Learning impurity spectral functions from density of states.

Area of Science:

• Condensed Matter Physics
• Computational Materials Science
• Machine Learning in Physics

Background:

• Predicting spectral functions is crucial for understanding material properties.
• Traditional methods for spectral function calculation are computationally intensive.
• Density of states (DOS) provides foundational information about material electronic structure.

Purpose of the Study:

• To develop and evaluate machine learning models for predicting spectral functions directly from DOS.
• To compare the performance of various neural network architectures for this task.
• To assess the computational efficiency of machine learning approaches versus traditional solvers.

Main Methods:

• Constructed a dataset of 100,000 samples using numerical renormalization group calculations.
• Trained and evaluated six different neural network architectures, including gated recurrent unit (GRU) and bidirectional GRU (BiGRU).
• Validated model performance on original and independent datasets using mean absolute error (MAE).

Main Results:

• The GRU + BiGRU network demonstrated superior performance, achieving MAE values of 0.052 and 0.043 on different datasets.
• Machine learning predictions were 10^5-10^6 times faster than traditional impurity solvers.
• Identified GRU and BiGRU as highly effective for spectral function prediction from DOS.

Conclusions:

• Recurrent neural networks, particularly GRU and BiGRU, offer a highly efficient and accurate method for spectral function prediction.
• This machine learning approach significantly reduces computational cost for magnetic impurity problems.
• The study opens new avenues for applying deep learning in computational physics and materials science.