Towards a Foundation Model for Partial Differential Equation: Multi-Operator Learning and Extrapolation

arXiv:2404.12355v1 Announce Type: new
Abstract: Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our model, designed for bi-modality to bi-modality learning, is a multi-operator learning approach which can predict future states of spatiotemporal systems while concurrently learning the underlying governing equations of the physical system. Specifically, we focus on multi-operator learning by training distinct one-dimensional time-dependent …

abstract arxiv cs.lg cs.na differential differential equation equation foundation foundation model image image processing language language models large language large language models math.na modal multi-modal processing prose scientific success tasks type work