Description
- Abstract:
- Motivated by the ubiquitous demand of leveraging both data and partial knowledge of physical laws for stochastic modeling and uncertainty quantification, in the dissertation, a series of methods are developed centered around generative adversarial networks (GANs) for physics-informed learning. Physics-informed GANs are firstly proposed to solve time-independent stochastic differential equation (SDE) problems. Using neural networks to parameterize the stochastic processes, and the automatic differentiation to encode the SDE into the learning algorithm, physics-informed GANs can solve forward, inverse, and mixed problems in the same framework, even for problems with high stochastic dimensions. The application of GANs is then extended to dynamic inference. Using a physics-informed generative model and physics-informed loss functions, GANs can infer stochastic dynamics and nonlocal flocking dynamics, with observations of particle ensembles as data. A similar idea is also used in the development of the potential flow generator for GANs, which not only tries to transport the input distribution to the target one, but also aims to find the one with minimum transport cost. This special generator is effective in image translation tasks with unpaired training data. To address the oscillation problem of GANs, the measure-conditional discriminator is proposed for GANs. Due to its stationary target optimum during training, it is more robust than the vanilla discriminator. Finally, physics-informed GANs are applied to Bayesian uncertainty quantification for partial differential equation (PDE) problems. Using Bayesian physics-informed neural networks, the uncertainty arising from the scattered and noisy data can be well quantified in forward and inverse PDE problems. With the help of PDEs, physics-informed GANs can learn informative functional priors that benefit the Bayesian uncertainty quantification.
- Notes:
- Thesis (Ph. D.)--Brown University, 2021
Citation
Yang, Liu,
"Generative Adversarial Networks for Physics-Informed Learning"
(2021).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://repository.library.brown.edu/studio/item/bdr:evy4u6n5/
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Applied Mathematics Theses and Dissertations
Theses and Dissertations for the Applied Mathematics department....