  In Data Assimilation, observations are fused with simulations to obtain an
accurate estimate of the state and parameters for a given physical system.
Combining data with a model, however, while accurately estimating uncertainty,
is computationally expensive and infeasible to run in real-time for complex
systems. Here, we present a novel particle filter methodology, the Deep Latent
Space Particle filter or D-LSPF, that uses neural network-based surrogate
models to overcome this computational challenge. The D-LSPF enables filtering
in the low-dimensional latent space obtained using Wasserstein AEs with
modified vision transformer layers for dimensionality reduction and
transformers for parameterized latent space time stepping. As we demonstrate on
three test cases, including leak localization in multi-phase pipe flow and
seabed identification for fully nonlinear water waves, the D-LSPF runs orders
of magnitude faster than a high-fidelity particle filter and 3-5 times faster
than alternative methods while being up to an order of magnitude more accurate.
The D-LSPF thus enables real-time data assimilation with uncertainty
quantification for physical systems.
