The field of neural networks for differential equations is experiencing significant growth, with a focus on improving accuracy, interpretability, and generalization capabilities. Recent developments have led to the creation of novel architectures that integrate multiple nonlinear functions, allowing for more expressive power and reduced parameter counts. These advancements have enabled neural networks to achieve comparable or superior results to conventional approaches in various fields, including physics-informed settings. Additionally, there is a growing interest in exploring the connections between differential complexes, cohomology, and structure-preserving discretization, which has led to new insights and formulations in solid and fluid mechanics. Furthermore, the application of kernel methods and Kolmogorov-Arnold representation theorem has resulted in unified theoretical frameworks for function fitting and feature extraction. Noteworthy papers include:

• MixFunn, which introduces a novel neural network architecture with improved generalization and interpretability, achieving superior results in physics-informed settings.
• Enhancing Physics-Informed Neural Networks with a Hybrid Parallel Kolmogorov-Arnold and MLP Architecture, which proposes a novel architecture that synergistically integrates parallelized KAN and MLP branches, resulting in enhanced predictive performance and numerical stability.