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.

翻译：本文提出一种基于循环神经网络（RNN）与有限元（FE）方法的混合建模框架，用于逼近时间相关多保真度问题中的模型偏差，并利用训练后的混合模型对低保真度模型进行偏差校正。该混合模型以FE基函数作为空间基函数，并采用RNN近似FE基自由度的时变特性。训练数据集由预先从高低保真度动态FE模型轨迹数据中计算的偏差函数稀疏非均匀采样快照构成。为应对数据稀疏性并防止过拟合，引入数据上采样与局部加权因子，在物理一致性模型行为与神经网络回归之间建立权衡机制。所提出的混合建模方法在三个高度非平凡的工程测试案例中进行了验证，这些案例均涉及瞬态FE模型，具体包括散热器热扩散、四极磁体涡流以及空腔声波传播。结果表明，所提出的混合模型能够以高精度逼近模型偏差，并相应地对低保真度模型进行校正。