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)方法相结合的混合建模框架，用于逼近时间依赖型多保真度问题中的模型差异，并利用训练后的混合模型对低保真度模型进行偏差修正。该混合模型采用FE基函数作为空间基，通过RNN逼近FE基自由度的时变特性。训练数据集由稀疏非均匀采样的差异函数快照构成，这些快照预先通过高低保真度动态FE模型的轨迹数据计算得到。为应对数据稀疏性并防止过拟合，引入数据升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达成平衡。该混合建模方法在三个高度非常规的工程测试案例中得到验证，均涉及瞬态FE模型，具体包括：散热器热扩散、四极磁体涡流以及腔体内声波传播。结果表明，所提混合模型能够高精度逼近模型差异，并有效修正低保真度模型。