The field of solving partial differential equations (PDEs) using neural operators is rapidly advancing, with a focus on improving efficiency, accuracy, and scalability. Recent developments have explored new architectures, training methods, and applications, enabling the solution of complex PDEs with reduced computational costs and improved performance. Notably, researchers have proposed innovative approaches to accelerate data generation, revisit classical optimization frameworks, and leverage mixed precision training to enhance neural operator performance. Furthermore, studies have demonstrated the potential of neural emulators to surpass their training data's fidelity and achieve greater physical accuracy. Overall, these advancements are poised to significantly impact various fields, including scientific research, engineering, and machine learning. Noteworthy papers include: Accelerating Data Generation for Nonlinear temporal PDEs via homologous perturbation in solution space, which proposes a novel data generation algorithm to accelerate dataset generation while preserving precision. Revisiting Orbital Minimization Method for Neural Operator Decomposition, which adapts a classical optimization framework to train neural networks for decomposing positive semidefinite operators, demonstrating its practical advantages across benchmark tasks.