# FastLRNR and Sparse Physics Informed Backpropagation

arXiv: https://arxiv.org/abs/2410.04001 · HTML: https://mlsanity.com/paper/2410.04001/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 23 references that are in the map.
- First posted on arXiv 5 Oct 2024.

## Builds on (most cited first, 5 of 5)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networks](https://mlsanity.com/paper/2310.09528/) (2023)
- [A Low Rank Neural Representation of Entropy Solutions](https://mlsanity.com/paper/2406.05694/) (2024)

## Built on by (most cited first, 3 of 3)

- [An Overview of Low-Rank Structures in the Training and Adaptation of Large Models](https://mlsanity.com/paper/2503.19859/) (2025)
- [Fourier-Modulated Implicit Neural Representation for Multispectral Satellite Image Compression](https://mlsanity.com/paper/2506.01234/) (2025)
- [Learning Low Rank Neural Representations of Hyperbolic Wave Dynamics from Data](https://mlsanity.com/paper/2510.25123/) (2025)

## Abstract (arXiv)

We introduce Sparse Physics Informed Backpropagation (SPInProp), a new class of methods for accelerating backpropagation for a specialized neural network architecture called Low Rank Neural Representation (LRNR). The approach exploits the low rank structure within LRNR and constructs a reduced neural network approximation that is much smaller in size. We call the smaller network FastLRNR. We show that backpropagation of FastLRNR can be substituted for that of LRNR, enabling a significant reduction in complexity. We apply SPInProp to a physics informed neural networks framework and demonstrate how the solution of parametrized partial differential equations is accelerated.