Artificial Intelligence Applications In Engineering: Bridging Computational Models And Real-World Systems

The application of artificial intelligence as a supplement to classical mathematical models is becoming more common in the engineering field, but the high-level connection between formulations based on a set of differential equations and neural approximations has not been fully exploited. This study investigates how a simple neural network can approximate a canonical heat-conduction model and what this implies for bridging computational and AI-based representations. A one-dimensional steady-state heat-conduction problem with fixed boundary conditions is modelled using a linear second-order differential equation. The exact solution is derived in closed form and evaluated at discrete points on the spatial domain. A single-hidden-layer ReLU neural network with three neurons is then constructed to approximate the same temperature profile. Functional behaviour, pointwise approximation error, and computational structure are analyzed. The neural surrogate closely reproduces the classical linear temperature distribution, with absolute errors remaining below 2 °C at all evaluation points. The approximation is most accurate in the central region of the domain, while small deviations appear near the boundaries due to activation transitions. Despite its simplicity, the network provides a flexible piecewise-linear representation with modest computational overhead. The findings demonstrate that compact neural networks can act as effective surrogates for classical engineering models, supporting an integrated view in which AI complements, rather than replaces, traditional mathematical formulations.