Data-Efficient Operator Learning via Unsupervised Pretraining and In-Context Learning

arXiv:2402.15734v1 Announce Type: new
Abstract: Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insight for solving scientific problems based on partial differential equations (PDEs). However, being data-intensive, these methods still require a large amount of PDE data. This reintroduces the need for expensive numerical PDE solutions, partially undermining the original goal of avoiding these expensive simulations. In this work, seeking data efficiency, we design unsupervised pretraining and in-context learning methods for PDE operator learning. …

abstract arxiv context cs.lg data differential domain in-context learning insight machine machine learning numerical pretraining stat.ml type unsupervised via