基于参数引导通道注意力的神经偏微分方程求解器学习
Learning Neural PDE Solvers with Parameter-Guided Channel Attention
AI总结：
针对现有神经PDE求解器难以泛化到未见过参数的问题，提出参数嵌入引导的通道注意力模块CAPE与课程学习策略，在基准上实现显著提升，且未大幅增加推理开销与参数量。
摘要：
科学机器学习（SciML）致力于构建由偏微分方程（PDE）支配的物理系统的学习型仿真器。在天气预报、分子动力学、逆向设计等应用领域，基于机器学习的代理模型正越来越多地用于增强或替代效率低下且通常不可微的数值模拟算法。尽管近年来已有多种用于近似PDE解的机器学习方法被提出，但它们通常无法适配PDE的参数，难以泛化到训练期间未见过的PDE参数。\n我们提出了一种用于神经代理模型的、由PDE参数嵌入引导的通道注意力（CAPE）组件，以及一种简单却有效的课程学习策略。CAPE模块可与神经PDE求解器结合，使求解器能够适配未见过的PDE参数。课程学习策略则实现了教师强制训练与完全自回归训练之间的平滑过渡。\n我们在一个常用的PDE基准上对结合课程学习策略的CAPE进行了对比实验，结果显示其相较基线模型取得了一致且显著的性能提升。实验还展现了CAPE的多项优势，例如在未大幅增加推理时间和参数量的前提下，提升了模型对未见过PDE参数的泛化能力。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
