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

arXiv: https://arxiv.org/abs/2406.02204 · HTML: https://mlsanity.com/paper/2406.02204/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 53 references that are in the map.
- First posted on arXiv 4 Jun 2024.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [Rethinking Spatial Dimensions of Vision Transformers](https://mlsanity.com/paper/2103.16302/) (2021)
- [Transformers for Modeling Physical Systems](https://mlsanity.com/paper/2010.03957/) (2020)
- [Filtering Variational Objectives](https://mlsanity.com/paper/1705.09279/) (2017)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [A Probabilistic Graphical Model Foundation for Enabling Predictive Digital Twins at Scale](https://mlsanity.com/paper/2012.05841/) (2020)
- [Latent Space Data Assimilation by using Deep Learning](https://mlsanity.com/paper/2104.00430/) (2021)
- [Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models](https://mlsanity.com/paper/2204.03497/) (2022)
- [Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systems](https://mlsanity.com/paper/2301.10391/) (2023)
- [Reduced-Order Autodifferentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2301.11961/) (2023)
- [Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems](https://mlsanity.com/paper/2102.03169/) (2021)
- [AI enhanced data assimilation and uncertainty quantification applied to Geological Carbon Storage](https://mlsanity.com/paper/2402.06110/) (2024)
- [Particle Smoothing Variational Objectives](https://mlsanity.com/paper/1909.09734/) (2019)
- [A Stabilised Nodal Spectral Element Method for Fully Nonlinear Water Waves](https://mlsanity.com/paper/1512.02548/) (2015)
- [Generative Network-Based Reduced-Order Model for Prediction, Data Assimilation and Uncertainty Quantification](https://mlsanity.com/paper/2105.13859/) (2021)
- [Stein particle filtering](https://mlsanity.com/paper/2106.10568/) (2021)
- [Model and Data Reduction for Data Assimilation: Particle Filters Employing Projected Forecasts and Data with Application to a Shallow Water Model](https://mlsanity.com/paper/2101.09252/) (2021)
- [Transformer-based dimensionality reduction](https://mlsanity.com/paper/2210.08288/) (2022)

## Built on by (most cited first, 3 of 3)

- [LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2411.19305/) (2024)
- [A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants](https://mlsanity.com/paper/2610.03396/) (2026)
- [LD-EnFF: Latent-Dynamics Ensemble Flow Filtering for Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2610.04034/) (2026)

## Abstract (arXiv)

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.