Tensor-Reduced Atomic Density Representations.

Area of Science:

• Computational Materials Science
• Machine Learning in Chemistry and Physics
• Data Analysis and Representation

Background:

• Density-based atomic environment representations are crucial for machine learning in atomistic modeling.
• Current methods using tensor products of element-specific densities exhibit poor scalability with increasing element numbers.
• Graph neural networks offer an alternative by learning embeddings but lack explicit connection to density-based descriptors.

Purpose of the Study:

• To develop a compact, element-number-independent representation of local atomic environments.
• To connect graph neural network approaches with traditional density-based descriptors through tensor factorization.
• To create a systematically improvable representation for diverse data-driven atomistic tasks.

Main Methods:

• Recasting graph neural network principles as tensor factorization of neighbor-density-based descriptors.
• Development of a novel notation to identify connections with existing data compression algorithms.
• Formulation of a tensor-reduced representation for atomic environments.

Main Results:

• A compact tensor-reduced representation of local atomic environments was successfully derived.
• The size of the new representation is independent of the number of chemical elements involved.
• The method demonstrates systematic convergence and applicability to various data analysis and regression tasks.

Conclusions:

• The proposed tensor-reduced representation overcomes the scalability limitations of traditional methods.
• This approach bridges the gap between density-based descriptors and graph neural networks.
• The new representation is a versatile tool for machine learning in materials science and related fields.