Homogenization Approach

Homogenization is a mathematical technique used to simplify complex multiscale systems by replacing fine-scale details with effective macroscopic properties. Current research focuses on applying homogenization to diverse fields, including material science (modeling composite material behavior using neural networks and addressing challenges posed by material discontinuities), optimization (developing efficient algorithms like stochastic homogenization methods for gradient-dominated problems), and image analysis (leveraging U-Net architectures to reduce domain biases in medical image processing). These advancements improve the accuracy and efficiency of simulations and analyses across various scientific and engineering disciplines, leading to better predictions of material performance and optimized designs.