Domain-Decomposition Neural Surrogates for Scalable Decentralized Ensemble Kalman Filter Based Parameter Identification in High-Dimensional Stochastic PDEs
2026-07-27 • Computational Engineering, Finance, and Science
Computational Engineering, Finance, and Science
AI summaryⓘ
The authors present a method to speed up how we estimate material properties from spatial data by combining neural networks (NN) with a technique called Ensemble Kalman Filters (EnKF). Instead of using many samples for predictions, they use NN models that focus on local regions to reduce complexity and improve accuracy. They also develop a way for these local models to communicate and produce a consistent overall estimate efficiently. Tested on a 3D problem, their approach gave results similar to traditional methods but was faster. The method balances accuracy and computation better than some existing solutions.
Ensemble Kalman FilterNeural NetworkSurrogate ModelDomain Decomposition MethodParameter IdentificationBayesian InferenceMaterial Parameter EstimationMarkov Chain Monte CarloSpatially Distributed MeasurementsPosterior Distribution
Authors
Timm Gödde, Bojana Rosić
Abstract
Ensemble Kalman filters (EnKF) provide an efficient framework for parameter identification of physics based laws from spatially distributed measurements. Their forecast models require a large number of samples to accurately represent uncertainties, leading to high computational costs. A NN-based surrogate model is introduced to replace the sample-based forecast model. The proposed NN surrogate maps spatial coordinates and physics-based parameters to the forecasted observation. Such maps require a large number of parameters for high-dimensional spatial domains. To overcome this limitation, a augmented Lagrange multiplier domain decomposition method (DDM) is developed, where local NN models are optimized independently before global communication and coupling. This reduces the number of NN parameters while improving local approximation accuracy. Furthermore, a distributed and decentralized ensemble Kalman filter approach based on DDM-NN surrogate model is investigated, where the parameter identification problem is decomposed into local subproblems. Each local estimator updates the material parameters using locally available information, while communication between neighboring subdomains enables the reconstruction of a consistent global estimate to reduce the computational cost. The proposed method is evaluated on a three-dimensional material parameter identification problem and compared with an EnKF and a MCMC reference solution. The results show that the proposed DDM NN-based KF captures the posterior parameter distribution and approaches the solutions obtained with both EnKF and MCMC. While MCMC provides the most accurate representation of the posterior distribution, the proposed approach achieves comparable parameter estimates with reduced computational requirements for the forecast model.