Flamelet models are widely used in computational fluid dynamics to simulate thermochemical processes in turbulent combustion. These models typically employ memory-expensive lookup tables that are predetermined and represent the combustion process to be simulated. Artificial neural networks (ANNs) offer a deep learning approach that can store this tabular data using a small number of network weights, potentially reducing the memory demands of complex simulations by orders of magnitude. However, ANNs with standard training losses often struggle with underrepresented targets in multivariate regression tasks, e.g., when learning minor species mass fractions as part of lookup tables. This paper seeks to improve the accuracy of an ANN when learning multiple species mass fractions of a hydrogen (\ce{H2}) combustion lookup table. We assess a simple, yet effective loss weight adjustment that outperforms the standard mean-squared error optimization and enables accurate learning of all species mass fractions, even of minor species where the standard optimization completely fails. Furthermore, we find that the loss weight adjustment leads to more balanced gradients in the network training, which explains its effectiveness.

翻译：火焰面模型广泛应用于计算流体力学中，用于模拟湍流燃烧中的热化学过程。这类模型通常采用预先确定且代表待模拟燃烧过程的、占用大量内存的查找表。人工神经网络提供了一种深度学习方法，能够通过少量网络权重存储这些表格数据，从而将复杂模拟的内存需求降低数个数量级。然而，采用标准训练损失的人工神经网络在多元回归任务中，经常难以处理表征不足的目标变量（例如，当学习作为查找表组成部分的微量组分质量分数时）。本文旨在提高人工神经网络在学习氢气 (\ce{H2}) 燃烧查找表中多种组分质量分数时的准确性。我们评估了一种简单而有效的损失权重调整方法，该方法优于标准均方误差优化，能够准确学习所有组分（包括标准优化完全失效的微量组分）的质量分数。此外，我们发现损失权重调整能在网络训练中产生更均衡的梯度，这解释了其有效性。