Discovering Message Passing Hierarchies for Mesh-Based Physics Simulation

2024-10-03

arXiv.org

AI Summary

Existing graph neural network–based physical simulation methods rely on handcrafted, static hierarchical graph structures, limiting their adaptability to dynamically evolving physical systems. To address this, we propose a learnable dynamic message-passing hierarchical framework tailored for grid-based physical simulation. Our method introduces a novel differentiable node selection mechanism that enables physics-aware hierarchical transitions, and incorporates anisotropic message passing to support directionally non-uniform feature aggregation and flexible modeling of long-range interactions. The framework unifies dynamic multi-scale graph construction, differentiable node sampling, and anisotropic aggregation into a single end-to-end trainable architecture. Evaluated on five canonical physical simulation datasets, our approach achieves an average error reduction of 22.7% compared to fixed-hierarchy baselines. This work establishes a new paradigm for multi-scale modeling of dynamic and complex physical systems.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Graph neural networks have emerged as a powerful tool for large-scale mesh-based physics simulation. Existing approaches primarily employ hierarchical, multi-scale message passing to capture long-range dependencies within the graph. However, these graph hierarchies are typically fixed and manually designed, which do not adapt to the evolving dynamics present in complex physical systems. In this paper, we introduce a novel neural network named DHMP, which learns Dynamic Hierarchies for Message Passing networks through a differentiable node selection method. The key component is the anisotropic message passing mechanism, which operates at both intra-level and inter-level interactions. Unlike existing methods, it first supports directionally non-uniform aggregation of dynamic features between adjacent nodes within each graph hierarchy. Second, it determines node selection probabilities for the next hierarchy according to different physical contexts, thereby creating more flexible message shortcuts for learning remote node relations. Our experiments demonstrate the effectiveness of DHMP, achieving 22.7% improvement on average compared to recent fixed-hierarchy message passing networks across five classic physics simulation datasets.

Problem

• Adaptive learning of graph hierarchies for dynamic physical systems
• Anisotropic message passing for direction-specific feature aggregation
• Enhancing long-range dependency capture in mesh-based simulations

Innovation

• Differentiable framework learns graph hierarchies adaptively
• Anisotropic message passing for dynamic feature aggregation
• Node selection based on physical context enhances flexibility