FMint: Bridging Human Designed and Data Pretrained Models for Differential Equation Foundation Model

arXiv:2404.14688v1 Announce Type: new
Abstract: Human-designed algorithms have long been fundamental in solving a variety of scientific and engineering challenges. Recently, data-driven deep learning methods have also risen to prominence, offering innovative solutions across numerous scientific fields. While traditional algorithms excel in capturing the core aspects of specific problems, they often lack the flexibility needed for varying problem conditions due to the absence of specific data. Conversely, while data-driven approaches utilize vast datasets, they frequently fall short in domain-specific knowledge. …

abstract algorithms arxiv challenges core cs.ai cs.ce cs.lg cs.na data data-driven deep learning differential differential equation engineering equation excel fields foundation foundation model fundamental human math.ds math.na pretrained models scientific solutions type