Tensor-Var: Variational Data Assimilation in Tensor Product Feature Space

• URL: http://arxiv.org/abs/2501.13312v2
• Date: Wed, 12 Feb 2025 18:22:42 GMT
• Title: Tensor-Var: Variational Data Assimilation in Tensor Product Feature Space
• Authors: Yiming Yang, Xiaoyuan Cheng, Daniel Giles, Sibo Cheng, Yi He, Xiao Xue, Boli Chen, Yukun Hu,
• Abstract summary: Variational data assimilation estimates the dynamical system states by minimizing a cost function that fits the numerical models with observational data. The widely used method, four-dimensionalal assimilation (4D-Var), has two primary challenges: (1) computationally demanding for complex nonlinear systems and (2) relying on state-observation mappings, which are often not perfectly known. Deep learning (DL) has been used as a more expressive class of efficient model approximators to address these challenges. In this paper, we propose Conditional Mean Embedding (CME) to address these challenges using kernel Conditional-Var.
• Score: 30.63086465547801
• License:
• Abstract: Variational data assimilation estimates the dynamical system states by minimizing a cost function that fits the numerical models with observational data. The widely used method, four-dimensional variational assimilation (4D-Var), has two primary challenges: (1) computationally demanding for complex nonlinear systems and (2) relying on state-observation mappings, which are often not perfectly known. Deep learning (DL) has been used as a more expressive class of efficient model approximators to address these challenges. However, integrating such models into 4D-Var remains challenging due to their inherent nonlinearities and the lack of theoretical guarantees for consistency in assimilation results. In this paper, we propose Tensor-Var to address these challenges using kernel Conditional Mean Embedding (CME). Tensor-Var improves optimization efficiency by characterizing system dynamics and state-observation mappings as linear operators, leading to a convex cost function in the feature space. Furthermore, our method provides a new perspective to incorporate CME into 4D-Var, offering theoretical guarantees of consistent assimilation results between the original and feature spaces. To improve scalability, we propose a method to learn deep features (DFs) using neural networks within the Tensor-Var framework. Experiments on chaotic systems and global weather prediction with real-time observations show that Tensor-Var outperforms conventional and DL hybrid 4D-Var baselines in accuracy while achieving efficiency comparable to the static 3D-Var method.

Related papers

• Optimality and Adaptivity of Deep Neural Features for Instrumental Variable Regression [57.40108516085593]
  Deep feature instrumental variable (DFIV) regression is a nonparametric approach to IV regression using data-adaptive features learned by deep neural networks. We prove that the DFIV algorithm achieves the minimax optimal learning rate when the target structural function lies in a Besov space.
  arXiv  Detail & Related papers  (2025-01-09T01:22:22Z)
• Learning Controlled Stochastic Differential Equations [61.82896036131116]
  This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled differential equations with non-uniform diffusion. We provide strong theoretical guarantees, including finite-sample bounds for (L2), (Linfty), and risk metrics, with learning rates adaptive to coefficients' regularity. Our method is available as an open-source Python library.
  arXiv  Detail & Related papers  (2024-11-04T11:09:58Z)
• 3D Equivariant Pose Regression via Direct Wigner-D Harmonics Prediction [50.07071392673984]
  Existing methods learn 3D rotations parametrized in the spatial domain using angles or quaternions. We propose a frequency-domain approach that directly predicts Wigner-D coefficients for 3D rotation regression. Our method achieves state-of-the-art results on benchmarks such as ModelNet10-SO(3) and PASCAL3D+.
  arXiv  Detail & Related papers  (2024-11-01T12:50:38Z)
• Adaptive debiased SGD in high-dimensional GLMs with streaming data [4.704144189806667]
  We introduce a novel approach to online inference in high-dimensional generalized linear models. Our method operates in a single-pass mode, significantly reducing both time and space complexity. We demonstrate that our method, termed the Approximated Debiased Lasso (ADL), not only mitigates the need for the bounded individual probability condition but also significantly improves numerical performance.
  arXiv  Detail & Related papers  (2024-05-28T15:36:48Z)
• Enhancing Low-Order Discontinuous Galerkin Methods with Neural Ordinary Differential Equations for Compressible Navier--Stokes Equations [0.1578515540930834]
  We introduce an end-to-end differentiable framework for solving the compressible Navier-Stokes equations. This integrated approach combines a differentiable discontinuous Galerkin solver with a neural network source term. We demonstrate the performance of the proposed framework through two examples.
  arXiv  Detail & Related papers  (2023-10-29T04:26:23Z)
• Dynamic Kernel-Based Adaptive Spatial Aggregation for Learned Image Compression [63.56922682378755]
  We focus on extending spatial aggregation capability and propose a dynamic kernel-based transform coding. The proposed adaptive aggregation generates kernel offsets to capture valid information in the content-conditioned range to help transform. Experimental results demonstrate that our method achieves superior rate-distortion performance on three benchmarks compared to the state-of-the-art learning-based methods.
  arXiv  Detail & Related papers  (2023-08-17T01:34:51Z)
• VTAE: Variational Transformer Autoencoder with Manifolds Learning [144.0546653941249]
  Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables. The nonlinearity of the generator implies that the latent space shows an unsatisfactory projection of the data space, which results in poor representation learning. We show that geodesics and accurate computation can substantially improve the performance of deep generative models.
  arXiv  Detail & Related papers  (2023-04-03T13:13:19Z)
• Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models [10.410970649045943]
  We develop a system which combines reduced-order surrogate models with a novel data assimilation technique. Generalised Latent Assimilation can benefit both the efficiency provided by the reduced-order modelling and the accuracy of data assimilation.
  arXiv  Detail & Related papers  (2022-04-07T15:13:12Z)
• Observation Error Covariance Specification in Dynamical Systems for Data assimilation using Recurrent Neural Networks [0.5330240017302621]
  We propose a data-driven approach based on long short term memory (LSTM) recurrent neural networks (RNN) The proposed approach does not require any knowledge or assumption about prior error distribution. We have compared the novel approach with two state-of-the-art covariance tuning algorithms, namely DI01 and D05.
  arXiv  Detail & Related papers  (2021-11-11T20:23:00Z)
• Efficient Semi-Implicit Variational Inference [65.07058307271329]
  We propose an efficient and scalable semi-implicit extrapolational (SIVI) Our method maps SIVI's evidence to a rigorous inference of lower gradient values.
  arXiv  Detail & Related papers  (2021-01-15T11:39:09Z)
• SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks [14.564168076456822]
  We propose a flexible model for survival analysis using neural networks along with scalable optimization algorithms. We demonstrate the effectiveness of the proposed method in comparison to existing state-of-the-art deep learning survival analysis models.
  arXiv  Detail & Related papers  (2020-08-19T19:11:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.