arXiv Machine Learning July 7, 2026 By Janine Strotherm, Luca Hermes, Andr\'e Artelt, Barbara Hammer

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

Read the original on arXiv Machine Learning →

arXiv:2607. 05167v1 Announce Type: new Abstract: Many real-world systems are organized as networks where spatio-temporal dynamics unfold along connections and not discretely between nodes.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

safety

arXiv AI

Aug 10

Fluid-DiT: Graph-Free Diffusion Transformers for Fluid Flow Simulations Learning

arXiv:2608. 07161v1 Announce Type: cross Abstract: Simulating complex fluid flows requires capturing full equilibrium distributions rather than just mean trajectories, yet high-fidelity solvers remain computationally prohibitive.

By Shentong Mo, Guolin Ke

llms diffusion benchmarks

arXiv Machine Learning

Jul 20

Discovering Generalizable Governing Equations for Graph Dynamical Systems with Interpretable Neural Networks

arXiv:2508. 18173v2 Announce Type: replace Abstract: The discovery of symbolic governing equations is a central goal in science; yet, it remains challenging particularly for graph dynamical systems, where the network topology further shapes the system behavior.

By Riccardo Cappi, Paolo Frazzetto, Nicol\`o Navarin, Alessandro Sperduti

benchmarks

arXiv Machine Learning

Jun 18

INDEQS: Informed Neural controlled Differential EQuationS

arXiv:2606. 19138v1 Announce Type: new Abstract: Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where a directed graph structure is known a priori.

By Michael Detzel, Gabriel Nobis, Kristiyan Blagov, Juri Schubert, Jackie Ma, Wojciech Samek

benchmarks

arXiv AI

Jul 24

HypNO: A Graph-Based Neural Operator with Physics-Informed Message Passing for Hyperbolic Conservation Laws

arXiv:2607. 20541v1 Announce Type: cross Abstract: We introduce HypNO, a graph-based neural operator for scalar hyperbolic conservation laws.

By Dimitrije \v{Z}drale, Cassie An Jeng, Katie Wang, Sonia Vanier, Alexandre Bayen, Hossein Nick Zinat Matin

benchmarks

arXiv Machine Learning

Jun 2

Graph Navier Stokes Networks

arXiv:2605. 21247v3 Announce Type: replace Abstract: Graph Neural Networks (GNNs) have emerged as a cornerstone of deep learning, with most existing methods rooted in graph signal processing and diffusion equations to model message passing.

By Zexing Zhao, Guangsi Shi, Yu Gong, Tianyu Wang, Shirui Pan, Hongye Cheng, Yuxiao Li

diffusion benchmarks

arXiv Machine Learning

Aug 11

HOPPER: Learnable Hop Extraction for Linearized Graph Sequence Models

arXiv:2608. 09031v1 Announce Type: new Abstract: Graph neural networks typically propagate information through repeated message-passing layers, coupling the distance over which information travels with the number of nonlinear transformations applied.

By Isuru Herath, Arin Gopakumar, Sharan Sahu

benchmarks

Related stories

Fluid-DiT: Graph-Free Diffusion Transformers for Fluid Flow Simulations Learning

Discovering Generalizable Governing Equations for Graph Dynamical Systems with Interpretable Neural Networks

INDEQS: Informed Neural controlled Differential EQuationS

HypNO: A Graph-Based Neural Operator with Physics-Informed Message Passing for Hyperbolic Conservation Laws

Graph Navier Stokes Networks

HOPPER: Learnable Hop Extraction for Linearized Graph Sequence Models