Scientific Machine Learning (SciML) is concerned with the development of
learned emulators of physical systems governed by partial differential
equations (PDE). In application domains such as weather forecasting, molecular
dynamics, and inverse design, ML-based surrogate models are increasingly used
to augment or replace inefficient and often non-differentiable numerical
simulation algorithms. While a number of ML-based methods for approximating the
solutions of PDEs have been proposed in recent years, they typically do not
adapt to the parameters of the PDEs, making it difficult to generalize to PDE
parameters not seen during training. We propose a Channel Attention mechanism
guided by PDE Parameter Embeddings (CAPE) component for neural surrogate models
and a simple yet effective curriculum learning strategy. The CAPE module can be
combined with neural PDE solvers allowing them to adapt to unseen PDE
parameters. The curriculum learning strategy provides a seamless transition
between teacher-forcing and fully auto-regressive training. We compare CAPE in
conjunction with the curriculum learning strategy using a popular PDE benchmark
and obtain consistent and significant improvements over the baseline models.
The experiments also show several advantages of CAPE, such as its increased
ability to generalize to unseen PDE parameters without large increases
inference time and parameter count.

本研究提出了一种基于科学机器学习（SciML）的渠道关注机制导向的偏微分方程（PDE）参数嵌入（CAPE）组件来实现神经替代模型，以及一种简单而有效的课程学习策略，通过流畅的过渡学习使得这些神经替代模型能够适应未见过的 PDE 参数，并在常见的 PDE 基准测试中进行了实验验证，获得了一致且显著的改进，并在推断时间和参数计数方面展现了 CAPE 的几个优点。