The field of partial differential equations (PDEs) is witnessing significant advancements with the integration of physics-informed neural operators. Recent developments are focused on improving the accuracy and efficiency of these operators in solving complex PDE problems. Notably, researchers are exploring the use of localized Fourier neural operators, heterogeneous multiscale methods, and data-driven approaches to enhance the resolution and stability of PDE solutions. These innovative methods are being applied to various domains, including fluid dynamics, oceanography, and biomedical imaging. The incorporation of machine learning techniques, such as low-rank adaptation and bilevel optimization, is also leading to improved uncertainty quantification and parameter inference. Overall, the field is moving towards the development of more accurate, efficient, and robust physics-informed neural operators for PDEs. Noteworthy papers include: Localized FNO for Spatiotemporal Hemodynamic Upsampling in Aneurysm MRI, which proposes a novel 3D architecture for enhancing spatial and temporal resolution in hemodynamic analysis. Data-Driven Adaptive Gradient Recovery for Unstructured Finite Volume Computations presents a novel approach for improving gradient reconstruction in unstructured finite volume methods. Multiscale Neural PDE Surrogates for Prediction and Downscaling demonstrates the application of neural operators for solving PDEs and providing arbitrary resolution solutions.