Generative Reconstruction of Flows Based on Incomplete Data

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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.