Probabilistic Neural Networks: An Overview.

Probabilistic neural networks (PNNs) are a type of artificial neural network based on Bayesian probability. They are particularly useful when data need to be assigned to a class based on membership probability rather than a strict classification. By leveraging lazy learning and avoiding iterative backpropagation processes, PNNs can be both fast and effective, especially when working with small datasets. First introduced in 1988, PNNs have been applied across a wide range of scientific fields for diverse goals. In this survey, we begin by explaining the architecture of probabilistic neural networks and their operational principles. Next, we present and discuss dozens of studies that employ this probabilistic model across various domains, including audio and speech signal processing, bioinformatics, cheminformatics, cybersecurity, energy, industrial engineering, physics, finance, economics, geology, earth sciences, image processing, computer vision, medical research, healthcare, natural language processing, robotics, smart cities, transportation, traffic management, and theoretical research. Additionally, we provide a curated list of open-source software libraries in Python, Scala, and Julia that implement PNNs, along with a selection of online tutorials and video lectures aimed at making this model accessible to a broader audience.