{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T00:57:08Z","timestamp":1782176228752,"version":"3.54.5"},"reference-count":51,"publisher":"IOP Publishing","issue":"1","license":[{"start":{"date-parts":[[2025,2,4]],"date-time":"2025-02-04T00:00:00Z","timestamp":1738627200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,2,4]],"date-time":"2025-02-04T00:00:00Z","timestamp":1738627200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2025,3,31]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems and the absence of time-invariance. The nonequilibrium properties of many-body systems can be described by the dynamics of the correlator, or the Green\u2019s function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff\u2013Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time numerical simulation. In this paper, we develop an operator-learning framework based on recurrent neural networks (RNNs) to address this challenge. We utilize RNNs to learn the nonlinear mapping between Green\u2019s functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green\u2019s functions. Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                           <mml:mi>O<\/mml:mi>\n                           <mml:mo stretchy=\"false\">(<\/mml:mo>\n                           <mml:msubsup>\n                              <mml:mi>N<\/mml:mi>\n                              <mml:mi>t<\/mml:mi>\n                              <mml:mn>3<\/mml:mn>\n                           <\/mml:msubsup>\n                           <mml:mo stretchy=\"false\">)<\/mml:mo>\n                        <\/mml:mrow>\n                     <\/mml:math>\n                  <\/jats:inline-formula> to <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                           <mml:mi>O<\/mml:mi>\n                           <mml:mo stretchy=\"false\">(<\/mml:mo>\n                           <mml:msub>\n                              <mml:mi>N<\/mml:mi>\n                              <mml:mi>t<\/mml:mi>\n                           <\/mml:msub>\n                           <mml:mo stretchy=\"false\">)<\/mml:mo>\n                        <\/mml:mrow>\n                     <\/mml:math>\n                  <\/jats:inline-formula> where <jats:italic>N<jats:sub>t<\/jats:sub>\n                  <\/jats:italic> is the number of steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through various numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.<\/jats:p>","DOI":"10.1088\/2632-2153\/ada99d","type":"journal-article","created":{"date-parts":[[2025,1,17]],"date-time":"2025-01-17T11:39:58Z","timestamp":1737113998000},"page":"015027","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Predicting nonequilibrium Green\u2019s function dynamics and photoemission spectra via nonlinear integral operator learning"],"prefix":"10.1088","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6851-4161","authenticated-orcid":true,"given":"Yuanran","family":"Zhu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jia","family":"Yin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cian C","family":"Reeves","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7172-7539","authenticated-orcid":true,"given":"Chao","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2836-7619","authenticated-orcid":true,"given":"Vojt\u011bch","family":"Vl\u010dek","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2025,2,4]]},"reference":[{"key":"mlstada99dbib1","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1103\/RevModPhys.81.163","article-title":"Attosecond physics","volume":"81","author":"Krausz","year":"2009","journal-title":"Rev. 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Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2024-10-18","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-01-13","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-02-04","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}