α-separable graph Hamiltonian network: A robust model for learning particle interactions in lattice systems.

Area of Science:

• Computational Physics
• Machine Learning
• Materials Science

Background:

• Lattice systems exhibit complex particle interactions crucial for material properties.
• Traditional graph neural networks struggle with inferring interactions without predefined connections.
• Preserving physical laws like conservation laws is essential for accurate trajectory prediction.

Purpose of the Study:

• To develop a novel graph Hamiltonian network (α-SGHN) capable of revealing complex interaction patterns in lattice systems.
• To infer particle interactions from trajectory data without requiring prior knowledge of coupling.
• To ensure the model preserves all fundamental conservation laws during trajectory prediction.

Main Methods:

• Proposed an α-separable graph Hamiltonian network (α-SGHN) architecture.
• Utilized particle trajectory data as input for interaction inference.
• Incorporated structural information of the lattice system into the model.
• Compared α-SGHN performance against baseline conventional neural network models.

Main Results:

• α-SGHN successfully inferred potential interactions without prior knowledge of particle coupling.
• The model demonstrated the preservation of all conservation laws during trajectory prediction.
• Experimental results showed α-SGHN significantly outperformed baseline models in predicting lattice systems.
• The model's effectiveness was validated through its incorporation of structural information.

Conclusions:

• The proposed α-SGHN is effective in revealing complex interaction patterns in lattice systems.
• The model overcomes limitations of traditional graph neural networks by inferring interactions dynamically.
• α-SGHN offers a robust framework for trajectory prediction while respecting physical conservation laws.
• The approach is expected to have broad applicability to various lattice models, including Frenkel-Kontorova, rotator, and Toda lattices.