Neural operators have emerged as a powerful data-driven approach for solving time-dependent PDEs. Among recent advances, memory-augmented neural operators explicitly incorporate past states and have achieved remarkable performance under low-resolution observation settings. However, existing approaches apply a fixed memory weight regardless of observation conditions, such as resolution or physical parameters, limiting their adaptability. Our preliminary experiments reveal that optimal memory weight varies with resolution and viscosity, implying that a fixed memory weight cannot simultaneously optimize performance across diverse settings. We propose AMGFNO, which dynamically modulates memory weight through a learnable gate. On the Kuramoto-Sivashinsky and Burgers' equations, AMGFNO achieves 55-79% nRMSE reduction over at low resolution, with the learned gate value automatically decreasing from $\bar{g} \approx 0.7$ to near-zero as resolution increases.

翻译：神经算子已成为一种强大的数据驱动方法，用于求解含时偏微分方程。在近期进展中，记忆增强型神经算子显式地整合了过往状态，并在低分辨率观测设定下取得了显著性能。然而，现有方法无论观测条件（如分辨率或物理参数）如何，都采用固定的记忆权重，这限制了其适应性。我们的预实验表明，最优记忆权重随分辨率和粘性变化，这意味着固定记忆权重无法同时优化多种设定下的性能。我们提出AMGFNO，它通过一个可学习门动态调节记忆权重。在Kuramoto-Sivashinsky方程和Burgers方程上，AMGFNO在低分辨率下实现了55-79%的nRMSE降低，且学习到的门值随分辨率增加从$\bar{g} \approx 0.7$自动降至接近零。