Design of a Graph Neural Network

Abstract

Graph Neural Networks are a unique type of Deep Learning models that have a capability to exploit an explicitly stated structure of data representation. By design they carry a strong relational inductive bias, which is a set of assumptions that makes the algorithm prioritize some solutions over another, independent of observed data. This makes the method especially interesting for applications to problems, that are naturally relation-centric, or in which local interactions between features are the main value of interest. The presented research case, aims to explore GNN potential in application to an Ocean Acoustics problem. Using the geometric ray-tracing algorithm, BELLHOP, a large number of underwater sound propagation scenarios was simulated. Each scenario is described by a limited set of parameters and a Sound Speed Profile function. The latter, acting as a guideline for estimating paths of rays travelling through a water column, has a critical impact on sound propagation mode. For the data-driven model to effectively capture the acoustic phenomena, requires a mean of representing interactions in very scarce feature space and especially with respect to the nonlinear function representation of the sound speed. First, the solution of the problem is approached with a traditional Machine Learning model, a decision-tree algorithm XGBoost. In effect, some important characteristics of the collected data sample are revealed. Moreover, by testing inference capacity of the database with a reliable algorithm, gives an estimate of the properties of the Sound Speed Profile that have the biggest impact on sound propagation. It is proven, that with carefully engineered features, that include a degree of added expert knowledge, a standard model can achieve good accuracy of prediction. Secondly, a Knowledge Graph is designed to represent the whole context of explicitly stated expert knowledge, using concepts from Hydroacoustics. They are encoded in a form of relational structure connecting actual features of the data into logical categories. In this representation it can be used by the Knowledge Graph Convolutional Network model designed for the problem. A range of tests performed on KGCN proves that using a Graph Neural Network can be feasible to solve the problem, however it also reveals a range of issues regarding model's capability to handle the complexity of problem statement.