Machine-Learning Accelerated Calculations of Reduced Density Matrices

  • Principal Investigator (PI) Name: Dr. Jiabin Yu
  • In Collaboration With: Prof. Jiabin Yu (supervisor), Lexu Zhao (Gavin)
  • Institution and Department: Department of Physics, College of Liberal Arts and Sciences, University of Florida
  • Timeline: October 2024 - present
  • Research focus: n-particle reduced density matrices (n-RDMs) play a central role in understanding correlated phases of matter, but their calculation is often computationally inefficient for strongly-correlated states at large system sizes. In this work, we use neural network (NN) architectures to accelerate and even predict n-RDMs for large systems. Our underlying intuition is that, for gapped states, n-RDMs are often smooth functions over the Brillouin zone (BZ) and therefore interpolable, allowing NNs trained on small-size to predict large-size ones. (From the abstract of our arXiv preprint).
  • Project responsibilities: I am primarily responsible for the machine learning aspects of the project, including data preprocessing and postprocessing, as well as designing, implementing, and training neural networks, and fine-tuning their hyperparameters.
  • Sample Media:
    Figure showing percent reduction vs. L
    Above: Summary of results for the Hubbard model using a self-attention NN (U = 1) and SIRENs (U = 1, 2, 3) showing the percent reduction in the number of Hartree-Fock (HF) iterations as a function of the system size L. See our paper for more!