Neural Graph Simulator for Complex Systems

TL;DR

The paper introduces the Neural Graph Simulator (NGS), a graph neural network-based framework that efficiently simulates complex dynamical systems on graphs, outperforming traditional numerical methods in speed and robustness.

Contribution

It presents a novel neural network approach for simulating diverse complex systems on graphs without requiring explicit governing equations.

Findings

Achieves over 100,000 times speedup in stiff problems

Demonstrates state-of-the-art traffic flow forecasting accuracy

Handles noisy and missing data effectively

Abstract

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.