Generative Reconstruction of Flows Based on Incomplete Data

我们建议开发一种生成式深度学习模型，以从不完整的流场观察中创建缺失数据。开发策略基于对抗网络（GAN）的能力，通过学习生成具有高度物理真实感的合成图像，并通过多视图概念和归纳偏差在随后的两个步骤中得到增强。实际影响是双重的。首先，我们将推导出一种算法工具，通过生成具有不确定性估计范围的缺失场数据来增强血流成像测量。我们将证明这一概念，该仪器可以用来重建从流量测量数据的流场信息，而不依赖于基于模拟的同化技术。其次，生成网络提供了一种算法工具，用于低成本生成具有高度物理真实性的大量合成数据。这样一个低成本的仪器，使物理现实的数据库的推理算法的训练，从而补充稀疏的高保真数据集的创建。作为概念验证，我们考虑超声速流的纹影图像，因为训练数据可以以高保真度生成，并且底层的流动物理学已经很好地理解，而场重建的任务仍然具有挑战性。第一步，我们制定了一个GAN架构，以生成物理上逼真的纹影图像，这是最接近GAN的原始动机。我们评估了网络从图像数据集中捕获特征的能力。随后，我们解决现场重建问题，这需要一个显着的增强多视图的概念。由于现在的任务与图像生成有很大的不同，我们预计需要对普通GAN进行重大修改。最后，我们评估是否纳入差分进化规律作为归纳偏差提高了重建能力的开发重建GAN。当前项目所面临的科学挑战是在不诉诸于全局数值解的情况下，从可观测的二维数据（光束路径集成光强度分布）重建多变量场信息。这样的问题是高度不适定的，如果没有通过训练获得的特定领域的知识，就无法解决。该方法超越了数据同化，因为我们不支持通过时空观测域上的模拟进行场重建。将对GAN进行解剖，以了解它们如何在其潜在结构中表示纹影图像和场。对潜在结构的干预将揭示因果关系，并将为网络如何编码部分内在的潜在物理定律提供线索。我们将依靠生成和记录的真实的纹影图像和场数据之间的Fréchet起始距离来评估生成的图像和场的物理真实性。

We propose the development of a generative deep-learning model to create missing data from incomplete flow-field observations. The development strategy is based on the capability of adversarial networks (GAN) to generate synthetic images with high physical realism from learning, enhanced in two subsequent steps by a multi-view concept and by inductive bias. The practical implications are twofold. First, we will derive an algorithmic instrument to augment flow imaging measurements by generation of missing field data with an estimated bound on uncertainties. We will prove the concept that this instrument may be employed to reconstruct from flow-measurement data a full flow-field information without recourse to simulation-based assimilation techniques. Second, the generative network provides an algorithmic instrument for low-cost generation of an abundance of synthetic data with high physical realism. Such a low-cost instrument enables the creation of of physically realistic data bases for training of inference algorithms and thus supplements sparse high-fidelity data sets. As proof-of-concept we consider Schlieren images of supersonic flows, as training data can be generated with high fidelity, and as the underlying flow physics is well understood, while the task of field reconstruction remains challenging. With the first step we formulate a GAN architecture to generate physically realistic Schlieren images, which is closest to the original motivation of GAN. We assess the capability of the network to capture features from image datasets. Subsequently, we address the field-reconstruction problem, which requires a significant enhancement by a multi-view concept. As the task now differs significantly from image generation we expect the need for major modifications of plain GAN. Finally, we assess whether the incorporation of differential evolution laws as inductive bias improves the reconstruction capacity of the developed reconstructive GAN. The scientific challenge addressed by the current project is to reconstruct without recourse to a global numerical solution multi-variable field information from two-dimensional data of an observable (beam-path integrated light intensity distributions). Such a problem is highly ill-posed and cannot be solved without domain-specific knowledge through training. The approach goes beyond data assimilation, as we do not support the field reconstruction by simulations on the spatiotemporal observation domain. Dissection will be applied to the GANs in order to understand how they represent the Schlieren images and fields within their latent structure. Interventions on the latent structure will reveal causal interrelation and will provide hints on how the networks have already encoded part of the inherent underlying physical laws. We will rely on the Fréchet inception distance between generated and recorded real Schlieren images and field data to assess the physical realism of the generated images and fields.