Joint state-parameter estimation for the reduced fracture model via the united filter

Journal Article · Fri Jun 13 00:00:00 EDT 2025 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2025.114159· OSTI ID:3002347

Huynh, Phuoc Toan ^[1]; Hoang, Thi-Thao-Phuong ^[2]; Zhang, Guannan ^[3]; Bao, Feng ^[1]

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1. Florida State Univ., Tallahassee, FL (United States)
2. Auburn Univ., AL (United States)
3. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Here, in this paper, we introduce an effective United Filter method for jointly estimating the solution state and physical parameters in flow and transport problems within fractured porous media. Fluid flow and transport in fractured porous media are critical in subsurface hydrology, geophysics, and reservoir geomechanics. Reduced fracture models, which represent fractures as lower-dimensional interfaces, enable efficient multi-scale simulations. However, reduced fracture models also face accuracy challenges due to modeling errors and uncertainties in physical parameters such as permeability and fracture geometry. To address these challenges, we propose a United Filter method, which integrates the Ensemble Score Filter (EnSF) for state estimation with the Direct Filter for parameter estimation. EnSF, based on a score-based diffusion model framework, produces ensemble representations of the state distribution without deep learning. Meanwhile, the Direct Filter, a recursive Bayesian inference method, estimates parameters directly from state observations. The United Filter combines these methods iteratively: EnSF estimates are used to refine parameter values, which are then fed back to improve state estimation. Numerical experiments demonstrate that the United Filter method surpasses the state-of-the-art Augmented Ensemble Kalman Filter, delivering more accurate state and parameter estimation for reduced fracture models. This framework also provides a robust and efficient solution for PDE-constrained inverse problems with uncertainties and sparse observations.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: AC05-00OR22725; SC0024703; SC0025412
• OSTI ID: 3002347
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 538; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

Bayesian inference
Data assimilation
Ensemble score filter
Joint state-parameter estimation
Reduced fracture model