  We propose a multi-resolution convolutional autoencoder (MrCAE) architecture
that integrates and leverages three highly successful mathematical
architectures: (i) multigrid methods, (ii) convolutional autoencoders and (iii)
transfer learning. The method provides an adaptive, hierarchical architecture
that capitalizes on a progressive training approach for multiscale
spatio-temporal data. This framework allows for inputs across multiple scales:
starting from a compact (small number of weights) network architecture and
low-resolution data, our network progressively deepens and widens itself in a
principled manner to encode new information in the higher resolution data based
on its current performance of reconstruction. Basic transfer learning
techniques are applied to ensure information learned from previous training
steps can be rapidly transferred to the larger network. As a result, the
network can dynamically capture different scaled features at different depths
of the network. The performance gains of this adaptive multiscale architecture
are illustrated through a sequence of numerical experiments on synthetic
examples and real-world spatial-temporal data.
