{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/learning-thermodynamics-with-boltzmann","title":"Learning Thermodynamics with Boltzmann Machines","arxiv_id":"1606.02718","date":"2016-06-08","proceeding":null,"authors":["Giacomo Torlai","Roger G. Melko"],"abstract":"A Boltzmann machine is a stochastic neural network that has been extensively\nused in the layers of deep architectures for modern machine learning\napplications. In this paper, we develop a Boltzmann machine that is capable of\nmodelling thermodynamic observables for physical systems in thermal\nequilibrium. Through unsupervised learning, we train the Boltzmann machine on\ndata sets constructed with spin configurations importance-sampled from the\npartition function of an Ising Hamiltonian at different temperatures using\nMonte Carlo (MC) methods. The trained Boltzmann machine is then used to\ngenerate spin states, for which we compare thermodynamic observables to those\ncomputed by direct MC sampling. We demonstrate that the Boltzmann machine can\nfaithfully reproduce the observables of the physical system. Further, we\nobserve that the number of neurons required to obtain accurate results\nincreases as the system is brought close to criticality.","url_abs":"http://arxiv.org/abs/1606.02718v1","url_pdf":"http://arxiv.org/pdf/1606.02718v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"learning-thermodynamics-with-boltzmann","repo_url":"https://github.com/loppy1243/IsingBoltzmann","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1606.02718","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}