Turbulence is still one of the main challenges in accurate prediction of reactive flows. Therefore, the development of new turbulence closures that can be applied to combustion problems is essential. Over the last few years, data-driven modeling has become popular in many fields as large, often extensively labeled datasets are now available and training of large neural networks has become possible on graphics processing units (GPUs) that speed up the learning process tremendously. However, the successful application of deep neural networks in fluid dynamics, such as in subfilter modeling in the context of large-eddy simulations (LESs), is still challenging. Reasons for this are the large number of degrees of freedom in natural flows, high requirements of accuracy and error robustness, and open questions, for example, regarding the generalization capability of trained neural networks in such high-dimensional, physics-constrained scenarios. This work presents a novel subfilter modeling approach based on a generative adversarial network (GAN), which is trained with unsupervised deep learning (DL) using adversarial and physics-informed losses. A two-step training method is employed to improve the generalization capability, especially extrapolation, of the network. The novel approach gives good results in a priori and a posteriori tests with decaying turbulence including turbulent mixing, and the importance of the physics-informed continuity loss term is demonstrated. The applicability of the network in complex combustion scenarios is furthermore discussed by employing it in reactive and inert LESs of the Spray A case defined by the Engine Combustion Network (ECN).

湍流仍然是精确预测反应流的主要挑战之一。因此，开发可应用于燃烧问题的新型湍流闭合器至关重要。在过去的几年中，数据驱动的建模已在许多领域变得流行，因为现在可以使用大型的，通常带有广泛标记的数据集，并且可以在图形处理单元（GPU）上进行大型神经网络的训练，从而极大地加快了学习过程。然而，深层神经网络在流体动力学中的成功应用，例如在大涡模拟（LESs）的子过滤器建模中，仍然具有挑战性。造成这种情况的原因是，例如，自然流中的自由度很高，对准确性和错误鲁棒性的要求很高，还有一些未解决的问题，例如，关于在这种高维度，受物理限制的场景中训练后的神经网络的泛化能力。这项工作提出了一种基于生成对抗网络（GAN）的新颖子过滤器建模方法，该方法利用对抗性和物理信息损失进行无监督深度学习（DL）训练。采用两步训练方法来提高网络的泛化能力，尤其是外推能力。这种新颖的方法在先验和后验测试中均获得了良好的结果，该测试具有包括湍流混合在内的衰减湍流，并且证明了物理信息连续性损失项的重要性。通过在发动机燃烧网络（ECN）定义的Spray A案例的反应性和惰性LES中使用该网络，进一步讨论了该网络在复杂燃烧场景中的适用性。