Naslov
Numerical Solution of the Schrödinger Equation Using a Neural Network Approach

Autori
Lojić Kapetanović, Ante ; Poljak, Dragan

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Symposium on Environmental Electromagnetic Compatibility (EEMC), SoftCOM 2020 / - , 2020, 1-4

Skup
The 28th International Conference on Software, Telecommunications and Computer Networks

Mjesto i datum
Hvar, Hrvatska, 17.09.2020. - 19.09.2020

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
neural network ; unsupervised learning ; automatic differentiation ; eigenvalue problem ; Schrördinger equation

Sažetak
This paper overviews the solution of the Schrödinger equation for the case of one-dimensional infinite potential well with a neural network approach. Using a single hidden layer neural network, which is proved to be a universal function approximator, and by exploiting the automatic differentiation capabilities, it is possible to achieve very accurate values of the wave function and eigenvalues of the ground state. The loss function with integrated physical knowledge is set up as an unconstrained nonlinear problem and parameters of a neural network are being learnt in a completely unsupervised manner. Such a technique could potentially serve as a door opener for solving high-dimensional quantum mechanics problems, otherwise tedious to set up for standard mesh-based numerical methods.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA