Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Hur, Jihyeon, Kwon, Yongseok, Jo, Min-Gi, Choi, Jeongwhan, Park, Noseong
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G4862202413
OpenAlex ID: W7164553247
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