Hamiltonian Graph Networks with ODE Integrators
Alvaro Sanchez-Gonzalez DeepMind London, UK、Victor Bapst DeepMind London, UK、Kyle Cranmer NYU New York, USA、Peter Battaglia DeepMind London, UK
Abstract
We introduce an approach for imposing physically informed inductive biases in learned simulation models. We combine graph networks with a differentiable ordinary differential equation integrator as a mechanism for predicting future states, and a Hamiltonian as an internal representation. We find that our approach outperforms baselines without these biases in terms of predictive accuracy, energy accuracy, and zero-shot generalization to time-step sizes and integrator orders not experienced during training. This advances the state-of-the-art of learned simulation, and in principle is applicable beyond physical domains.
中文速览
物理模拟中一个核心难题是如何让神经网络学到真正符合物理规律的动力学，而不只是拟合数据表面的规律。研究者将图神经网络（Graph Network）与可微分常微分方程（ODE）积分器以及哈密顿力学（Hamiltonian Mechanics）结合，构建了一个名为 HOGN 的模型：网络内部先用图网络预测系统的哈密顿量（即能量标量），再通过解析求导得到位置和动量的时间导数，最后用龙格-库塔（Runge-Kutta）积分器推演未来状态。在弹簧粒子系统上的实验表明，HOGN 不仅预测精度优于不含这些物理约束的基线模型，还能更好地守恒能量，并且在从未见过的时间步长和积分器阶数上实现零样本泛化。这项工作的重要意义在于，它系统地证明了将 ODE 结构与哈密顿约束同时嵌入图网络能带来质的提升，且该思路并不局限于物理领域，对任何可用正则坐标描述的多体系统都有潜在适用价值。
原文 arXiv:1909.12790;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1909.12790v1