For centuries, flow visualization has been the art of making fluid motion visible in physical and biological systems. Although such flow patterns can be, in principle, described by the Navier-Stokes equations, extracting the velocity and pressure fields directly from the images is challenging. We addressed this problem by developing hidden fluid mechanics (HFM), a physics-informed deep-learning framework capable of encoding the Navier-Stokes equations into the neural networks while being agnostic to the geometry or the initial and boundary conditions. We demonstrate HFM for several physical and biomedical problems by extracting quantitative information for which direct measurements may not be possible. HFM is robust to low resolution and substantial noise in the observation data, which is important for potential applications.

No abstract

This paper explores a variety of strategies for understanding the formation, structure, efficiency, and vulnerability of water distribution networks. Water supply systems are studied as spatially organized networks for which the practical applications of abstract evaluation methods are critically evaluated. Empirical data from benchmark networks are used to study the interplay between network structure and operational efficiency, reliability, and robustness. Structural measurements are undertaken to quantify properties such as redundancy and optimal-connectivity, herein proposed as constraints in network design optimization problems. The role of the supply demand structure toward system efficiency is studied, and an assessment of the vulnerability to failures based on the disconnection of nodes from the source(s) is undertaken. The absence of conventional degree-based hubs (observed through uncorrelated nonheterogeneous sparse topologies) prompts an alternative approach to studying structural vulnerability based on the identification of network cut-sets and optimal-connectivity invariants. A discussion on the scope, limitations, and possible future directions of this research is provided.