Deep learning for inverse problems in quantum mechanics

Inverse problems are important in quantum mechanics and involve such questions as finding which potential give a certain spectrum or which arrangement of atoms give certain properties to a molecule or solid. Inverse problems are typically very hard to solve and tend to be very compute intense. We here show that neural networks can easily solve inverse problems in quantum mechanics. It is known that a neural network can compute the spectrum of a given potential, a result which we reproduce. We find that the (much harder) inverse problem of computing the correct potential that gives a prescribed spectrum is equally easy for a neural network. We extend previous work where neural networks were used to find the electronic many-particle density given a potential by considering the inverse problem. That is, we show that neural networks can compute the potential that gives a prescribed many-electron density.

Abiri, NajmehLund University,Lunds universitet,Beräkningsbiologi och biologisk fysik - Genomgår omorganisation,Institutionen för astronomi och teoretisk fysik - Genomgår omorganisation,Naturvetenskapliga fakulteten,Computational Biology and Biological Physics - Undergoing reorganization,Department of Astronomy and Theoretical Physics - Undergoing reorganization,Faculty of Science(Swepub:lu)thep-nma (author)
Carlsson, GillisLund University,Lunds universitet,Matematisk fysik,Fysiska institutionen,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematical Physics,Department of Physics,Departments at LTH,Faculty of Engineering, LTH(Swepub:lu)matf-gca (author)
Pistol, Mats ErikLund University,Lunds universitet,NanoLund: Centre for Nanoscience,Annan verksamhet, LTH,Lunds Tekniska Högskola,Fasta tillståndets fysik,Fysiska institutionen,Institutioner vid LTH,Other operations, LTH,Faculty of Engineering, LTH,Solid State Physics,Department of Physics,Departments at LTH,Faculty of Engineering, LTH(Swepub:lu)ftf-mpi (author)
Lund UniversityBeräkningsbiologi och biologisk fysik - Genomgår omorganisation (creator_code:org_t)

By the author/editor: Lantz, Victor; Abiri, Najmeh; Carlsson, Gillis; Pistol, Mats Eri ...

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Chemical Science ...; and Theoretical Chem ...

NATURAL SCIENCES: NATURAL SCIENCES; and Physical Science ...; and Condensed Matter ...

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