@Article{NMTMA-16-4,
author = {Yufeng, Wang and Yang, Min and Ruisong, Gao and Chuanjun, Chen and Yufeng, Wang and Yang, Min and Chuanjun, Chen},
title = {PI-VEGAN: Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2023},
volume = {16},
number = {4},
pages = {931--953},
abstract = {<p style="text-align: justify;">We present a new category of physics-informed neural networks called
physics informed variational embedding generative adversarial network (PI-VEGAN),
that effectively tackles the forward, inverse, and mixed problems of stochastic differential equations. In these scenarios, the governing equations are known, but only
a limited number of sensor measurements of the system parameters are available.
We integrate the governing physical laws into PI-VEGAN with automatic differentiation, while introducing a variational encoder for approximating the latent variables
of the actual distribution of the measurements. These latent variables are integrated
into the generator to facilitate accurate learning of the characteristics of the stochastic partial equations. Our model consists of three components, namely the encoder,
generator, and discriminator, each of which is updated alternatively employing the
stochastic gradient descent algorithm. We evaluate the effectiveness of PI-VEGAN in
addressing forward, inverse, and mixed problems that require the concurrent calculation of system parameters and solutions. Numerical results demonstrate that the
proposed method achieves satisfactory stability and accuracy in comparison with the
previous physics-informed generative adversarial network (PI-WGAN).</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2023-0044},
url = {https://global-sci.com/article/90233/pi-vegan-physics-informed-variational-embedding-generative-adversarial-networks-for-stochastic-differential-equations}
}