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Workshop: The Symbiosis of Deep Learning and Differential Equations -- III

TANGO: Time-reversal Latent GraphODE for Multi-Agent Dynamical Systems

Zijie Huang · Wanjia Zhao · Jingdong Gao · Ziniu Hu · Xiao Luo · Yadi Cao · Yuanzhou Chen · Yizhou Sun · Wei Wang

Keywords: [ NeuralODE ] [ Dynamical Systems ] [ physical simulations ] [ Physics-Informed Neural Networks ] [ graph neural networks ]

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Sat 16 Dec 1 p.m. PST — 1:15 p.m. PST


Learning complex multi-agent system dynamics from data is crucial across many domains like physical simulations and material modeling. Existing physics-informed approaches, like Hamiltonian Neural Network, introduce inductive bias by strictly following energy conservation law. However, many real-world systems do not strictly conserve energy. Thus, we focus on Time-Reversal Symmetry, a broader physical principle indicating that system dynamics should remain invariant when time is reversed. This principle not only preserves energy in conservative systems but also serves as a strong inductive bias for non-conservative, reversible systems.In this paper, we propose a simple-yet-effective self-supervised regularization term as a soft constraint that aligns the forward and backward trajectories predicted by a continuous graph neural network-based ordinary differential equation (GraphODE). In addition, we theoretical show that our regularization essentially minimizes higher-order Taylor expansion terms during the ODE integration steps, which enables our model to be more noise-tolerant and even applicable to irreversible systems.

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