Hamiltonian Graph Networks with ODE Integrators

2019/09/27 by Álvaro Sánchez‐González, Alvaro Sanchez-Gonzalez, Sanchez-Gonzalez, Alvaro +7 · 1 voice · 4 citations
Computer Science · #Advanced Graph Neural Networks #Explainable Artificial Intelligence (XAI) #Topic Modeling #cs.LG #physics.comp-ph

paper · pdf · doi:10.48550/arxiv.1909.12790

openalex publication_date 2019/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Hamiltonian Neural Networks
• HMSPC: A Hybrid Mechanistic-Stochastic Physical-Continuous Model for Battery Dynamics

Cited by

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• Domain-Decomposed Graph Neural Network Surrogate Modeling for Ice Sheets
• Physics-Inspired All-Pair Interaction Learning for 3D Dynamics Modeling
• Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach

Discussions

• I haven’t read it carefully, but +1 to works like the one below. It mentions learning artifacts from discreetness. We saw some things like that in this paper, where bad integration of the true Hamilto [bsky, 27 points, 0 comments]

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