Multiscale Problem

Multiscale problems involve systems exhibiting significant variations across different length or time scales, posing challenges for traditional numerical methods due to computational cost and accuracy limitations. Current research focuses on developing data-driven approaches, particularly employing physics-informed neural networks (PINNs) and deep operator networks (DeepONets), often enhanced with techniques like multiresolution grids, hierarchical architectures, and transfer learning to improve efficiency and accuracy. These advancements aim to enable more efficient and accurate simulations of complex phenomena across diverse scientific and engineering domains, such as material science, fluid dynamics, and topology optimization, by effectively bridging the gap between micro- and macro-scale behaviors.