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Generative Adversarial Network
Communications in Computational Physics • Vol 39 • No 2
Adaptive Neural Network Basis Methods for Partial Differential Equations with Low-Regular Solutions
2025
This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semi-linear partial differential equation with low-regular solutions in two/three dimensions. The method is obtained by combining basis functions from a c…
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Generative Adversarial Network

Deep learning method

A generative adversarial network (GAN) is a class of machine learning frameworks and a prominent framework for approaching generative artificial intelligence. The concept was initially developed by Ian Goodfellow and his colleagues in June 2014. In a GAN, two neural networks compete with each other in the form of a zero-sum game, where one agent's gain is another agent's loss.

Given a training set, this technique learns to generate new data with the same statistics as the training set. For example, a GAN trained on photographs can generate new photographs that look at least superficially authentic to human observers, having many realistic characteristics.

Exploring foci of:
Communications in Computational Physics • Vol 39 • No 2
Adaptive Neural Network Basis Methods for Partial Differential Equations with Low-Regular Solutions
2025
This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semi-linear partial differential equation with low-regular solutions in two/three dimensions. The method is obtained by combining basis functions from a class of shallow neural networks and the resulting multi-scale analogues, a residual strategy in adaptive methods and the non-overlapping domain decomposition method. Firstly, based on the solution residual, the domain $\Omega$ is iteratively decomposed and eve…
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