PARAMETRIC MODEL REDUCTION WITH CONVOLUTIONALNEURAL NETWORKS Br

Reduced order modeling (ROM) has been widely used to solve parametric PDEs.However, most existing ROM methods rely on linear projections, which face e ciency challengeswhen dealing with complex nonlinear problems. In this paper, we propose a convolutional neuralnetwork-based ROM method to solve parametric PDEs. Our approach consists of two compo-nents: a convolutional autoencoder (CAE) that learns a low-dimensional representation of thesolutions, and a convolutional neural network (CNN) that maps the model parameters to thelatent representation. For time-dependent problems, we incorporate timetinto the surrogatemodel by treating it as an additional parameter. To reduce computational costs, we use a de-coupled training strategy to train the CAE and latent CNN separately. The advantages of ourmethod are that it does not require training data to be sampled at uniform time steps and canpredict the solution at any timetwithin the time domain. Extensive numerical experiments haveshown that our surrogate model can accurately predict solutions for both time-independent andtime-dependent problems. Comparison with traditional numerical methods further demonstratesthe computational e ectiveness of our surrogate solver, especially for solving nonlinear parametricPDEs