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This paper presents a new data-driven non-intrusive reduced-ordermodel(NIROM) that outperforms the traditional Proper orthogonal decomposition(POD) based reducedorder model. This is achieved by using Auto-Encoder(AE) andattention-based deep learning methods. The novelty of the present work lies inthat it uses Stacked AutoEncoder(SAE) network to project originalhigh-dimensional dynamical systems onto a low dimensional nonlinear subspaceand predict the fluid dynamics using an attentionbased deep learning method. Anew model reduction neural network architecture for fluid flow problem ispresented. The SAE network compresses high-dimensional physical informationinto several much smaller sized representations in a latent space. Theserepresentations are expressed by a number of codes in the middle layer of SAEneural network. Then, those codes at different time levels are trained toconstruct a set of hyper-surfaces with multi variable response functions usingattention-based deep learning methods. The inputs of the attention-basednetwork are previous time levels' codes and the outputs of the network arecurrent time levels' codes. The codes at current time level are then projectedback to the original full space by the decoder layers in the SAE network. Thecapability of this data-driven reduced order model (DDROM) is illustratednumerically by two test cases: flow past a cylinder, and a lock exchange,respectively. The results obtained show that the DDROM performs better in termsof accuracy than the popular model reduction method namely proper orthogonaldecomposition. The improvement is assessed by comparison with a high fidelityPOD model.

A data driven reduced order model of fluid flow by Auto-Encoder and self-attention deep learning methods