GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencoder

arXiv:2308.05882v2 Announce Type: replace-cross
Abstract: Numerically solving partial differential equations (PDEs) can be challenging and computationally expensive. This has led to the development of reduced-order models (ROMs) that are accurate but faster than full order models (FOMs). Recently, machine learning advances have enabled the creation of non-linear projection methods, such as Latent Space Dynamics Identification (LaSDI). LaSDI maps full-order PDE solutions to a latent space using autoencoders and learns the system of ODEs governing the latent space dynamics. By interpolating …

abstract advances arxiv autoencoder cs.ce cs.lg cs.na development differential dynamics faster identification linear machine machine learning math.na non-linear process projection space through type