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The Kolmogorov $n$-width of the solution manifolds of transport-dominatedproblems can decay slowly. As a result, it can be challenging to designefficient and accurate reduced order models (ROMs) for such problems. Toaddress this issue, we propose a new learning-based projection method toconstruct nonlinear adaptive ROMs for transport problems. The constructionfollows the offline-online decomposition. In the offline stage, we train aneural network to construct adaptive reduced basis dependent on time and modelparameters. In the online stage, we project the solution to the learned reducedmanifold. Inheriting the merits from both deep learning and the projectionmethod, the proposed method is more efficient than the conventional linearprojection-based methods, and may reduce the generalization error of a solelylearning-based ROM. Unlike some learning-based projection methods, the proposedmethod does not need to take derivatives of the neural network in the onlinestage.

A learning-based projection method for model order reduction of transport problems