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Title: | ADAPTIVE NEURAL NETWORK FOR DISCRETIZATION INVARIANT OPERATOR LEARNING | Authors: | ONG YONG ZHENG | ORCID iD: | orcid.org/0000-0003-3909-318X | Keywords: | Deep Learning, Operator Learning, Discretization Invariant, Integral Autoencoder, Forward and Inverse Problems, Predictive Data Science | Issue Date: | 5-Aug-2023 | Citation: | ONG YONG ZHENG (2023-08-05). ADAPTIVE NEURAL NETWORK FOR DISCRETIZATION INVARIANT OPERATOR LEARNING. ScholarBank@NUS Repository. | Abstract: | 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 applications and creates a wide range of new applications where existing methods fail. | URI: | https://scholarbank.nus.edu.sg/handle/10635/246601 |
Appears in Collections: | Ph.D Theses (Open) |
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