mlsanityData to 7 Oct 2026

Latent assimilation with implicit neural representations for unknown dynamics

arXiv 2309.09574 ↗First posted 18 Sep 2023cs.LG math-ph math.MPcited by 8

Not on the map. Why?

Abstract (arXiv)

Data assimilation is crucial in a wide range of applications, but it often faces challenges such as high computational costs due to data dimensionality and incomplete understanding of underlying mechanisms. To address these challenges, this study presents a novel assimilation framework, termed Latent Assimilation with Implicit Neural Representations (LAINR). By introducing Spherical Implicit Neural Representations (SINR) along with a data-driven uncertainty estimator of the trained neural networks, LAINR enhances efficiency in assimilation process. Experimental results indicate that LAINR holds certain advantage over existing methods based on AutoEncoders, both in terms of accuracy and efficiency.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 38 of its 91 references that are in the map. First posted on arXiv 18 Sep 2023.

Builds on

38 of 91 references.

References · 38

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  4. 2018Neural Ordinary Differential Equationscited by 3,733
  5. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  6. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
  7. 2014Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modelingcited by 2,341
  8. 2017FiLM: Visual Reasoning with a General Conditioning Layercited by 2,286
  9. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  10. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  11. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  12. 2018Learning Implicit Fields for Generative Shape Modelingcited by 1,060
26 more
  1. 2015Scheduled Sampling for Sequence Prediction with Recurrent Neural Networkscited by 779
  2. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 748
  3. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  4. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 581
  5. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 536
  6. 2020WeatherBench: A benchmark dataset for data-driven weather forecastingcited by 272
  7. 2022GraphCast: Learning skillful medium-range global weather forecastingcited by 261
  8. 2020ReZero is All You Need: Fast Convergence at Large Depthcited by 260
  9. 2015A Critical Review of Recurrent Neural Networks for Sequence Learningcited by 223
  10. 2018PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Networkcited by 208
  11. 2022From data to functa: Your data point is a function and you can treat it like onecited by 183
  12. 2023FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Leadcited by 170
  13. 2022Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecastcited by 164
  14. 2021Modulated Periodic Activations for Generalizable Local Functional Representationscited by 140
  15. 2020A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEscited by 105
  16. 2020Improving data-driven global weather prediction using deep convolutional neural networks on a cubed spherecited by 95
  17. 2022COIN++: Neural Compression Across Modalitiescited by 81
  18. 2020MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Frameworkcited by 78
  19. 2022Continuous PDE Dynamics Forecasting with Implicit Neural Representationscited by 71
  20. 2022CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representationscited by 56
  21. 2020Using machine learning to correct model error in data assimilation and forecast applicationscited by 40
  22. 2021Latent Space Data Assimilation by using Deep Learningcited by 29
  23. 2022Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Modelscited by 24
  24. 2021A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modelingcited by 22
  25. 2021Integrating Recurrent Neural Networks with Data Assimilation for Scalable Data-Driven State Estimationcited by 20
  26. 2021Combining distribution-based neural networks to predict weather forecast probabilitiescited by 18

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 3; 2025: 2; 2026: 2.

8 papers.

  1. 2023Towards an end-to-end artificial intelligence driven global weather forecasting systemcited by 20
  2. 2024LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observationscited by 10
  3. 2024FNP: Fourier Neural Processes for Arbitrary-Resolution Data Assimilationcited by 8
  4. 2024State-observation augmented diffusion model for nonlinear assimilation with unknown dynamicscited by 7
  5. 2026Latent Autoencoder Ensemble Kalman Filter for Nonlinear Data assimilationcited by 3
  6. 2025Probabilistic Spatial Interpolation of Sparse Data using Diffusion Modelscited by 0
  7. 2025On the Effect of Neural Field Reparameterization for 4DVARcited by 0
  8. 2026Ensemble Controlled-Flow Filtering for Implicit Data Assimilationcited by 0