The field of machine learning applied to partial differential equations (PDEs) is witnessing significant advancements, particularly in the development and optimization of neural network architectures tailored for scientific computing applications. Recent studies have focused on enhancing the efficiency and accuracy of predictions by integrating physical principles into neural network models, such as Physics-Informed Neural Networks (PINNs) and Deep Operator Networks (DeepONets). These models are being refined to better handle complex, high-dimensional, and low-regularity PDEs, often through the incorporation of learnable activation functions and basis sets that improve spectral bias and convergence behavior. Additionally, innovative sampling techniques, such as the use of good lattice points, are being explored to enhance the data efficiency and robustness of these models. The field is also grappling with the fundamental question of what these physics-informed models truly learn, leading to research on model interpretability and the development of transfer learning strategies to improve training across different PDEs. Overall, the trend is towards more sophisticated, physically interpretable, and data-efficient neural network models that can serve as powerful tools for solving complex PDEs in various scientific and engineering domains.