Predicting Quantum Potentials by Deep Neural Network and Metropolis Sampling

06/06/2021
by   Rui Hong, et al.
0

The hybridizations of machine learning and quantum physics have caused essential impacts to the methodology in both fields. Inspired by quantum potential neural network, we here propose to solve the potential in the Schrodinger equation provided the eigenstate, by combining Metropolis sampling with deep neural network, which we dub as Metropolis potential neural network (MPNN). A loss function is proposed to explicitly involve the energy in the optimization for its accurate evaluation. Benchmarking on the harmonic oscillator and hydrogen atom, MPNN shows excellent accuracy and stability on predicting not just the potential to satisfy the Schrodinger equation, but also the eigen-energy. Our proposal could be potentially applied to the ab-initio simulations, and to inversely solving other partial differential equations in physics and beyond.

READ FULL TEXT

page 1

page 2

page 3

page 4

06/19/2022

Enforcing Continuous Physical Symmetries in Deep Learning Network for Solving Partial Differential Equations

As a typical application of deep learning, physics-informed neural netwo...
07/19/2021

Quantum Deep Learning: Sampling Neural Nets with a Quantum Annealer

We demonstrate the feasibility of framing a classically learned deep neu...
12/09/2020

Emergent Quantumness in Neural Networks

It was recently shown that the Madelung equations, that is, a hydrodynam...
08/03/2022

Quantum-Inspired Tensor Neural Networks for Partial Differential Equations

Partial Differential Equations (PDEs) are used to model a variety of dyn...
01/29/2021

Recurrent Localization Networks applied to the Lippmann-Schwinger Equation

The bulk of computational approaches for modeling physical systems in ma...
10/29/2020

Quantum advantage for differential equation analysis

Quantum algorithms for both differential equation solving and for machin...