动态调节记忆权重，让神经算子在不同分辨率下更准更快。
How Much Memory Do We Need? Adaptive Memory Gate for Neural Operators
- 用可学习门控机制动态调整记忆权重，适应不同观测条件。
- 在低分辨率下相比基线模型误差降低55%至79%。
- 适合需要高效处理多分辨率物理模拟的科研与工程场景。
神经算子已成为求解时变偏微分方程的强大数据驱动方法。近年来，带记忆的神经算子显式引入历史状态，在低分辨率观测下表现优异。然而，现有方法采用固定记忆权重，不随观测条件（如分辨率或物理参数）变化，限制了其适应性。初步实验表明，最优记忆权重随分辨率和黏性变化，固定权重无法在多种设置下同时优化性能。本文提出AMGFNO，通过可学习门控机制动态调节记忆权重。在Kuramoto-Sivashinsky和Burgers方程上，AMGFNO在低分辨率下相较基线模型实现55%-79%的nRMSE降低，且学习到的门控值从约0.7自动下降至接近零，随分辨率提升而自适应衰减。
原文摘要 · Abstract (English)
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.
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