TANGO: Time-Reversal Latent GraphODE for Multi-Agent Dynamical Systems
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Keywords: NeuralODE, Graph Neural Networks, Dynamical Systems, Physical Simulations, Physics-informed Neural Networks
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TL;DR: Time-reversal Latent GraphODE for Modeling Multi-Agent 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 re-
main 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 pa-
per, we propose a simple-yet-effective self-supervised regularization term as a soft
constraint that aligns the forward and backward trajectories predicted by a contin-
uous graph neural network-based ordinary differential equation (GraphODE). It
effectively imposes time-reversal symmetry to enable more accurate model pre-
dictions 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 inte-
gration steps, which enables our model to be more noise-tolerant and even applica-
ble 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
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Supplementary Material: pdf
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Submission Number: 9050
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