Random-walk-based methods for solving partial differential equations (PDEs) exhibit significant advantages and applicability to numerous domains. One of these is parasitic capacitance extraction in modern silicon technologies, where they are essentially called upon to solve a boundary-value problem. In this regime, fast and accurate calculation of Green’s function within the transition domains of the random walk is critical for competitive performance. Silicon processes in advanced nodes introduce complex or special dielectric structures that challenge currently established methods for characterizing Green’s function. In this article, a novel approximation method for Green’s function and Green’s function gradient is presented, which leverages group-equivariant convolutional neural networks (G-CNNs). This can accompany existing multitier Green’s function data precomputation schemes. Additionally, it enables performing the crucial step of sampling according to Green’s function without explicit calculation of Green’s function itself. A novel end-to-end random-walk architecture is discussed which incorporates such deep neural networks, and its utility is demonstrated through numerical experiments. The proposed scheme enjoys massive gains in terms of speed for advanced CMOS nm node setups with nonplanar dielectric media, compared to a straight finite differences method (FDM) solution, while maintaining good accuracy levels.

An important class of sensor network applications aims at estimating the spatiotemporal behavior of a physical phenomenon, such as temperature variations over an area of interest. In such a scenario, the network essentially acts as a distributed sampling system. However, unlike in the event detection case, the notion of sensing range is largely meaningless for sampling-interpolation applications. As a result, existing techniques to exploit sensing redundancy in event detection settings, which rely on the existence of such sensing range, become unusable. Instead, this article presents a new method to exploit redundancy for the sampling class of applications by selecting a suitable set of sensors to act as sampling points. Through online estimation of process characteristics, sufficiently accurate interpolation can be achieved. We illustrate an algorithm to obtain multiple disjoint sets and demonstrate significant reductions in the number of active sensors for a wide range of synthetic sensor data.

We focus on dense networks of wireless sensors used for distributed sampling and interpolation. Sensors periodically sample a physical quantity of interest, e.g. temperature, and report their measurements to a data center. A continuous spatial estimate of the quantity can then be constructed through interpolation. In these cases, density in deployment can be exploited to achieve longer operational time for the network. The challenge is how to select multiple disjoint subsets of sensors such that each of them is individually capable of meeting the quality demands of the monitoring application. In this paper we present an efficient sensor selection scheme for the min-max monitoring application, i.e., minimizing the maximum distortion incurred over space through interpolation. Evaluation with synthetic sensor network data shows that significant reductions in the number of active sensors and energy consumption are possible compared to simpler selection methods.