# MeGA-MP: Metric Graph Advection Message Passing -- A Physics-Informed Message Passing Operator for Advection-Dominated Metric Graphs

arXiv: https://arxiv.org/abs/2607.05167 · HTML: https://mlsanity.com/paper/2607.05167/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Builds on (most cited first, 9 of 9)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [SpecAugment: A Simple Data Augmentation Method for Automatic Speech Recognition](https://mlsanity.com/paper/1904.08779/) (2019)
- [EEGNet: A Compact Convolutional Network for EEG-based Brain-Computer Interfaces](https://mlsanity.com/paper/1611.08024/) (2016)
- [MUSAN: A Music, Speech, and Noise Corpus](https://mlsanity.com/paper/1510.08484/) (2015)
- [Large Brain Model for Learning Generic Representations with Tremendous EEG Data in BCI](https://mlsanity.com/paper/2405.18765/) (2024)
- [Decoding speech perception from non-invasive brain recordings](https://mlsanity.com/paper/2208.12266/) (2022)
- [ICLabel: An automated electroencephalographic independent component classifier, dataset, and website](https://mlsanity.com/paper/1901.07915/) (2019)
- [Unlocking Non-Invasive Brain-to-Text](https://mlsanity.com/paper/2505.13446/) (2025)
- [MEGConformer: Conformer-Based MEG Decoder for Robust Speech and Phoneme Classification](https://mlsanity.com/paper/2512.01443/) (2025)

## Abstract (arXiv)

Many real-world systems are organized as networks where spatio-temporal dynamics unfold along connections and not discretely between nodes. Examples include utility networks such as water distribution systems or gas networks, electrical grids, and traffic flow networks. Such systems are naturally modeled as metric graphs, where edges correspond to one-dimensional Euclidean subspaces connected at vertices. Metric graphs are independent of an underlying global Euclidean space, limiting direct application of typical PINNs and operator-learning methods. Especially transport dynamics like advection require a methodology able to capture antisymmetric and long-range dependencies on graphs, which is itself a challenge. We propose a novel physics-informed message passing operator that encodes linear advection on metric graphs as an inductive bias. In the purely advective setting, the operator provably recovers the exact dynamics up to a theoretically derived discretization error without any training. Combined with trainable components like MLPs, our message passing operator extends to realistic advection-reaction dynamics in water distribution systems, where we achieve superior performance compared to baselines and zero-shot generalization across different graph topologies.