Data-Driven Autoencoder Numerical Solver with Uncertainty Quantification
  for Fast Physical Simulations
Christophe Bonneville Youngsoo Choi Debojyoti Ghosh Jonathan L. Belof
Traditional partial differential equation (PDE) solvers can be
computationally expensive, which motivates the development of faster methods,
such as reduced-order-models (ROMs). We present GPLaSDI, a hybrid deep-learning
and Bayesian ROM. GPLaSDI trains an autoencoder on full-order-model (FOM) data
and simultaneously learns simpler equations governing the latent space. These
equations are interpolated with Gaussian Processes, allowing for uncertainty
quantification and active learning, even with limited access to the FOM solver.
Our framework is able to achieve up to 100,000 times speed-up and less than 7%
relative error on fluid mechanics problems.