The field of partial differential equations (PDEs) is experiencing significant advancements with the integration of neural networks and machine learning techniques. Recent developments focus on improving the efficiency, accuracy, and scalability of neural PDE solvers. A notable trend is the incorporation of adaptive and hybrid approaches, combining different neural network architectures and numerical methods to leverage their respective strengths. These innovations enable the solving of complex PDEs with enhanced performance, reduced computational costs, and improved handling of multiscale phenomena. Furthermore, research is exploring the application of these neural solvers to various domains, including porous media, fluid dynamics, and material science. Noteworthy papers in this area include: Scaling Kinetic Monte-Carlo Simulations of Grain Growth with Combined Convolutional and Graph Neural Networks, which proposes a hybrid architecture for grain growth simulations, demonstrating significant reductions in computational costs and improved accuracy. Active Learning with Selective Time-Step Acquisition for PDEs presents a novel framework for active learning in PDE surrogate modeling, reducing the cost of generating training data and improving performance by large margins. Reduced-Basis Deep Operator Learning for Parametric PDEs with Independently Varying Boundary and Source Data introduces a hybrid operator-learning framework, achieving a strict offline-online split and significant speedups. Adaptive Mesh-Quantization for Neural PDE Solvers addresses the challenge of spatially varying complexity in physical systems, introducing an adaptive bit-width allocation strategy for efficient resource utilization. SAOT: An Enhanced Locality-Aware Spectral Transformer for Solving PDEs proposes a novel Wavelet Attention module and a hybrid spectral Transformer framework, achieving state-of-the-art performance on operator learning benchmarks.