The Deep Latent Space Particle Filter for Real-Time Data Assimilation with Uncertainty Quantification

TL;DR

The paper addresses real-time data assimilation for high-dimensional PDEs with uncertainty quantification and introduces the Deep Latent Space Particle Filter (D-LSPF). D-LSPF uses a latent-space surrogate built from a Wasserstein autoencoder with a Transformer based dimensionality reduction layer and a Transformer based latent time stepping network. It performs a bootstrap particle filter in the latent space to estimate the augmented latent state $a_n=(z_n,m_n)$ and posterior $\rho(a_0:n|y_0:n)$. The approach yields orders of magnitude speedups over high-fidelity particle filters and outperforms ROAD-EnKF in accuracy while maintaining real-time feasibility across three test problems: viscous Burgers equation, harmonic wave generation over a submerged bar, and leak localization in a multi-phase pipe flow. The work highlights potential for real-time data assimilation and digital twins in engineering systems.

Abstract

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.

Figures (11)

• Figure 1: Schematic of the D-LSPF.
• Figure 2: Visualization of the ViT dimensionality reduction/expansion layer.
• Figure 3: Illustration of the transformer model for parameterized time stepping.
• Figure 4: State estimation for the viscous Burgers equations with observations every 10 time step using the high-fidelity particle filter, the D-LSPF and the ROAD-EnKF. The high-fidelity particle filter was run with 1000 particles and the D-LSPF and ROAD-EnKF were run with 100 particles. we see the state estimation for the using the D-LSPF, ROAD-EnKF, and the high-fidelity model for case 2. It is clear that all methods approximates the state well. However, the ROAD-EnKF is visibly worse at the end.
• Figure 5: Wave tank setup and physical variables. Figure comes from engsig2016stabilised.