Comparative Study of Bending Analysis using Physics-Informed Neural Networks and Numerical Dynamic Deflection in Perforated nanobeam

In a new arXiv preprint (arXiv:2604.24768), researchers Ramanath Garai, Iswari Sahu, and S. Chakraverty propose a computationally efficient Physics-Informed Functional Link Constrained Framework with Domain Mapping (DFL-TFC) to analyze bending in perforated nanobeams under sinusoidal loading. The method leverages the Theory of Functional Connections (TFC) to embed governing differential equation constraints into a constrained expression that exactly satisfies initial and boundary conditions. Instead of deep neural networks, it uses a functional link neural network (FLNN) to represent the free function, reducing training complexity while maintaining high accuracy.

Static bending is computed via the FL-TFC with domain mapping, while dynamic deflection is determined using the Galerkin method. The framework maps the problem domain to orthogonal polynomials, enabling efficient training by minimizing the mean square residual of the differential equation. The study explores the relationship between static and dynamic deflection for simply-supported perforated nanobeams across various perforation cases, demonstrating that DFL-TFC eliminates the need for deep, complex architectures while strictly satisfying boundary conditions—a key advantage over standard PINNs.