ODE^2VAE Deep generative second order ODEs with Bayesian neural networks

VAE

• data associated with a single latent code
  • what about sequential data?
• latent space governed by a continuous-time ODE
• first order ODE
  • got it!
  • derivative parametrised as a NN
  • cannot modlelling high-order dynamics
• second-order ODE
  • similar to HMC…
• model
  • position encoder
  • velocity encoder
  • simulate dynamics
  • decoder
• loss
  • regularization: KL
  • VAE loss: loss for x_0
  • dynamic loss