PnP-DA: Towards Principled Plug-and-Play Integration of Variational Data Assimilation and Generative Models

• URL: http://arxiv.org/abs/2508.00325v1
• Date: Fri, 01 Aug 2025 05:19:19 GMT
• Title: PnP-DA: Towards Principled Plug-and-Play Integration of Variational Data Assimilation and Generative Models
• Authors: Yongquan Qu, Matthieu Blanke, Sara Shamekh, Pierre Gentine,
• Abstract summary: Earth system modeling presents a fundamental challenge in scientific computing.<n>Even the most powerful AI- or physics-based forecast system suffer from gradual error accumulation.<n>We propose a Plug-and-Play algorithm that alternates a lightweight, gradient-based analysis update with a single forward pass through a pretrained prior conditioned on the background forecast.
• Score: 0.1052166918701117
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Earth system modeling presents a fundamental challenge in scientific computing: capturing complex, multiscale nonlinear dynamics in computationally efficient models while minimizing forecast errors caused by necessary simplifications. Even the most powerful AI- or physics-based forecast system suffer from gradual error accumulation. Data assimilation (DA) aims to mitigate these errors by optimally blending (noisy) observations with prior model forecasts, but conventional variational methods often assume Gaussian error statistics that fail to capture the true, non-Gaussian behavior of chaotic dynamical systems. We propose PnP-DA, a Plug-and-Play algorithm that alternates (1) a lightweight, gradient-based analysis update (using a Mahalanobis-distance misfit on new observations) with (2) a single forward pass through a pretrained generative prior conditioned on the background forecast via a conditional Wasserstein coupling. This strategy relaxes restrictive statistical assumptions and leverages rich historical data without requiring an explicit regularization functional, and it also avoids the need to backpropagate gradients through the complex neural network that encodes the prior during assimilation cycles. Experiments on standard chaotic testbeds demonstrate that this strategy consistently reduces forecast errors across a range of observation sparsities and noise levels, outperforming classical variational methods.

Related papers

• Interpretable Deep Regression Models with Interval-Censored Failure Time Data [1.2993568435938014]
  Deep learning methods for interval-censored data remain underexplored and limited to specific data type or model.<n>This work proposes a general regression framework for interval-censored data with a broad class of partially linear transformation models.<n>Applying our method to the Alzheimer's Disease Neuroimaging Initiative dataset yields novel insights and improved predictive performance compared to traditional approaches.
  arXiv  Detail & Related papers  (2025-03-25T15:27:32Z)
• Topological Approach for Data Assimilation [0.4972323953932129]
  We introduce a new data assimilation algorithm with a foundation in topological data analysis.<n>By leveraging the differentiability of functions of persistence, gradient descent optimization is used to minimize topological differences between measurements and forecast predictions.
  arXiv  Detail & Related papers  (2024-11-12T20:24:46Z)
• On conditional diffusion models for PDE simulations [53.01911265639582]
  We study score-based diffusion models for forecasting and assimilation of sparse observations. We propose an autoregressive sampling approach that significantly improves performance in forecasting. We also propose a new training strategy for conditional score-based models that achieves stable performance over a range of history lengths.
  arXiv  Detail & Related papers  (2024-10-21T18:31:04Z)
• Model-Based Reparameterization Policy Gradient Methods: Theory and Practical Algorithms [88.74308282658133]
  Reization (RP) Policy Gradient Methods (PGMs) have been widely adopted for continuous control tasks in robotics and computer graphics. Recent studies have revealed that, when applied to long-term reinforcement learning problems, model-based RP PGMs may experience chaotic and non-smooth optimization landscapes. We propose a spectral normalization method to mitigate the exploding variance issue caused by long model unrolls.
  arXiv  Detail & Related papers  (2023-10-30T18:43:21Z)
• Exact nonlinear state estimation [0.0]
  The majority of data assimilation methods in the geosciences are based on Gaussian assumptions.<n>Non-parametric, particle-based DA algorithms have superior accuracy, but their application to high-dimensional models still poses operational challenges.<n>This article introduces a new nonlinear estimation theory which attempts to bridge the existing gap in DA methodology.
  arXiv  Detail & Related papers  (2023-10-17T03:44:29Z)
• Episodic Gaussian Process-Based Learning Control with Vanishing Tracking Errors [10.627020714408445]
  We develop an episodic approach for learning GP models, such that an arbitrary tracking accuracy can be guaranteed. The effectiveness of the derived theory is demonstrated in several simulations.
  arXiv  Detail & Related papers  (2023-07-10T08:43:28Z)
• Koopman Kernel Regression [6.116741319526748]
  We show that Koopman operator theory offers a beneficial paradigm for characterizing forecasts via linear time-invariant (LTI) ODEs. We derive a universal Koopman-invariant kernel reproducing Hilbert space (RKHS) that solely spans transformations into LTI dynamical systems. Our experiments demonstrate superior forecasting performance compared to Koopman operator and sequential data predictors.
  arXiv  Detail & Related papers  (2023-05-25T16:22:22Z)
• A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study [68.8204255655161]
  We investigate and compare the performance of several local and global smoothing techniques to a priori denoise the state measurements. We show that, in general, global methods, which use the entire measurement data set, outperform local methods, which employ a neighboring data subset around a local point.
  arXiv  Detail & Related papers  (2022-01-29T23:31:25Z)
• Imputation-Free Learning from Incomplete Observations [73.15386629370111]
  We introduce the importance of guided gradient descent (IGSGD) method to train inference from inputs containing missing values without imputation. We employ reinforcement learning (RL) to adjust the gradients used to train the models via back-propagation. Our imputation-free predictions outperform the traditional two-step imputation-based predictions using state-of-the-art imputation methods.
  arXiv  Detail & Related papers  (2021-07-05T12:44:39Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)
• CASTLE: Regularization via Auxiliary Causal Graph Discovery [89.74800176981842]
  We introduce Causal Structure Learning (CASTLE) regularization and propose to regularize a neural network by jointly learning the causal relationships between variables. CASTLE efficiently reconstructs only the features in the causal DAG that have a causal neighbor, whereas reconstruction-based regularizers suboptimally reconstruct all input features.
  arXiv  Detail & Related papers  (2020-09-28T09:49:38Z)
• LSTM-based Anomaly Detection for Non-linear Dynamical System [11.797156206007612]
  We propose a novel anomaly detection scheme in non-linear dynamical system based on Long Short-Term Memory (LSTM) We first present the framework of LSTM-based anomaly detection in non-linear dynamical system, including data preprocessing, multi-step prediction and anomaly detection. Our proposed multi-step prediction method can achieve a higher prediction accuracy than traditional method in wall shear stress dataset.
  arXiv  Detail & Related papers  (2020-06-05T01:09:36Z)

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.