Error Approximation and Bias Correction in Dynamic Problems using a Recurrent Neural Network/Finite Element Hybrid Model

TL;DR

This paper introduces a hybrid RNN-FE modeling framework for approximating discrepancies in multi-fidelity, time-dependent problems, enabling bias correction of low-fidelity models with high accuracy.

Contribution

It presents a novel hybrid approach combining RNNs and FE basis functions for discrepancy approximation and bias correction in complex dynamic systems.

Findings

High-accuracy discrepancy approximation in three engineering cases

Effective bias correction of low-fidelity models demonstrated

Method handles sparse, non-uniform data effectively

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.