Variational autoencoder reconstruction of complex many-body physics
Given the notably increasing complexity of mathematical models to study realistic systems and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models, show limitations in scope or applicability. On the other hand...
Uloženo v:
| Vydáno v: | arXiv.org |
|---|---|
| Hlavní autoři: | , , , , |
| Médium: | Paper |
| Jazyk: | angličtina |
| Vydáno: |
Ithaca
Cornell University Library, arXiv.org
09.10.2019
|
| Témata: | |
| ISSN: | 2331-8422 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Given the notably increasing complexity of mathematical models to study realistic systems and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models, show limitations in scope or applicability. On the other hand, machine learning, i.e. data-driven, methods prove to be increasingly efficient for the study of complex quantum systems. Deep neural networks in particular have been successfully applied to many-body quantum dynamics simulations and to quantum matter phase characterization. In the present work, we show how to use a variational autoencoder (VAE) -- a state-of-the-art tool in the field of deep learning for the simulation of probability distributions of complex systems. More precisely, we transform a quantum mechanical problem of many-body state reconstruction into a statistical problem, suitable for VAE, by using informationally complete positive operator-valued measure. We show with the paradigmatic quantum Ising model in a transverse magnetic field, that the ground-state physics, such as, e.g., magnetization and other mean values of observables, of a whole class of quantum many-body systems can be reconstructed by using VAE learning of tomographic data, for different parameters of the Hamiltonian, and even if the system undergoes a quantum phase transition. We also discuss challenges related to our approach as entropy calculations pose particular difficulties. |
|---|---|
| AbstractList | Given the notably increasing complexity of mathematical models to study realistic systems and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models, show limitations in scope or applicability. On the other hand, machine learning, i.e. data-driven, methods prove to be increasingly efficient for the study of complex quantum systems. Deep neural networks in particular have been successfully applied to many-body quantum dynamics simulations and to quantum matter phase characterization. In the present work, we show how to use a variational autoencoder (VAE) -- a state-of-the-art tool in the field of deep learning for the simulation of probability distributions of complex systems. More precisely, we transform a quantum mechanical problem of many-body state reconstruction into a statistical problem, suitable for VAE, by using informationally complete positive operator-valued measure. We show with the paradigmatic quantum Ising model in a transverse magnetic field, that the ground-state physics, such as, e.g., magnetization and other mean values of observables, of a whole class of quantum many-body systems can be reconstructed by using VAE learning of tomographic data, for different parameters of the Hamiltonian, and even if the system undergoes a quantum phase transition. We also discuss challenges related to our approach as entropy calculations pose particular difficulties. |
| Author | Luchnikov, I Filippov, S N Stas, P -J C Ryzhov, A Ouerdane, H |
| Author_xml | – sequence: 1 givenname: I surname: Luchnikov fullname: Luchnikov, I – sequence: 2 givenname: A surname: Ryzhov fullname: Ryzhov, A – sequence: 3 givenname: P surname: Stas middlename: -J C fullname: Stas, P -J C – sequence: 4 givenname: S surname: Filippov middlename: N fullname: Filippov, S N – sequence: 5 givenname: H surname: Ouerdane fullname: Ouerdane, H |
| BookMark | eNotjs1KxDAYRYMoOI7zAO4Krjvmy5c06VKKfzDgZnA7pPnBDp2kJq1M396Kri7cczncG3IZYnCE3AHdciUEfdDp3H1voV4KirWQF2TFEKFUnLFrssn5SClllWRC4Io0Hzp1euxi0H2hpzG6YKJ1qUjOxJDHNJlfWERfmHgaencuTjrMZRvtXAyfc-5MviVXXvfZbf5zTfbPT_vmtdy9v7w1j7tSCwZlrVzVagrQttKoigvUHmzdSo-2YkZKUXMQRgm1DDi1yJX3Ho2SIBS3gGty_6cdUvyaXB4Pxzil5Xc-MKTIeQUK8Af9l04- |
| ContentType | Paper |
| Copyright | 2019. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: 2019. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | 8FE 8FG ABJCF ABUWG AFKRA AZQEC BENPR BGLVJ CCPQU DWQXO HCIFZ L6V M7S PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| DOI | 10.48550/arxiv.1910.03957 |
| DatabaseName | ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials ProQuest Central Technology collection ProQuest One Community College ProQuest Central SciTech Premium Collection ProQuest Engineering Collection Engineering Database ProQuest Central Premium ProQuest One Academic ProQuest Publicly Available Content ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection |
| DatabaseTitle | Publicly Available Content Database Engineering Database Technology Collection ProQuest One Academic Middle East (New) ProQuest Central Essentials ProQuest One Academic Eastern Edition ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest One Academic UKI Edition ProQuest Central Korea Materials Science & Engineering Collection ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) Engineering Collection |
| DatabaseTitleList | Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: PIMPY name: ProQuest - Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 2331-8422 |
| Genre | Working Paper/Pre-Print |
| GroupedDBID | 8FE 8FG ABJCF ABUWG AFKRA ALMA_UNASSIGNED_HOLDINGS AZQEC BENPR BGLVJ CCPQU DWQXO FRJ HCIFZ L6V M7S M~E PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| ID | FETCH-LOGICAL-a521-98e6ba011bb7c86453af1d9b7f3d62c7759415c858bb740d348fff3c871584d13 |
| IEDL.DBID | BENPR |
| IngestDate | Mon Jun 30 09:11:54 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a521-98e6ba011bb7c86453af1d9b7f3d62c7759415c858bb740d348fff3c871584d13 |
| Notes | SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50 |
| OpenAccessLink | https://www.proquest.com/docview/2303446181?pq-origsite=%requestingapplication% |
| PQID | 2303446181 |
| PQPubID | 2050157 |
| ParticipantIDs | proquest_journals_2303446181 |
| PublicationCentury | 2000 |
| PublicationDate | 20191009 |
| PublicationDateYYYYMMDD | 2019-10-09 |
| PublicationDate_xml | – month: 10 year: 2019 text: 20191009 day: 09 |
| PublicationDecade | 2010 |
| PublicationPlace | Ithaca |
| PublicationPlace_xml | – name: Ithaca |
| PublicationTitle | arXiv.org |
| PublicationYear | 2019 |
| Publisher | Cornell University Library, arXiv.org |
| Publisher_xml | – name: Cornell University Library, arXiv.org |
| SSID | ssj0002672553 |
| Score | 1.7015071 |
| SecondaryResourceType | preprint |
| Snippet | Given the notably increasing complexity of mathematical models to study realistic systems and their coupling to their environment that constrains their... |
| SourceID | proquest |
| SourceType | Aggregation Database |
| SubjectTerms | Complex systems Complexity Computer simulation Ising model Machine learning Mathematical models Neural networks Numerical methods Phase transitions Quantum mechanics Reconstruction Statistical analysis |
| Title | Variational autoencoder reconstruction of complex many-body physics |
| URI | https://www.proquest.com/docview/2303446181 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1NT8JAEJ0oaOLJ7_iBpAevBcrudrcnEwlEEyWNEoMnst2PxIMUWyT4751dCh5MvHhr0x7abTvz3szrG4BrzhHk6wi5CWE8pLE2oRurjVuRlCZTlkj_o_ADHw7FeJykVcGtrGSV65joA7XOlauRtxEqE6QumJBuZh-hmxrluqvVCI1tqDunMlqD-m1_mD5tqizdmCNmJqt2pjfvasti-bZoIU3ptDquSfUrCPvMMtj_7zUdQD2VM1McwpaZHsGuV3Sq8hh6L8iCq0pfID_nuXOs1KYIPAXe2MYGuQ28rNwsg3cMDGGW669gVe8oT2A06I96d2E1MSGUzEkthIkziV9slnElYsqItJFOMm6JjruKc5ZgvlaCCTyBdjShwlpLFJImxCE6IqdQm-ZTcwaBpMRorRVx_uhCE0FZRhWSM8qSrmTiHBrrJZlUb305-VmPi78PX8IeAo_Ei-KSBtTwns0V7KjF_K0smtVDbDod5jPupfeP6es3L42qMA |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LT8JAEJ4gaPTkOz5Qe9BjgXa33e3BeEAJhEc4EIMnst3dJhykSBHhR_kfnS0tHky8efDWpE3T3ZnOzDfz7QzALWMY5CsHsQnxmE19pW0zVhuvHCF0KCMi0oPCHdbr8eEw6BfgMz8LY2iVuU1MDbWKpcmRVzFUJghd0CE9TN9sMzXKVFfzERprtWjr1QdCtuS-9YjyvXPdxtOg3rSzqQK28AwdgWs_FKjVYcgk96lHROSoIGQRUb4rGfMC9GmSexwfoDVFKI-iiEgEFuirlUPwtVtQoqjrvAilfqvbf9kkdVyfYYhO1tXTtFdYVcyW40UFUVGtUjM1sR82P3Vkjf1_tgUHuHQx1bNDKOjJEeykfFWZHEP9GTF-lse0xPs8Nv04lZ5ZKcDfNMW14shKSfN6ab2i2bPDWK2sdTYnOYHBX3z2KRQn8USfgSUo0UopSUz3d64Ip15IJUJP6gWu8Pg5lHMJjLJ_Ohl9b__F77dvYLc56HZGnVavfQl7GGIFKf0vKEMR16-vYFsu5uNkdp3pjwWjPxbXF7CJAhs |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Variational+autoencoder+reconstruction+of+complex+many-body+physics&rft.jtitle=arXiv.org&rft.au=Luchnikov%2C+I&rft.au=Ryzhov%2C+A&rft.au=Stas%2C+P+-J+C&rft.au=Filippov%2C+S+N&rft.date=2019-10-09&rft.pub=Cornell+University+Library%2C+arXiv.org&rft.eissn=2331-8422&rft_id=info:doi/10.48550%2Farxiv.1910.03957 |