Onur Kara

Onur Kara, Arijit Sehanobish, Hector H Corzo

Transformers are state-of-the-art deep learning models that are composed of stacked attention and point-wise, fully connected layers designed for handling sequential data. Transformers are not only ubiquitous throughout Natural Language Processing (NLP), but, recently, they have inspired a new wave of Computer Vision (CV) applications research. In this work, a Vision Transformer (ViT) is applied to predict the state variables of 2-dimensional Ising model simulations. Our experiments show that ViT outperform state-of-the-art Convolutional Neural Networks (CNN) when using a small number of microstate images from the Ising model corresponding to various boundary conditions and temperatures. This work opens the possibility of applying ViT to other simulations, and raises interesting research directions on how attention maps can learn about the underlying physics governing different phenomena.

Hector H. Corzo, Arijit Sehanobish, Onur Kara

In this report, we present a deep learning framework termed the Electron Correlation Potential Neural Network (eCPNN) that can learn succinct and compact potential functions. These functions can effectively describe the complex instantaneous spatial correlations among electrons in many--electron atoms. The eCPNN was trained in an unsupervised manner with limited information from Full Configuration Interaction (FCI) one--electron density functions within predefined limits of accuracy. Using the effective correlation potential functions generated by eCPNN, we can predict the total energies of each of the studied atomic systems with a remarkable accuracy when compared to FCI energies.

Arijit Sehanobish, Hector H. Corzo, Onur Kara et al.

Attempts to apply Neural Networks (NN) to a wide range of research problems have been ubiquitous and plentiful in recent literature. Particularly, the use of deep NNs for understanding complex physical and chemical phenomena has opened a new niche of science where the analysis tools from Machine Learning (ML) are combined with the computational concepts of the natural sciences. Reports from this unification of ML have presented evidence that NNs can learn classical Hamiltonian mechanics. This application of NNs to classical physics and its results motivate the following question: Can NNs be endowed with inductive biases through observation as means to provide insights into quantum phenomena? In this work, this question is addressed by investigating possible approximations for reconstructing the Hamiltonian of a quantum system in an unsupervised manner by using only limited information obtained from the system's probability distribution.