  A parametric adaptive greedy Latent Space Dynamics Identification (gLaSDI)
framework is developed for accurate, efficient, and certified data-driven
physics-informed greedy auto-encoder simulators of high-dimensional nonlinear
dynamical systems. In the proposed framework, an auto-encoder and dynamics
identification models are trained interactively to discover intrinsic and
simple latent-space dynamics. To effectively explore the parameter space for
optimal model performance, an adaptive greedy sampling algorithm integrated
with a physics-informed error indicator is introduced to search for optimal
training samples on the fly, outperforming the conventional predefined uniform
sampling. Further, an efficient k-nearest neighbor convex interpolation scheme
is employed to exploit local latent-space dynamics for improved predictability.
Numerical results demonstrate that the proposed method achieves 121 to 2,658x
speed-up with 1 to 5% relative errors for radial advection and 2D Burgers
dynamical problems.
