The field of numerical methods for complex systems is rapidly evolving, with a focus on developing innovative algorithms and techniques to simulate and analyze complex phenomena. Recent research has emphasized the importance of boundary constraints, nonlocal effects, and nonlinear interactions in shaping the behavior of complex systems. Notable advancements include the development of multiharmonic algorithms, optimized subspace methods, and hybrid optimization frameworks, which have improved the accuracy and efficiency of simulations. Furthermore, new methods have been proposed for solving nonlinear spectral problems, acoustic scattering problems, and acoustic-elastic interaction problems, demonstrating the versatility and breadth of current research. Some papers are particularly noteworthy, including:

• The development of a novel machine learning-based method for solving acoustic scattering problems, which achieves high accuracy and outperforms existing methods.
• The proposal of a hybrid optimization framework that accelerates training convergence for physics-informed neural networks, enabling faster and more accurate simulations.
• The presentation of a general, convergent computational method for computing the spectra and pseudospectra of nonlinear spectral problems, which has far-reaching implications for various fields.