IAE-Net: Integral Autoencoders for Discretization-Invariant Learning
This addresses the challenge of processing heterogeneous discrete representations of functions for researchers in data science and scientific computing, though it appears incremental as it builds on existing autoencoder concepts.
The paper tackles the problem of discretization-invariant learning in infinite-dimensional function spaces by proposing IAE-Net, a deep learning framework based on integral autoencoders, which achieves state-of-the-art performance in applications like predictive data science and scientific computing.
Discretization invariant learning aims at learning in the infinite-dimensional function spaces with the capacity to process heterogeneous discrete representations of functions as inputs and/or outputs of a learning model. This paper proposes a novel deep learning framework based on integral autoencoders (IAE-Net) for discretization invariant learning. The basic building block of IAE-Net consists of an encoder and a decoder as integral transforms with data-driven kernels, and a fully connected neural network between the encoder and decoder. This basic building block is applied in parallel in a wide multi-channel structure, which are repeatedly composed to form a deep and densely connected neural network with skip connections as IAE-Net. IAE-Net is trained with randomized data augmentation that generates training data with heterogeneous structures to facilitate the performance of discretization invariant learning. The proposed IAE-Net is tested with various applications in predictive data science, solving forward and inverse problems in scientific computing, and signal/image processing. Compared with alternatives in the literature, IAE-Net achieves state-of-the-art performance in existing applications and creates a wide range of new applications.