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

The Kolmogorov n-width of the solution manifolds transport-dominated problems can decay slowly. As a result, it be challenging to design efficient and accurate reduced order models (ROMs) for such problems. To address this issue, we propose new learning-based projection method construct nonlinear adaptive ROMs transport construction follows offline–online decomposition. In offline stage, train neural network basis dependent on time model parameters. online project learned manifold. Inheriting merits from both deep learning method, proposed is more than conventional linear projection-based methods, may reduce generalization error solely ROM. Unlike some does not need take derivatives in stage.