# How Much Memory Do We Need? Adaptive Memory Gate for Neural Operators

arXiv: https://arxiv.org/abs/2606.13443 · HTML: https://mlsanity.com/paper/2606.13443/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 11 Jun 2026.

## Builds on (most cited first, 18 of 18)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [Training Very Deep Networks](https://mlsanity.com/paper/1507.06228/) (2015)
- [Scalable Transformer for PDE Surrogate Modeling](https://mlsanity.com/paper/2305.17560/) (2023)
- [Lie Point Symmetry Data Augmentation for Neural PDE Solvers](https://mlsanity.com/paper/2202.07643/) (2022)
- [On the Benefits of Memory for Modeling Time-Dependent PDEs](https://mlsanity.com/paper/2409.02313/) (2024)
- [Learning from many trajectories](https://mlsanity.com/paper/2203.17193/) (2022)

## Built on by (most cited first, 1 of 1)

- [Spatial Context or Memory? Sizing the Inputs of Neural Surrogates for Partially Observed Fields](https://mlsanity.com/paper/2610.12723/) (2026)

## Abstract (arXiv)

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 barg ≈ 0.7 to near-zero as resolution increases.