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Data-driven operator inference for parameter estimation in nonlinear partial differential equations
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DOI：10.1016/j.jcp.2025.114442.png)
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Abstract
En 中文
Reduced-order models (ROMs) combined with ensemble Kalman filter (EnKF) method have gained attention for parameter estimation in systems governed by nonlinear partial differential equations (PDEs). However, offline-constructed ROMs frequently lose accuracy over long time periods, limiting their effectiveness in dynamic scenarios. To address this issue, we propose a continuous data assimilation-enhanced reduced-order ensemble Kalman filter (CDA-R-EnKF) for efficient and accurate state and parameter estimation. The proposed framework begins by employing a data-driven Operator Inference approach to construct short-term reduced-order models (S-ROMs) using high-fidelity simulation data over a limited time window. For longer-term predictions, we incorporate a continuous data assimilation technique into the EnKF prediction step. This integration leverages low-resolution online simulations to iteratively correct and maintain the accuracy of S-ROMs over long time periods, while retaining the low-dimensional structure of the ROM. As a result, the framework achieves a balance between computational efficiency and long-term prediction accuracy. The effectiveness of the CDA-R-EnKF framework is demonstrated through numerical experiments on benchmark PDE systems, including Burgers’ equation, the advection-diffusion equation, a fractional heat equation, and heat source inversion problem.
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