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
TL;DR
This paper introduces TANGO, a novel method that incorporates time-reversal symmetry as a regularization in graph neural ODEs to improve modeling of diverse multi-agent dynamical systems, including non-conservative and irreversible ones.
Contribution
It proposes a self-supervised regularization based on time-reversal symmetry for graph neural ODEs, extending physics-informed modeling to a broader class of systems.
Findings
Achieves 11.5% MSE improvement on chaotic triple-pendulum systems.
Enhances noise tolerance and applicability to irreversible systems.
Effectively models both conservative and non-conservative dynamical systems.
Abstract
Learning complex multi-agent system dynamics from data is crucial across many domains, such as in physical simulations and material modeling. Extended from purely data-driven approaches, existing physics-informed approaches such as Hamiltonian Neural Network strictly follow energy conservation law to introduce inductive bias, making their learning more sample efficiently. However, many real-world systems do not strictly conserve energy, such as spring systems with frictions. Recognizing this, we turn our attention to a broader physical principle: Time-Reversal Symmetry, which depicts that the dynamics of a system shall remain invariant when traversed back over time. It still helps to preserve energies for conservative systems and in the meanwhile, serves as a strong inductive bias for non-conservative, reversible systems. To inject such inductive bias, in this paper, we propose a…
Peer Reviews
Decision·Submitted to ICLR 2024
The paper puts forward an interesting motivation when it claims that engaging with Hamiltonian-type neural models might pose too stringent requirements, both on energy preservation as well as on the learning model. The idea of focusing on symmetry/reversibility properties rather than on strict energy preservation requirements is interesting. Even more so if this can be coupled with an approach that is fairly general and computationally efficient to achieve (as it seems reasonable to assume with
W1) As highlighted in the “Strengths” part, the motivation of the work is compelling and the idea of addressing reversibility through a simple regularization term is interesting. Unfortunately these are not novel contributions of this paper. Rather they are adapted from Huh et al, NeurIPS 2020, essentially adding the graph NN dimension (which is straightforward extension) and the simplified reversibility regularization with associated theoretical analysis (which is a less straightforward one). H
- TANGO, the model proposed in this study, consistently outperforms major competitors, including baseline Latent NODEs, Hamiltonian NODEs, TRS (Time-Reversal-Symmetric) NODEs, and graph NODEs, across a range of physics and dynamics forecasting problems. - The paper is generally well-written and easy to follow (although there are some technically confusing points, please see the Weaknesses). Figure 1 and Figure 2 effectively summarize the motivation and core concept of this work.
**1. Reversing operator** First, I would appreciate clarification on the precise calculation of the reversing operator $R$ for TANGO. While the reversing operator holds a significant role in addressing time-reversal symmetry, the current version of the paper lacks a detailed description and computation method for it (if this information is located in the appendix, I apologize; however, I would recommend including it in the main text of the revised version for clarity). Considering that the reve
The idea of integrating time reversal symmetry into machine learning models is interesting, and comparing different formulations with each other, and investigating to which extent these implementations differ in training stability and numerical errors, is a relevant area of study. I particularily appreciated the formal treatment of time reversal symmetry as accounting for numerical errors in Theorem 1 as an interesting contribution.
Main Contribution and Ablation Study As the authors point out, closely related ideas to those one proposed here have been around for a while (see e.g. https://arxiv.org/abs/2003.02236 for Koopman operators, or, as the authors point out, in a very similar form in Huang et al. 2020). To my understanding, the main contribution is a slight reformulation of the consistency loss from Huang et al. 2020, Eq.11, so that the consistency is computed between forward and backward generated trajectories (as
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Taxonomy
TopicsModel Reduction and Neural Networks · Machine Learning in Materials Science · Gaussian Processes and Bayesian Inference