# Data Assimilation in the Latent Space of a Neural Network

arXiv: https://arxiv.org/abs/2012.12056 · HTML: https://mlsanity.com/paper/2012.12056/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2020.

## Built on by (most cited first, 9 of 9)

- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models](https://mlsanity.com/paper/2204.03497/) (2022)
- [Bridging observation, theory and numerical simulation of the ocean using Machine Learning](https://mlsanity.com/paper/2104.12506/) (2021)
- [A generative model for surrogates of spatial-temporal wildfire nowcasting](https://mlsanity.com/paper/2308.02810/) (2023)
- [State-observation augmented diffusion model for nonlinear assimilation with unknown dynamics](https://mlsanity.com/paper/2407.21314/) (2024)
- [Observation Error Covariance Specification in Dynamical Systems for Data assimilation using Recurrent Neural Networks](https://mlsanity.com/paper/2111.06447/) (2021)
- [TorchDA: A Python package for performing data assimilation with deep learning forward and transformation functions](https://mlsanity.com/paper/2409.00244/) (2024)
- [VAE-Var: Variational-Autoencoder-Enhanced Variational Assimilation](https://mlsanity.com/paper/2405.13711/) (2024)
- [ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiability](https://mlsanity.com/paper/2608.23297/) (2026)

## Abstract (arXiv)

There is an urgent need to build models to tackle Indoor Air Quality issue. Since the model should be accurate and fast, Reduced Order Modelling technique is used to reduce the dimensionality of the problem. The accuracy of the model, that represent a dynamic system, is improved integrating real data coming from sensors using Data Assimilation techniques. In this paper, we formulate a new methodology called Latent Assimilation that combines Data Assimilation and Machine Learning. We use a Convolutional neural network to reduce the dimensionality of the problem, a Long-Short-Term-Memory to build a surrogate model of the dynamic system and an Optimal Interpolated Kalman Filter to incorporate real data. Experimental results are provided for CO2 concentration within an indoor space. This methodology can be used for example to predict in real-time the load of virus, such as the SARS-COV-2, in the air by linking it to the concentration of CO2.