Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient

From characterizing the speed of a thermal system's response to computing natural modes of vibration, eigenvalue analysis is ubiquitous in engineering. In spite of this, eigenvalue problems have received relatively little treatment compared to standard forward and inverse problems in the physics-informed machine learning literature. In particular, neural network discretizations of solutions to eigenvalue problems have seen only a handful of studies. Owing to their nonlinearity, neural network discretizations prevent the conversion of the continuous eigenvalue differential equation into a standard discrete eigenvalue problem. In this setting, eigenvalue analysis requires more specialized techniques. Using a neural network discretization of the eigenfunction, we show that a variational form of the eigenvalue problem called the "Rayleigh quotient" in tandem with a Gram-Schmidt orthogonalization procedure is a particularly simple and robust approach to find the eigenvalues and their corresponding eigenfunctions. This method is shown to be useful for finding sets of harmonic functions on irregular domains, parametric and nonlinear eigenproblems, and high-dimensional eigenanalysis. We also discuss the utility of harmonic functions as a spectral basis for approximating solutions to partial differential equations. Through various examples from engineering mechanics, the combination of the Rayleigh quotient objective, Gram-Schmidt procedure, and the neural network discretization of the eigenfunction is shown to offer unique advantages for handling continuous eigenvalue problems.

Corn Ear Detection and Orientation Estimation Using Deep Learning

Monitoring growth behavior of maize plants such as the development of ears can give key insights into the plant's health and development. Traditionally, the measurement of the angle of ears is performed manually, which can be time-consuming and prone to human error. To address these challenges, this paper presents a computer vision-based system for detecting and tracking ears of corn in an image sequence. The proposed system could accurately detect, track, and predict the ear's orientation, which can be useful in monitoring their growth behavior. This can significantly save time compared to manual measurement and enables additional areas of ear orientation research and potential increase in efficiencies for maize production. Using an object detector with keypoint detection, the algorithm proposed could detect 90 percent of all ears. The cardinal estimation had a mean absolute error (MAE) of 18 degrees, compared to a mean 15 degree difference between two people measuring by hand. These results demonstrate the feasibility of using computer vision techniques for monitoring maize growth and can lead to further research in this area.

Artificial Intelligence for Digital Agriculture at Scale: Techniques, Policies, and Challenges

Digital agriculture has the promise to transform agricultural throughput. It can do this by applying data science and engineering for mapping input factors to crop throughput, while bounding the available resources. In addition, as the data volumes and varieties increase with the increase in sensor deployment in agricultural fields, data engineering techniques will also be instrumental in collection of distributed data as well as distributed processing of the data. These have to be done such that the latency requirements of the end users and applications are satisfied. Understanding how farm technology and big data can improve farm productivity can significantly increase the world's food production by 2050 in the face of constrained arable land and with the water levels receding. While much has been written about digital agriculture's potential, little is known about the economic costs and benefits of these emergent systems. In particular, the on-farm decision making processes, both in terms of adoption and optimal implementation, have not been adequately addressed. For example, if some algorithm needs data from multiple data owners to be pooled together, that raises the question of data ownership. This paper is the first one to bring together the important questions that will guide the end-to-end pipeline for the evolution of a new generation of digital agricultural solutions, driving the next revolution in agriculture and sustainability under one umbrella.