用神经图网络模拟复杂系统，速度比传统方法快十万倍
Neural Graph Simulator for Complex Systems
- 用图神经网络建模系统动态，支持任意时间步和拓扑变化
- 在刚性问题中计算效率提升超10万倍，处理噪声数据能力强
- 适合交通流预测等实际场景，无需知道物理方程
数值模拟是研究复杂系统动态的主要工具，但大规模模拟常受计算能力限制。本文提出神经图模拟器（NGS），用于在图结构上模拟时不变自治系统。通过图神经网络，NGS构建了一个统一框架，可在不固定时间步长和自回归机制下，对不同拓扑与规模的系统进行仿真。该方法无需预先知晓控制方程，且在鲁棒训练策略下能有效处理噪声或缺失数据。相比传统数值求解器，其在刚性问题中性能提升超过10⁵倍。此外，将NGS应用于真实交通数据，实现了领先水平的流量预测。NGS的通用性远超当前案例，具备广泛拓展潜力。
原文摘要 · Abstract (English)
Numerical simulation is a predominant tool for studying the dynamics in complex systems, but large-scale simulations are often intractable due to computational limitations. Here, we introduce the Neural Graph Simulator (NGS) for simulating time-invariant autonomous systems on graphs. Utilizing a graph neural network, the NGS provides a unified framework to simulate diverse dynamical systems with varying topologies and sizes without constraints on evaluation times through its non-uniform time step and autoregressive approach. The NGS offers significant advantages over numerical solvers by not requiring prior knowledge of governing equations and effectively handling noisy or missing data with a robust training scheme. It demonstrates superior computational efficiency over conventional methods, improving performance by over $10^5$ times in stiff problems. Furthermore, it is applied to real traffic data, forecasting traffic flow with state-of-the-art accuracy. The versatility of the NGS extends beyond the presented cases, offering numerous potential avenues for enhancement.
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