The field of partial differential equations (PDEs) is witnessing significant advancements with the integration of neural networks and machine learning techniques. Recent developments have focused on improving the efficiency, accuracy, and interpretability of neural solvers for PDEs. A key direction is the use of spectral methods, such as Fourier neural operators, which have shown promise in capturing complex dynamics and global correlations. Another area of research is the development of adaptive spectral layers, which enable neural networks to dynamically tune their spectral basis during training. This has led to improved performance on challenging PDE problems, such as the Ginzburg-Landau equation. Additionally, there is a growing interest in using generative models, such as transformer-operator frameworks, to generate high-resolution PDE solutions from sparse input grids. These advancements have the potential to revolutionize the field of PDEs and enable more efficient and accurate simulations. Noteworthy papers include: Beyond Loss Guidance: Using PDE Residuals as Spectral Attention in Diffusion Neural Operators, which introduces a novel diffusion-based solver that embeds PDE residuals into the model's architecture. ASPEN: An Adaptive Spectral Physics-Enabled Network for Ginzburg-Landau Dynamics, which presents a new architecture that overcomes the spectral bias of standard multilayer perceptron architectures. Efficient Generative Transformer Operators For Million-Point PDEs, which introduces a transformer-operator framework for generating million-point PDE trajectories.