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Traditional partial differential equation (PDE) solvers can becomputationally expensive, which motivates the development of faster methods,such as reduced-order-models (ROMs). We present GPLaSDI, a hybrid deep-learningand Bayesian ROM. GPLaSDI trains an autoencoder on full-order-model (FOM) dataand simultaneously learns simpler equations governing the latent space. Theseequations are interpolated with Gaussian Processes, allowing for uncertaintyquantification 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.

Data-Driven Autoencoder Numerical Solver with Uncertainty Quantification for Fast Physical Simulations