Flow networks are ubiquitous in natural and engineered systems, and in order to understand and manage these networks, one must quantify the flow of commodities across their edges. This paper considers the estimation problem of predicting unlabeled edge flows from nodal supply and demand. We propose an implicit neural network layer that incorporates two fundamental physical laws: conservation of mass, and the existence of a constitutive relationship between edge flows and nodal states (e.g., Ohm's law). Computing the edge flows from these two laws is a nonlinear inverse problem, which our layer solves efficiently with a specialized contraction mapping. Using implicit differentiation to compute the solution's gradients, our model is able to learn the constitutive relationship within a semi-supervised framework. We demonstrate that our approach can accurately predict edge flows in several experiments on AC power networks and water distribution systems.

Many tasks regarding the monitoring, management, and design of communication networks rely on knowledge of the routing topology. However, the standard approach to topology mapping—namely, active probing with traceroutes—relies on cooperation from increasingly non-cooperative routers, leading to missing information. Network tomography, which uses end-to-end measurements of additive link metrics (like delays or log packet loss rates) across monitor paths, is a possible remedy. Network tomography does not require that routers cooperate with traceroute probes, and it has already been used to infer the structure of multicast trees. This paper goes a step further. We provide a tomographic method to infer the underlying routing topology of an arbitrary set of monitor paths using the joint distribution of end-to-end measurements, without making any assumptions on routing behavior. Our approach, called the Möbius Inference Algorithm (MIA), uses cumulants of this distribution to quantify high-order interactions among monitor paths, and it applies Möbius inversion to “disentangle” these interactions. In addition to MIA, we provide a more practical variant called Sparse Möbius Inference, which uses various sparsity heuristics to reduce the number and order of cumulants required to be estimated. We show the viability of our approach using synthetic case studies based on real-world ISP topologies.

This paper presents a graph-based model of periodic migrations of tagged fish populations and two multi-AUV stochastic controllers developed to track these fish from the model. The model presented in this paper characterizes patterns in the historical movement of tagged fish and is used to develop stochastic tracking by a “model based control” and a “feedback control”. These two controllers permit swarms of AUVs to track the transition probabilities of the tagged population between vertices of the model. To validate these controllers, a periodic model is developed for a simulated population based on three months of geolocation data from a kelp bass (Paralabrax clathratus), and AUV teams utilizing both controllers are simulated in tracking this population. Results show the viability of stochastic controls for multi-AUV tracking of populations whose behavior is well-approximated by the graph-based model. Preliminary trials with physical AUV systems indicate the plausibility of hardware implementation.