Ahmad S, Zaman N, Asif M, Qasim M, Shah AH, Shahzadi A, Arshid F, Israr M. PDFP-enhanced physics-informed neural networks for solving higher-order PDEs: Application to engineering beam problems. Mech. Eng. Adv. Published online January 27, 2026;4(1). doi:10.59400/mea4125