Visualizing a neural network that develops quantum perturbation theory

Wu, Yu; Zhang, Pengfei; Shen, Huitao; Zhai, Hui

doi:10.1103/physreva.98.010701

Cited by 17 publications

(18 citation statements)

References 47 publications

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“…Several recent papers have discussed the application of deep learning in forward problems: see Khoo, Lu and Ying (2017), Raissi and Karniadakis (2017), Sirignano and Spiliopoulos (2017), Tompson, Schlachter, Sprechmann and Perlin (2017), E, Han and Jentzen (2017) and Wu, Zhang, Shen and Zhai (2018).…”

Section: Special Topicsmentioning

confidence: 99%

Solving inverse problems using data-driven models

et al. 2019

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Recent research in inverse problems seeks to develop a mathematically coherent foundation for combining data-driven models, and in particular those based on deep learning, with domain-specific knowledge contained in physical–analytical models. The focus is on solving ill-posed inverse problems that are at the core of many challenging applications in the natural sciences, medicine and life sciences, as well as in engineering and industrial applications. This survey paper aims to give an account of some of the main contributions in data-driven inverse problems.

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Section: Special Topicsmentioning

confidence: 99%

Solving inverse problems using data-driven models

et al. 2019

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“…In lattice quantum chromodynamics, DNNs have been used to learn action parameters in regions of parameter space where principal component analysis fails (Shanahan et al , 2018). Last but not least, DNNs also found place in the study of quantum control (Yang et al , 2017), and in scattering theory to learn s -wave scattering length (Wu et al , 2018) of potentials.…”

Section: An Introduction To Feed-forward Deep Neural Network (Dnns)mentioning

confidence: 99%

A high-bias, low-variance introduction to Machine Learning for physicists

et al. 2019

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Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, generalization, and gradient descent before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python Jupyter notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists may be able to contribute.

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“…DL methods have also been used to solve Schrödinger equations as differential equations [21][22][23][24] , following the development of DL solvers for differential equations [25][26][27]30 . The objective of these studies is to design a DL solver for Schrödinger equations which is applicable to various situations.…”

Section: Introductionmentioning

confidence: 99%

Weakly-supervised learning on Schrodinger equation

Shiina¹,

Lee²,

Okabe³

et al. 2021

Preprint

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We propose a machine learning method to solve Schrödinger equations for a Hamiltonian that consists of an unperturbed Hamiltonian and a perturbation. We focus on the cases where the unperturbed Hamiltonian can be solved analytically or solved numerically with some fast way. Given a potential function as input, our deep learning model predicts wave functions and energies using a weakly-supervised method. Information of first-order perturbation calculation for randomly chosen perturbations is used to train the model. In other words, no label (or exact solution) is necessary for the training, which is why the method is called weakly-supervised, not supervised. The trained model can be applied to calculation of wave functions and energies of Hamiltonian containing arbitrary perturbation. As an example, we calculated wave functions and energies of a harmonic oscillator with a perturbation and results were in good agreement with those obtained from exact diagonalization.

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Visualizing a neural network that develops quantum perturbation theory

Cited by 17 publications

References 47 publications

Solving inverse problems using data-driven models

Solving inverse problems using data-driven models

A high-bias, low-variance introduction to Machine Learning for physicists

Weakly-supervised learning on Schrodinger equation

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