Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning

A deep understanding of the intricate interactions between particles within a system is a key approach to revealing the essential characteristics of the system, whether it is an in-depth analysis of molecular properties in the field of chemistry or the design of new materials for specific performance requirements in materials science. To this end, we propose Graph Attention Hamiltonian Neural Network (GAHN), a neural network method that can understand the underlying structure of lattice Hamiltonian systems solely through the dynamic trajectories of particles. We can determine which particles in the system interact with each other, the proportion of interactions between different particles, and whether the potential energy of interactions between particles exhibits even symmetry or not. The obtained structure helps the neural network model to continue predicting the trajectory of the system and further understand the dynamic properties of the system. In addition to understanding the underlying structure of the system, it can be used for detecting lattice structural abnormalities, such as link defects, abnormal interactions, etc. These insights benefit system optimization, design, and detection of aging or damage. Moreover, this approach can integrate other components to deduce the link structure needed for specific parts, showcasing its scalability and potential. We tested it on a challenging molecular dynamics dataset, and the results proved its ability to accurately infer molecular bond connectivity, highlighting its scientific research potential.

Data-Driven Discovery of Conservation Laws from Trajectories via Neural Deflation

In an earlier work by a subset of the present authors, the method of the so-called neural deflation was introduced towards identifying a complete set of functionally independent conservation laws of a nonlinear dynamical system. Here, we extend by a significant step this proposal. Instead of using the explicit knowledge of the underlying equations of motion, we develop the method directly from system trajectories. This is crucial towards enhancing the practical implementation of the method in scenarios where solely data reflecting discrete snapshots of the system are available. We showcase the results of the method and the number of associated conservation laws obtained in a diverse range of examples including 1D and 2D harmonic oscillators, the Toda lattice, the Fermi-Pasta-Ulam-Tsingou lattice and the Calogero-Moser system.