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 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). It effectively imposes
time-reversal symmetry to enable more accurate model predictions across a wider
range of dynamical systems under classical mechanics. In addition, we further
provide theoretical analysis to 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. Experimental results on a variety of physical systems
demonstrate the effectiveness of our proposed method. Particularly, it achieves
an MSE improvement of 11.5 % on a challenging chaotic triple-pendulum systems.

本文介绍了一种基于时间反演对称性的自我监督正则化方法，通过连续图神经网络的常微分方程预测前后轨迹，以更准确地模拟广泛范围的经典力学动力学系统，并通过实验证明了该方法的有效性。

TANGO: 多智能体动态系统的时空反转潜在图 ODE

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

Learning multi-agent system dynamics has been extensively studied for various
real-world applications, such as molecular dynamics in biology. Most of the
existing models are built to learn single system dynamics from observed
historical data and predict the future trajectory. In practice, however, we
might observe multiple systems that are generated across different
environments, which differ in latent exogenous factors such as temperature and
gravity. One simple solution is to learn multiple environment-specific models,
but it fails to exploit the potential commonalities among the dynamics across
environments and offers poor prediction results where per-environment data is
sparse or limited. Here, we present GG-ODE (Generalized Graph Ordinary
Differential Equations), a machine learning framework for learning continuous
multi-agent system dynamics across environments. Our model learns system
dynamics using neural ordinary differential equations (ODE) parameterized by
Graph Neural Networks (GNNs) to capture the continuous interaction among
agents. We achieve the model generalization by assuming the dynamics across
different environments are governed by common physics laws that can be captured
via learning a shared ODE function. The distinct latent exogenous factors
learned for each environment are incorporated into the ODE function to account
for their differences. To improve model performance, we additionally design two
regularization losses to (1) enforce the orthogonality between the learned
initial states and exogenous factors via mutual information minimization; and
(2) reduce the temporal variance of learned exogenous factors within the same
system via contrastive learning. Experiments over various physical simulations
show that our model can accurately predict system dynamics, especially in the
long range, and can generalize well to new systems with few observations.

通过学习多智能体系统动力学，我们提出了 GG-ODE（广义图形常微分方程）机器学习框架，使用神经常微分方程（ODE）通过图神经网络（GNN）捕捉智能体之间的连续交互，并假设不同环境下的动力学都受到相同物理定律的支配。通过实验证明，我们的模型可以准确预测系统动力学，尤其在长期范围内，并能够很好地推广到观测数据稀缺的新系统。