Model order reduction method based on (r)POD-ANNs for parameterized time-dependent partial differential equations

Abstract

In this paper, we propose a non-intrusive data-driven model order reduction method, also known as (r)POD-ANNs model order reduction method. In this method, (r)POD priori dimension reduction is performed on high-fidelity data set, and then the mapping relationship between parameter space and generalized coordinates of (r)POD is implicitly constructed by using the universal approximation property of neural network. Through pre-training on small batch data sets, updating neural network parameters every several time steps, and combination of L-BFGS optimization algorithm and LM optimization algorithm, time cost of the reduced order model in the off-line calculation stage is reduced. This makes the (r)POD-ANNs model order reduction method suitable for high-fidelity models with larger spatial degrees of freedom and higher complexity. Finally, we verify effectiveness of the proposed method by comparing with the data-driven model reduction method, and then apply it to the Allen-Cahn equations with strong nonlinearity and cylinder flow problem with large spatial degrees of freedom.