Generative Reconstruction of Flows Based on Incomplete Data

我们建议开发一个生成性深度学习模型来从不完整的流场观测中创建缺失数据。开发策略基于对抗性网络(GAN)从学习中生成具有高度物理真实感的合成图像的能力，并通过多视角概念和归纳偏差在随后的两个步骤中增强。它的实际影响是双重的。首先，我们将推出一种算法仪器，通过生成具有不确定度估计界限的缺失现场数据来增强流动成像测量。我们将证明这个仪器可以用来从流量测量数据中重建完整的流场信息，而不需要依靠基于模拟的同化技术。其次，产生式网络为低成本地生成大量具有高物理真实感的合成数据提供了算法工具。这种低成本的仪器能够创建物理上真实的数据库，用于训练推理算法，从而补充稀疏的高保真数据集。作为概念验证，我们考虑超音速流动的纹影图像，因为训练数据可以高保真地生成，并且基本的流动物理被很好地理解，而场重建的任务仍然具有挑战性。在第一步中，我们制定了一种GaN结构来生成物理上逼真的纹影图像，这是最接近GaN最初动机的。我们评估网络从图像数据集中捕获特征的能力。随后，我们解决了场重建问题，这需要通过多视角概念来显著增强。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，我们评估了引入微分演化规律作为感应偏置是否提高了已开发的重建GaN的重建能力。目前项目处理的科学挑战是，在不借助全球数值解的情况下，从可观测物体的二维数据重建多变量场信息(光束-路径综合光强分布)。这样的问题是高度不适定的，如果没有通过培训获得的特定领域的知识，就无法解决。这种方法超越了数据同化，因为我们不支持在时空观察域上通过模拟来重建场。本文将对甘氏进行解剖，以了解它们如何在其潜在结构中表现纹影图像和场。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规律提供线索。我们将依靠生成和记录的真实纹影图像和现场数据之间的Fréchet初始距离来评估生成的图像和场的物理真实感。

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.