Can we build a single large model for a wide range of PDE-related scientific
learning tasks? Can this model generalize to new PDEs, even of new forms,
without any fine-tuning? In-context operator learning and the corresponding
model In-Context Operator Networks (ICON) [1] represent an initial exploration
of these questions. The capability of ICON regarding the first question has
been demonstrated in [1]. In this paper, we explore the second question by
investigating the generalization capabilities of ICON for conservation laws, a
family of PDEs with temporal evolution. We show the positive answer to the
second question, i.e., ICON can generalize well to some PDEs with new forms
without any fine-tuning. We also show how to broaden the range of problems that
ICON can address, by transforming functions and equations to ICON's capability
scope. We believe that the progress in this paper is a significant step towards
the goal of training a foundation model for PDE-related tasks under the
in-context operator learning framework.

在本文中，我们通过研究 ICON 对守恒定律的广义化能力，探讨了建立一个能够广泛应用于各种 PDE 相关科学学习任务的单个大型模型的可能性，而且这个模型即使对于新形式的 PDE 也不需要经过微调即可广义化。