Generative adversarial networks for PDE learning

2017-05-15 — 2020-08-25

Wherein generative adversarial networks are employed to infer solutions and operators of partial differential equations, and fluid-flow dynamics are illustrated through density-to-velocity reconstructions.

calculus

dynamical systems

geometry

Hilbert space

how do science

Lévy processes

machine learning

neural nets

PDEs

physics

regression

sciml

SDEs

signal processing

statistics

statmech

stochastic processes

surrogate

time series

uncertainty

GANs for PDE learning.

(Bao et al. 2020; Yang, Zhang, and Karniadakis 2020; Zang et al. 2020).

A recent example from fluid-flow dynamics (Chu et al. 2021) has particularly beautiful animations:

1 References

Bao, Ye, Zang, et al. 2020. “Numerical Solution of Inverse Problems by Weak Adversarial Networks.” Inverse Problems.

Chu, Thuerey, Seidel, et al. 2021. “Learning Meaningful Controls for Fluids.” ACM Transactions on Graphics.

Yang, Zhang, and Karniadakis. 2020. “Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations.” SIAM Journal on Scientific Computing.

Zang, Bao, Ye, et al. 2020. “Weak Adversarial Networks for High-Dimensional Partial Differential Equations.” Journal of Computational Physics.