In this paper, we propose a network model, the multiclass
classification-based ROM (MC-ROM), for solving time-dependent parametric
partial differential equations (PPDEs). This work is inspired by the
observation of applying the deep learning-based reduced order model (DL-ROM) to
solve diffusion-dominant PPDEs. We find that the DL-ROM has a good
approximation for some special model parameters, but it cannot approximate the
drastic changes of the solution as time evolves. Based on this fact, we
classify the dataset according to the magnitude of the solutions, and construct
corresponding subnets dependent on different types of data. Then we train a
classifier to integrate different subnets together to obtain the MC-ROM. When
subsets have the same architecture, we can use transfer learning technology to
accelerate the offline training. Numerical experiments show that the MC-ROM
improves the generalization ability of the DL-ROM both for diffusion- and
convection-dominant problems, and maintains the advantage of DL-ROM. We also
compare the approximation accuracy and computational efficiency of the proper
orthogonal decomposition (POD) which is not suitable for convection-dominant
problems. For diffusion-dominant problems, the MC-ROM can save about 100 times
online computational cost than the POD with a slightly better approximation in
the reduced space of the same dimension.Comment: 19 pages, 15 figure