# Design Your Own Universe: A Physics-Informed Agnostic Method for Enhancing Graph Neural Networks

arXiv: https://arxiv.org/abs/2401.14580 · HTML: https://mlsanity.com/paper/2401.14580/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 53 references that are in the map.
- First posted on arXiv 26 Jan 2024.

## Builds on (most cited first, 30 of 31)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [A Note on Over-Smoothing for Graph Neural Networks](https://mlsanity.com/paper/2006.13318/) (2020)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [FoSR: First-order spectral rewiring for addressing oversquashing in GNNs](https://mlsanity.com/paper/2210.11790/) (2022)
- [Understanding Oversquashing in GNNs through the Lens of Effective Resistance](https://mlsanity.com/paper/2302.06835/) (2023)
- [On the Trade-off between Over-smoothing and Over-squashing in Deep Graph Neural Networks](https://mlsanity.com/paper/2212.02374/) (2022)
- [Understanding convolution on graphs via energies](https://mlsanity.com/paper/2206.10991/) (2022)
- [Oversquashing in GNNs through the lens of information contraction and graph expansion](https://mlsanity.com/paper/2208.03471/) (2022)
- [Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvature](https://mlsanity.com/paper/2309.09384/) (2023)
- [Bag of Tricks for Node Classification with Graph Neural Networks](https://mlsanity.com/paper/2103.13355/) (2021)
- [p-Laplacian Based Graph Neural Networks](https://mlsanity.com/paper/2111.07337/) (2021)
- [ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networks](https://mlsanity.com/paper/2206.05437/) (2022)
- [From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyond](https://mlsanity.com/paper/2310.10121/) (2023)
- [Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challenges](https://mlsanity.com/paper/2311.07073/) (2023)
- [How Curvature Enhance the Adaptation Power of Framelet GCNs](https://mlsanity.com/paper/2307.09768/) (2023)
- [Unifying over-smoothing and over-squashing in graph neural networks: A physics informed approach and beyond](https://mlsanity.com/paper/2309.02769/) (2023)
- [Self-Enhanced GNN: Improving Graph Neural Networks Using Model Outputs](https://mlsanity.com/paper/2002.07518/) (2020)
- [Label-Enhanced Graph Neural Network for Semi-supervised Node Classification](https://mlsanity.com/paper/2205.15653/) (2022)
- [Generalized energy and gradient flow via graph framelets](https://mlsanity.com/paper/2210.04124/) (2022)
- [Bregman Graph Neural Network](https://mlsanity.com/paper/2309.06645/) (2023)
- [Frameless Graph Knowledge Distillation](https://mlsanity.com/paper/2307.06631/) (2023)

## Built on by (most cited first, 6 of 6)

- [What Is Missing In Homophily? Disentangling Graph Homophily For Graph Neural Networks](https://mlsanity.com/paper/2406.18854/) (2024)
- [When Graph Neural Networks Meet Dynamic Mode Decomposition](https://mlsanity.com/paper/2410.05593/) (2024)
- [Unleash Graph Neural Networks from Heavy Tuning](https://mlsanity.com/paper/2405.12521/) (2024)
- [Demystifying Topological Message-Passing with Relational Structures: A Case Study on Oversquashing in Simplicial Message-Passing](https://mlsanity.com/paper/2506.06582/) (2025)
- [Diffusing to the Top: Boost Graph Neural Networks with Minimal Hyperparameter Tuning](https://mlsanity.com/paper/2410.05697/) (2024)
- [Graph Pseudotime Analysis and Neural Stochastic Differential Equations for Analyzing Retinal Degeneration Dynamics and Beyond](https://mlsanity.com/paper/2502.06126/) (2025)

## Abstract (arXiv)

Physics-informed Graph Neural Networks have achieved remarkable performance in learning through graph-structured data by mitigating common GNN challenges such as over-smoothing, over-squashing, and heterophily adaption. Despite these advancements, the development of a simple yet effective paradigm that appropriately integrates previous methods for handling all these challenges is still underway. In this paper, we draw an analogy between the propagation of GNNs and particle systems in physics, proposing a model-agnostic enhancement framework. This framework enriches the graph structure by introducing additional nodes and rewiring connections with both positive and negative weights, guided by node labeling information. We theoretically verify that GNNs enhanced through our approach can effectively circumvent the over-smoothing issue and exhibit robustness against over-squashing. Moreover, we conduct a spectral analysis on the rewired graph to demonstrate that the corresponding GNNs can fit both homophilic and heterophilic graphs. Empirical validations on benchmarks for homophilic, heterophilic graphs, and long-term graph datasets show that GNNs enhanced by our method significantly outperform their original counterparts.