System and method for predictive analysis of 2-dimensional crystal structures

A method for generating invariant embeddings of defect configurations in two-dimensional crystal lattices using a machine learning model, the method comprising:

• utilizing a neural network to create embeddings invariant to symmetry operations specific to a lattice structure;
• employing a contrastive learning framework to ensure embeddings of equivalent configurations are close in an embedding space, while non-equivalent configurations are distant;
• generating invariant embeddings of defect configurations in two-dimensional crystal lattices using a machine learning model;
• training a Siamese Neural Network on labeled pairs of defect placements;
• optimizing said embeddings for classification accuracy through a distance-based loss function;
• computationally generating a base descriptor for defect configurations in two-dimensional crystal lattices;
• training for machine learning models applied to defect recognition;
• utilizing circular padding within a convolutional neural network architecture to ensure consistent feature representation during periodic translations of input data, enhancing invariance to defect placements;
• predicting physical properties of two-dimensional materials;
• retrieving lattice configurations based on embeddings;
• applying invariant embedding generation to various two-dimensional materials and accommodates different defect densities;
• and
• designing two-dimensional crystal structures for generation.

A system for predicting physical properties of two-dimensional crystals with defect configurations, comprising:

• at least one machine learning model used to generate invariant embeddings of defect configurations in two-dimensional crystal lattices;
• said at least one machine learning model applying a training methodology to defect recognition;
• a Siamese Neural Network trained on labeled pairs of defect placements;
• a distance-based loss function to optimize the embeddings for classification accuracy;
• a base descriptor computationally generated for defect configurations in two-dimensional crystal lattices;
• a convolutional neural network architecture utilizing circular padding to ensure consistent feature representation during periodic translations of input data, enhancing invariance to defect placements;
• wherein said convolutional neural network architecture includes three convolutional layers and three fully connected layers;
• a predictor of physical properties of two-dimensional materials;
• a retrieval of lattice configurations based on embeddings;
• a generalized approach for invariant embedding generation that applies to various two-dimensional materials and accommodates different defect densities;
• wherein application and accommodation includes standardizing input representations and preserving invariance under symmetry operations regardless of defect count;
• a designing of two-dimensional crystal structures;
• and
• an ability to enhance a classification of defect configurations by concatenating a base descriptor of defects, embeddings generated from multiple stages of neural network processing;
• and distinct components derived from hierarchical training.