Predicting the Dynamics of Complex System via Multiscale Diffusion Autoencoder

2025-05-05

AI Summary

Single-scale modeling struggles to capture multiscale dynamical structures in spatiotemporal evolution prediction of complex systems. Method: This paper proposes an end-to-end framework integrating multiscale diffusion autoencoding with attention-enhanced graph neural ordinary differential equations (GNN-ODEs). It is the first work to jointly embed multiscale diffusion generative modeling and graph-structured continuous-time dynamical modeling, explicitly capturing cross-scale co-evolutionary mechanisms and uncovering hierarchical intrinsic dynamics. The method unifies variational inference, attention mechanisms, and neural ODEs to ensure both representation robustness and dynamic interpretability. Results: Evaluated on multiple canonical complex systems, the approach achieves a 53.23% average reduction in prediction error, significantly improving long-term extrapolation accuracy, noise robustness, and cross-system generalization capability.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Predicting the dynamics of complex systems is crucial for various scientific and engineering applications. The accuracy of predictions depends on the model's ability to capture the intrinsic dynamics. While existing methods capture key dynamics by encoding a low-dimensional latent space, they overlook the inherent multiscale structure of complex systems, making it difficult to accurately predict complex spatiotemporal evolution. Therefore, we propose a Multiscale Diffusion Prediction Network (MDPNet) that leverages the multiscale structure of complex systems to discover the latent space of intrinsic dynamics. First, we encode multiscale features through a multiscale diffusion autoencoder to guide the diffusion model for reliable reconstruction. Then, we introduce an attention-based graph neural ordinary differential equation to model the co-evolution across different scales. Extensive evaluations on representative systems demonstrate that the proposed method achieves an average prediction error reduction of 53.23% compared to baselines, while also exhibiting superior robustness and generalization.

Problem

• Predicting dynamics of complex systems accurately
• Capturing multiscale structure in complex systems
• Modeling co-evolution across different scales

Innovation

• Multiscale diffusion autoencoder for feature encoding
• Attention-based graph neural ODE for co-evolution
• 53.23% lower prediction error than baselines