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Error approximation and bias correction in dynamic problems using a recurrent neural network/finite element hybrid model.
- Source :
-
Applied Mathematical Modelling . May2024, Vol. 129, p428-447. 20p. - Publication Year :
- 2024
-
Abstract
- This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time-dependent, multi-fidelity problems, and use the trained hybrid models to perform bias correction of the low-fidelity models. The hybrid model uses FE basis functions as a spatial basis and RNNs for the approximation of the time dependencies of the FE basis' degrees of freedom. The training data sets consist of sparse, non-uniformly sampled snapshots of the discrepancy function, pre-computed from trajectory data of low- and high-fidelity dynamic FE models. To account for data sparsity and prevent overfitting, data upsampling and local weighting factors are employed, to instigate a trade-off between physically conforming model behavior and neural network regression. The proposed hybrid modeling methodology is showcased in three highly non-trivial engineering test-cases, all featuring transient FE models, namely, heat diffusion out of a heat sink, eddy-currents in a quadrupole magnet, and sound wave propagation in a cavity. The results show that the proposed hybrid model is capable of approximating model discrepancies to a high degree of accuracy and accordingly correct low-fidelity models. • A RNN/FE hybrid model is developed to learn model discrepancies of multi-fidelity FE simulations based on trajectory data. • The RNN captures the dynamics of the discrepancy function while spatial discrepancies are resolved by a FE basis. • Upsampling and Gaussian priors are employed to account for sparsity in the discrepancy data and prevent overfitting. • The model is employed as a correction operator for low-fidelity models in three non-trivial test cases. • The bias corrected models are significantly more accurate compared to the original low-fidelity models. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0307904X
- Volume :
- 129
- Database :
- Academic Search Index
- Journal :
- Applied Mathematical Modelling
- Publication Type :
- Academic Journal
- Accession number :
- 176196295
- Full Text :
- https://doi.org/10.1016/j.apm.2024.02.004