced order modeling (UROM)approach through the integration of standard projection based methods with longshort-term memory (LSTM) embedding. Our approach has three modeling layers orcomponents. In the first layer, we utilize an intrusive projection approach tomodel dynamics represented by the largest modes. The second layer consists ofan LSTM model to account for residuals beyond this truncation. This closurelayer refers to the process of including the residual effect of the discardedmodes into the dynamics of the largest scales. However, the feasibility ofgenerating a low rank approximation tails off for higher Kolmogorov $n$-widthsystems due to the underlying nonlinear processes. The third uplifting layer,called super-resolution, addresses this limited representation issue byexpanding the span into a larger number of modes utilizing the versatility ofLSTM. Therefore, our model integrates a physics-based projection model with amemory embedded LSTM closure and an LSTM based super-resolution model. Inseveral applications, we exploit the use of Grassmann manifold to constructUROM for unseen conditions. We performed numerical experiments by using theBurgers and Navier-Stokes equations with quadratic nonlinearity. Our resultsshow robustness of the proposed approach in building reduced order models forparameterized systems and confirm the improved trade-off between accuracy andefficiency.

A long short-term memory embedding for hybrid uplifted reduced order models