# A Physics-Augmented GraphGPS Framework for the Reconstruction of 3D Riemann Problems from Sparse Data

arXiv: https://arxiv.org/abs/2505.21421 · HTML: https://mlsanity.com/paper/2505.21421/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 43 references that are in the map.
- First posted on arXiv 27 May 2025.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Effective Approaches to Attention-based Neural Machine Translation](https://mlsanity.com/paper/1508.04025/) (2015)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Exphormer: Sparse Transformers for Graphs](https://mlsanity.com/paper/2303.06147/) (2023)
- [Graph-Mamba: Towards Long-Range Graph Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2402.00789/) (2024)
- [Graph Mamba: Towards Learning on Graphs with State Space Models](https://mlsanity.com/paper/2402.08678/) (2024)
- [On the Unreasonable Effectiveness of Feature propagation in Learning on Graphs with Missing Node Features](https://mlsanity.com/paper/2111.12128/) (2021)
- [Deep Operator Learning for High-Fidelity Fluid Flow Field Reconstruction from Sparse Sensor Measurements](https://mlsanity.com/paper/2412.08009/) (2024)
- [Graph Neural Networks for Aerodynamic Flow Reconstruction from Sparse Sensing](https://mlsanity.com/paper/2301.03228/) (2023)
- [Flow reconstruction in time-varying geometries using graph neural networks](https://mlsanity.com/paper/2411.08764/) (2024)
- [FLRNet: A Deep Learning Method for Regressive Reconstruction of Flow Field From Limited Sensor Measurements](https://mlsanity.com/paper/2411.13815/) (2024)

## Abstract (arXiv)

In compressible fluid flow, reconstructing shocks, discontinuities, rarefactions, and their interactions from sparse measurements is an important inverse problem with practical applications. Moreover, physics-informed machine learning has recently become an increasingly popular approach for performing reconstructions tasks. In this work we explore a machine learning recipe, known as GraphGPS, for reconstructing canonical compressible flows known as 3D Riemann problems from sparse observations, in a physics-informed manner. The GraphGPS framework combines the benefits of positional encodings, local message-passing of graphs, and global contextual awareness, and we explore the latter two components through an ablation study. Furthermore, we modify the aggregation step of message-passing such that it is aware of shocks and discontinuities, resulting in sharper reconstructions of these features. Additionally, we modify message-passing such that information flows strictly from known nodes only, which results in computational savings, better training convergence, and no degradation of reconstruction accuracy. We also show that the GraphGPS framework outperforms numerous machine learning benchmarks.