PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations

Understand

We propose a new class of physics-informed neural networks, called physics-informed Variational Autoencoder (PI-VAE), to solve stochastic differential equations (SDEs) or inverse problems involving SDEs.

• In these problems the governing equations are known but only a limited number of measurements of system parameters are available.
• PI-VAE consists of a variational autoencoder (VAE), which generates samples of system variables and parameters.
• This generative model is integrated with the governing equations.