Efficient Real-Time Adaptation of ROMs for Unsteady Flows Using Data Assimilation

2026-02-26

AI Summary

This work addresses the challenge of degraded accuracy in parametric reduced-order models (ROMs) for unsteady flow fields when encountering out-of-sample parameters, coupled with the prohibitive cost of full model retraining. To this end, a lightweight online adaptation framework is proposed, built upon a variational autoencoder (VAE)–Transformer encoder–processor–decoder architecture integrated with the ensemble Kalman filter (EnKF) for data assimilation and uncertainty quantification under sparse observations. The key insight is that out-of-sample errors primarily stem from distortions in the latent manifold rather than inaccuracies in dynamic evolution, enabling efficient adaptation through fine-tuning only the VAE. Experiments demonstrate that the method achieves accuracy comparable to full retraining at minimal computational cost, facilitating real-time state reconstruction and uncertainty estimation.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while requiring only a fraction of the computational time and relying solely on sparse observations of the full system. The architecture employs an encode-process-decode structure: a Variational Autoencoder (VAE) to perform dimensionality reduction, and a transformer network to evolve the latent states and model the dynamics. The ROM is parameterized by an external control variable, the Reynolds number in the Navier-Stokes setting, with the transformer exploiting attention mechanisms to capture both temporal dependencies and parameter effects. The probabilistic VAE enables stochastic sampling of trajectory ensembles, providing predictive means and uncertainty quantification through the first two moments. After initial training on a limited set of dynamical regimes, the model is adapted to out-of-sample parameter regions using only sparse data. Its probabilistic formulation naturally supports ensemble generation, which we employ within an ensemble Kalman filtering framework to assimilate data and reconstruct full-state trajectories from minimal observations. We further show that, for the dynamical system considered, the dominant source of error in out-of-sample forecasts stems from distortions of the latent manifold rather than changes in the latent dynamics. Consequently, retraining can be limited to the autoencoder, allowing for a lightweight, computationally efficient, real-time adaptation procedure with very sparse fine-tuning data.

Problem

• Reduced Order Model
• Real-Time Adaptation
• Unsteady Flows
• Data Assimilation
• Out-of-Sample Prediction

Innovation

• Reduced Order Model
• Variational Autoencoder
• Transformer
• Data Assimilation
• Ensemble Kalman Filter