Mixed Precision Fermi-Operator Expansion on Tensor Cores from a Machine Learning Perspective.

Area of Science:

• Computational Physics
• Quantum Chemistry
• Machine Learning

Background:

• Electronic structure calculations are crucial for understanding material properties.
• Traditional methods face computational challenges with increasing system size and complexity.
• Mixed precision computing and specialized hardware offer potential for acceleration.

Purpose of the Study:

• To develop a high-performance computational scheme for electronic structure calculations.
• To leverage deep neural networks and tensor core units for quantum mechanical problems.
• To improve the accuracy and efficiency of representing electronic states at finite temperatures.

Main Methods:

• A second-order recursive Fermi-operator expansion scheme was developed.
• Mixed precision floating point operations were utilized on Nvidia A100 tensor core units.
• A differentiable deep neural network structure was formulated to solve the electronic structure problem.

Main Results:

• Achieved performance exceeding 100 teraFLOPs for half-precision operations.
• Demonstrated network acceleration by optimizing weights and biases, reducing required layers.
• Showcased machine learning optimization of expansion coefficients for accurate fractional occupation numbers.

Conclusions:

• The proposed scheme offers a significant performance boost for electronic structure calculations.
• The integration of deep neural networks provides a powerful framework for quantum mechanical simulations.
• This approach enhances the accurate representation of electronic states, particularly at finite temperatures.