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

Wuyang Chen, Jialin Song, Pu Ren, Shashank Subramanian, Dmitriy Morozov, Michael W. Mahoney

Keywords: scientific machine learning, unsupervised pretraining, neural operators, foundation models

TL;DR: We introduce unsupervised pretraining and in-context learning for Scientific Machine Learning, significantly enhancing data efficiency and generalizability of neural operators.

Abstract:

Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insights 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 for PDE operator learning. To reduce the need for training data with heavy simulation costs, we mine unlabeled PDE data without simulated solutions,
and we pretrain neural operators with physics-inspired reconstruction-based proxy tasks. To improve out-of-distribution performance, we further assist neural operators in flexibly leveraging a similarity-based method that learns in-context examples, without incurring extra training costs or designs. Extensive empirical evaluations on a diverse set of PDEs demonstrate that our method is highly data-efficient, more generalizable, and even outperforms conventional vision-pretrained models. We provide our code at https://github.com/delta-lab-ai/data_efficient_nopt.

Primary Area: Machine learning for physical sciences (for example: climate, physics)

Submission Number: 11275