Abstract

Artificial Neural Networks (ANNs) have evolved from a simple mathematical abstraction of biological neurons into one of the most influential computational paradigms in modern engineering. This review synthesises the mathematical foundations, architectural evolution, and cross-disciplinary applications of ANNs, drawing on peer-reviewed literature indexed in Scopus, Web of Science, and IEEE Xplore. We first revisit the mathematical formalism of the artificial neuron, activation functions, loss functions, and gradient-based optimisation, before examining the theoretical guarantees offered by the Universal Approximation Theorem (Hornik, Stinchcombe, & White, 1989). We then present a comparative taxonomy of feedforward, convolutional, recurrent, graph-based, and physics-informed architectures, and review their reported performance across civil, mechanical, electrical, electronics, chemical, and biomedical engineering domains. A quantitative synthesis of accuracy, error, and reliability metrics extracted from more than thirty recent studies is presented in tabular form to illustrate the comparative maturity of each application area. The review finds that convolutional architectures dominate vision-based inspection tasks with reported accuracies frequently exceeding 94–99%, recurrent and hybrid CNN–LSTM architectures are preferred for temporal forecasting problems such as load and traffic prediction, and physics-informed neural networks are an emerging solution for data-scarce, physics-governed problems. Persistent challenges include data quality and availability, interpretability, computational cost, and the integration of domain knowledge. The review concludes by outlining future research directions, including explainable AI, digital twins, federated learning, and hybrid physics–data models, that are likely to shape the next generation of ANN-enabled engineering systems.

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