# Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models

arXiv: https://arxiv.org/abs/2204.03497 · HTML: https://mlsanity.com/paper/2204.03497/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 71 references that are in the map.
- First posted on arXiv 7 Apr 2022.

## Builds on (most cited first, 21 of 21)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model](https://mlsanity.com/paper/2001.01520/) (2020)
- [Recurrent Kalman Networks: Factorized Inference in High-Dimensional Deep Feature Spaces](https://mlsanity.com/paper/1905.07357/) (2019)
- [Fully Convolutional Mesh Autoencoder using Efficient Spatially Varying Kernels](https://mlsanity.com/paper/2006.04325/) (2020)
- [Using machine learning to correct model error in data assimilation and forecast applications](https://mlsanity.com/paper/2010.12605/) (2020)
- [Latent Space Data Assimilation by using Deep Learning](https://mlsanity.com/paper/2104.00430/) (2021)
- [Data-driven polynomial chaos expansion for machine learning regression](https://mlsanity.com/paper/1808.03216/) (2018)
- [Learning ReLU Networks on Linearly Separable Data: Algorithm, Optimality, and Generalization](https://mlsanity.com/paper/1808.04685/) (2018)
- [An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion](https://mlsanity.com/paper/2008.10532/) (2020)
- [A Modified Perturbed Sampling Method for Local Interpretable Model-agnostic Explanation](https://mlsanity.com/paper/2002.07434/) (2020)
- [Data Assimilation in the Latent Space of a Neural Network](https://mlsanity.com/paper/2012.12056/) (2020)
- [Applying Convolutional Neural Networks to Data on Unstructured Meshes with Space-Filling Curves](https://mlsanity.com/paper/2011.14820/) (2020)
- [Observation Error Covariance Specification in Dynamical Systems for Data assimilation using Recurrent Neural Networks](https://mlsanity.com/paper/2111.06447/) (2021)
- [Background Error Covariance Iterative Updating with Invariant Observation Measures for Data Assimilation](https://mlsanity.com/paper/1910.09408/) (2019)
- [Neural Networks and Polynomial Regression. Demystifying the Overparametrization Phenomena](https://mlsanity.com/paper/2003.10523/) (2020)
- [Incremental Training of a Recurrent Neural Network Exploiting a Multi-Scale Dynamic Memory](https://mlsanity.com/paper/2006.16800/) (2020)
- [Adversarial autoencoders and adversarial LSTM for improved forecasts of urban air pollution simulations](https://mlsanity.com/paper/2104.06297/) (2021)
- [Data Assimilation Predictive GAN (DA-PredGAN): applied to determine the spread of COVID-19](https://mlsanity.com/paper/2105.07729/) (2021)
- [UCNN: A Convolutional Strategy on Unstructured Mesh](https://mlsanity.com/paper/2101.05207/) (2021)

## Built on by (most cited first, 26 of 26)

- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Deep Generative Data Assimilation in Multimodal Setting](https://mlsanity.com/paper/2404.06665/) (2024)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Data](https://mlsanity.com/paper/2409.00127/) (2024)
- [Towards an end-to-end artificial intelligence driven global weather forecasting system](https://mlsanity.com/paper/2312.12462/) (2023)
- [Efficient deep data assimilation with sparse observations and time-varying sensors](https://mlsanity.com/paper/2310.16187/) (2023)
- [Machine learning for modelling unstructured grid data in computational physics: a review](https://mlsanity.com/paper/2502.09346/) (2025)
- [LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2411.19305/) (2024)
- [Latent assimilation with implicit neural representations for unknown dynamics](https://mlsanity.com/paper/2309.09574/) (2023)
- [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)
- [Multi-fidelity physics constrained neural networks for dynamical systems](https://mlsanity.com/paper/2402.02031/) (2024)
- [TorchDA: A Python package for performing data assimilation with deep learning forward and transformation functions](https://mlsanity.com/paper/2409.00244/) (2024)
- [AeroJEPA: Learning Semantic Latent Representations for Scalable 3D Aerodynamic Field Modeling](https://mlsanity.com/paper/2605.05586/) (2026)
- [The Deep Latent Space Particle Filter for Real-Time Data Assimilation with Uncertainty Quantification](https://mlsanity.com/paper/2406.02204/) (2024)
- [Bridging Idealized and Operational Models: An Explainable AI Framework for Earth System Emulators](https://mlsanity.com/paper/2510.13030/) (2025)
- [Latent Autoencoder Ensemble Kalman Filter for Nonlinear Data assimilation](https://mlsanity.com/paper/2603.06752/) (2026)
- [On the uncertainty analysis of the data-enabled physics-informed neural network for solving neutron diffusion eigenvalue problem](https://mlsanity.com/paper/2303.08455/) (2023)
- [Hierarchical Autoencoder-based Lossy Compression for Large-scale High-resolution Scientific Data](https://mlsanity.com/paper/2307.04216/) (2023)
- [Estimating fire Duration using regression methods](https://mlsanity.com/paper/2308.08936/) (2023)
- [Spatiotemporal System Forecasting with Irregular Time Steps via Masked Autoencoder](https://mlsanity.com/paper/2603.25597/) (2026)
- [Ensemble Controlled-Flow Filtering for Implicit Data Assimilation](https://mlsanity.com/paper/2607.12975/) (2026)
- [Variational Parameter Calibration with Physics-Aware Latent-Space Surrogates](https://mlsanity.com/paper/2608.11435/) (2026)
- [Diffusion Distillation for Efficient Weather Ensembles](https://mlsanity.com/paper/2608.27728/) (2026)
- [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)

Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a system which combines reduced-order surrogate models with a novel data assimilation (DA) technique used to incorporate real-time observations from different physical spaces. We make use of local smooth surrogate functions which link the space of encoded system variables and the one of current observations to perform variational DA with a low computational cost. The new system, named Generalised Latent Assimilation can benefit both the efficiency provided by the reduced-order modelling and the accuracy of data assimilation. A theoretical analysis of the difference between surrogate and original assimilation cost function is also provided in this paper where an upper bound, depending on the size of the local training set, is given. The new approach is tested on a high-dimensional CFD application of a two-phase liquid flow with non-linear observation operators that current Latent Assimilation methods can not handle. Numerical results demonstrate that the proposed assimilation approach can significantly improve the reconstruction and prediction accuracy of the deep learning surrogate model which is nearly 1000 times faster than the CFD simulation.