Machine Learning has wide applications in a broad range of subjects, including physics. Recent works have shown that neural networks can learn classical Hamiltonian mechanics. The results of these works motivate the following question: Can we endow neural networks with inductive biases coming from quantum mechanics and provide insights for quantum phenomena? In this work, we try answering these questions by investigating possible approximations for reconstructing the Hamiltonian of a quantum system given one of its wave-functions. Instead of handcrafting the Hamiltonian and a solution of the Schrödinger equation, we design neural networks that aim to learn it directly from our observations. We show that our method, termed Quantum Potential Neural Networks (QPNN), can learn potentials in an unsupervised manner with remarkable accuracy for a wide range of quantum systems, such as the quantum harmonic oscillator, particle in a box perturbed by an external potential, hydrogen atom, Pöschl-Teller potential, and a solitary wave system. Furthermore, in the case of a particle perturbed by an external force, we also learn the perturbed wave function in a joint end-to-end manner. * Equal contribution Preprint. Under review.
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 also have recently inspired a new wave of Computer Vision (CV) applications research. In this work, a Vision Transformer (ViT) is finetuned to predict the state variables of 2-dimensional Ising model simulations. Our experiments show that ViT outperforms 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 explores the possible of applications of ViT to other simulations and introduces interesting research directions on how attention maps can learn the underlying physics governing different phenomena.
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