arXiv subjects

Timm Gödde

Publications and source records attributed to Timm Gödde.

2 recordsLinked to original sources

arXiv2026

Domain-Decomposition Neural Surrogates for Scalable Decentralized Ensemble Kalman Filter Based Parameter Identification in High-Dimensional Stochastic PDEs

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.

cs.CE↗

arXiv2026

Domain decomposition of large neural network surrogate models

Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power as global approximators, NNs often fail to accurately capture local nonlinearities without relying on a large number of training parameters. To address these limitations, in this paper we propose domain decomposition methods (DDM), which divide the input feature space into multiple local subdomains, each modeled by a simpler NN, trained in parallel. To recover the accuracy of a global approximation, interface constraints are introduced in the local loss functions to enforce continuity between subdomains. The interface constraints are enforced with two different approaches, by utilizing Lagrange multiplier or augmented Lagrange multiplier methods. Both approaches are validated using synthetic data from 2D and 3D linear compression problems, numerically solved using the finite element method. The study investigates computational time and accuracy across varying numbers of subdomains to identify optimal partitioning strategies. Compared to unconstrained approximations, both methods significantly improve continuity across subdomain interfaces. Also, the use of DDMs improves approximation accuracy in nonlinear regions when compared to standard global NN training. The augmented Lagrange method outperforms the standard Lagrange formulation by converging faster due to lower convergence requirements, albeit with a slightly lower accuracy. Its scalability makes it the preferred choice for large-scale problems, as the faster convergence outweighs the minor loss in accuracy. Overall, these results highlight the augmented Lagrange method as a promising DDM approach for training efficient and scalable NN surrogate models.

cs.CE↗