The field of partial differential equations (PDEs) is witnessing significant advancements with the integration of neural operators. Recent developments focus on improving the accuracy and efficiency of these operators, particularly in handling complex geometries and irregular meshes. Notably, the incorporation of locality-aware attention mechanisms and the use of kinematic neural bases are showing promise in enhancing the performance of neural operators. Furthermore, novel approaches such as the use of subspace parameterized attention and the integration of physics-informed neural networks with traditional system codes are being explored. These innovations have the potential to revolutionize the field of PDEs, enabling more accurate and efficient simulations of complex systems. Noteworthy papers in this area include the proposal of the Locality-Aware Attention Transformer (LA2Former), which achieves a balance between computational efficiency and predictive accuracy. Another significant contribution is the development of the SUPRA neural operator, which reduces error rates by up to 33% on various PDE datasets while maintaining state-of-the-art computational efficiency. The Node Assigned physics-informed neural networks (NA-PINN) is also a notable work, demonstrating acceptable accuracy in thermal-hydraulic system simulation. These papers demonstrate the rapid progress being made in the field and highlight the potential of neural operators to transform the way we approach PDEs.