The field of numerical methods for differential equations is witnessing significant developments, with a focus on improving the accuracy, efficiency, and robustness of various algorithms. Researchers are exploring new formulations, analyzing their stability and convergence, and applying them to real-world problems. Notably, the development of novel high-order numerical schemes for fractional differential equations and the application of machine learning techniques, such as operator learning, to solve complex differential equations are advancing the field. Additionally, reduced order modeling techniques are being used to improve the solving of inverse problems in hyperbolic systems. These advancements have the potential to accelerate simulations and facilitate their integration into clinical and industrial applications. Noteworthy papers include:

• A novel class of arbitrary high-order numerical schemes for fractional differential equations, which proposes a highly accurate and efficient method for solving time-fractional differential equations.
• Learning cardiac activation and repolarization times with operator learning, which demonstrates the potential of machine learning techniques in solving complex differential equations in cardiac electrophysiology.
• Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations, which introduces a sensitivity-based regularization strategy to improve the accuracy and robustness of neural operator-based methods.