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Generalization Error Guaranteed Auto-Encoder-Based Nonlinear Model Reduction for Operator Learning
The problem of operator learning, in this context, seeks to extract these physical processes from empirical data, which is challenging due to the infinite or high dimensionality of data.
On Deep Generative Models for Approximation and Estimation of Distributions on Manifolds
Many existing experiments have demonstrated that generative networks can generate high-dimensional complex data from a low-dimensional easy-to-sample distribution.
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