Training neural networks with a modified Dai–Liao conjugate gradient method inspired by Powell's equation

This study proposes a new Conjugate Gradient (CG) method that is both theoretically sound and computationally efficient for solving large-scale unconstrained optimization problems. The method integrates the Dai-Liao (DL) parameter with a gradient-difference vector formulation inspired by Powell (1978) and incorporates the Barzilai-Borwein step size to enhance convergence performance. Under standard assumptions, the proposed method is proven to satisfy the sufficient descent condition and to guarantee global convergence. Extensive numerical experiments demonstrate that the new method outperforms classical CG algorithms including the Hestenes-Stiefel (HS) and DL methods in terms of iteration count, function evaluations, and computational time. Furthermore, the method is applied to train a feedforward neural network aimed at predicting the seismic vulnerability of 641 multistory buildings in Zakho City, Iraq. Using a dataset of structural and geotechnical features, the neural network trained with the proposed CG method achieves faster convergence and maintains high prediction accuracy, confirming the method's practical utility in real-world applications.

Publication Link: https://www.aimsciences.org/article/doi/10.3934/naco.2026018

Doi:  10.3934/naco.2026018