Partial Differential Equations Meet Deep Neural Networks: A Survey.

Many problems in science and engineering can be mathematically modeled using partial differential equations (PDEs), which are essential for fields like computational fluid dynamics (CFD), molecular dynamics, and dynamical systems. Although traditional numerical methods like the finite difference/element method are widely used, their computational inefficiency, due to the large number of iterations required, has long been a challenge. Recently, deep learning (DL) has emerged as a promising alternative for solving PDEs, offering new paradigms beyond conventional methods.

EU-Net: Automatic U-Net neural architecture search with differential evolutionary algorithm for medical image segmentation.

Medical images are crucial in clinical practice, providing essential information for patient assessment and treatment planning. However, manual extraction of information from images is both time-consuming and prone to errors. The emergence of U-Net addresses this challenge by automating the segmentation of anatomical structures and pathological lesions in medical images, thereby significantly enhancing the accuracy of image interpretation and diagnosis.