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Title: Integral Autoencoder Network for Discretization-Invariant Learning
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 is 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  more » « less
Award ID(s):
2244988 2206333
PAR ID:
10426135
Author(s) / Creator(s):
; ;
Editor(s):
Stefan Harmeling
Date Published:
Journal Name:
Journal of machine learning research
Volume:
23
ISSN:
1532-4435
Page Range / eLocation ID:
1 - 45
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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