# AMStraMGRAM: Adaptive Multi-cutoff Strategy Modification for ANaGRAM

arXiv: https://arxiv.org/abs/2510.15998 · HTML: https://mlsanity.com/paper/2510.15998/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2025.

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

- [Beyond PINNs: A Unified Gauss--Newton and Petrov--Galerkin Framework for Neural and Hybrid PDE Solvers](https://mlsanity.com/paper/2609.20641/) (2026)

## Abstract (arXiv)

Recent works have shown that natural gradient methods can significantly outperform standard optimizers when training physics-informed neural networks (PINNs). In this paper, we analyze the training dynamics of PINNs optimized with ANaGRAM, a natural-gradient-inspired approach employing singular value decomposition with cutoff regularization. Building on this analysis, we propose a multi-cutoff adaptation strategy that further enhances ANaGRAM's performance. Experiments on benchmark PDEs validate the effectiveness of our method, which allows to reach machine precision on some experiments. To provide theoretical grounding, we develop a framework based on spectral theory that explains the necessity of regularization and extend previous shown connections with Green's functions theory.