Stable cheapest nonconforming finite elements for the Stokes equations

We introduce two pairs of stable cheapest nonconforming finite element space pairs to approximate the Stokes equations. One pair has each component of its velocity field to be approximated by the $P_1$ nonconforming quadrilateral element while the pressure field is approximated by the piecewise constant function with globally two-dimensional subspaces removed: one removed space is due to the integral mean--zero property and the other space consists of global checker--board patterns. The other pair consists of the velocity space as the $P_1$ nonconforming quadrilateral element enriched by a globally one--dimensional macro bubble function space based on $DSSY$ (Douglas-Santos-Sheen-Ye) nonconforming finite element space; the pressure field is approximated by the piecewise constant function with mean--zero space eliminated. We show that two element pairs satisfy the discrete inf-sup condition uniformly. And we investigate the relationship between them. Several numerical examples are shown to confirm the efficiency and reliability of the proposed methods

Subtask Gated Networks for Non-Intrusive Load Monitoring

Non-intrusive load monitoring (NILM), also known as energy disaggregation, is a blind source separation problem where a household's aggregate electricity consumption is broken down into electricity usages of individual appliances. In this way, the cost and trouble of installing many measurement devices over numerous household appliances can be avoided, and only one device needs to be installed. The problem has been well-known since Hart's seminal paper in 1992, and recently significant performance improvements have been achieved by adopting deep networks. In this work, we focus on the idea that appliances have on/off states, and develop a deep network for further performance improvements. Specifically, we propose a subtask gated network that combines the main regression network with an on/off classification subtask network. Unlike typical multitask learning algorithms where multiple tasks simply share the network parameters to take advantage of the relevance among tasks, the subtask gated network multiply the main network's regression output with the subtask's classification probability. When standby-power is additionally learned, the proposed solution surpasses the state-of-the-art performance for most of the benchmark cases. The subtask gated network can be very effective for any problem that inherently has on/off states

Real-Time Solar Power Estimation Through RNN-Based Attention Models

Solar power is an important renewable energy resource that plays a pivotal role in replacing fossil fuel generators and lowering carbon emissions. Since sunlight, which is highly dependent on meteorological factors, is highly volatile, the difficulty in collecting real-time data from renewable energy power plants poses a major threat to maintaining the stability of the entire power system in the target area. A high-performance wireless metering modem is required to monitor the renewable energy generation power of the entire target area in real-time. However, installing such devices on all sites is expensive, so we propose a system that uses deep learning to estimate the generation power of a target site based on the power generations of some sample sites. We use clustering and distance-based sampling to extract a sample site corresponding to each target site and use the recurrent neural network (RNN)-based attention techniques to estimate the generation of target sites from the sample sites. Our experiments show that the proposed RNN-based attention models significantly improve estimation accuracy compared to the baseline model or other deep learning models, irrespective of the number or location of sample sites

dealii/dealii: deal.II version 9.4.2

All download files are mirrored at https://dealii.43-1.org/downloads/ This is a minor update to 9.4.1 with the following changes: a compilation issue with step-70 has been resolved CMake: prefer -pthread for posix thread support a type mismatch for suitesparse has been fixed that lead to compilation failures on certain platforms a number of Microsoft Visual Code compatibility fixes concerning extern declaration