The field of numerical methods for partial differential equations (PDEs) is experiencing significant advancements, driven by the development of innovative techniques and algorithms. One notable direction is the increasing use of machine learning and neural networks to improve the efficiency and accuracy of PDE solvers. For instance, neural preconditioners are being explored to enhance the convergence rate of iterative solvers, while fully differentiable finite element-based machine learning frameworks are being developed to discover missing physics in complex systems. Additionally, novel domain decomposition methods and multiphysics embedding techniques are being proposed to tackle challenging problems in thermomechanical coupling and mixed-dimensional PDEs. These advancements have the potential to revolutionize the field of numerical PDEs and enable the solution of previously intractable problems. Noteworthy papers include PDEformer-2, which introduces a versatile foundation model for two-dimensional PDEs, and the learning-based domain decomposition method, which enables the efficient solution of complex PDEs using pre-trained neural operators.