[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125110-en":3,"doc-seo-125110-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},125110,687197207639,"Asher","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Modeling Dynamics of Classical and Quantum Systems Using Machine Learning Techniques - Dissertation","This dissertation investigates the dynamics of many-body systems in both quantum and classical settings, centering on order parameters that characterize whether a system is in an ordered phase. Using interpretable, physically consistent machine learning methods, it builds a framework for local and macroscopic degrees of freedom. For quantum systems, it learns a dynamical generator that evolves few-body observables while preserving key physical quantities like probabilistic interpretation, validated under full state access and under projective-measurement data with projection noise. For classical binary-spin systems, it models order-parameter dynamics via Itô stochastic differential equations, learning drift and diffusion with neural networks to extract critical properties.","Modeling Dynamics of Classical and Quantum Systems Using Machine Learning Techniques  \nDissertation  \nder Mathematisch-Naturwissenschaftlichen Fakultt der Eberhard Karls Universitt Tbingen zur Erlangung des Grades eines  \nDoktors der Naturwissenschaften  \n(Dr. rer. nat.)  \nvorgelegt von  \nFrancesco Carnazza  \naus Lecco, Italien  \nTbingen  \nGedruckt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakultt der Eberhard Karls Universitt Tbingen.  \nTag der mndlichen Qualifikation: 6.12.2024  \nDekan: Prof. Dr. Thilo Stehle  \n1. Berichterstatter: Prof. Dr. Igor Lesanovsky  \n2. Berichterstatterin: Prof. Dr. Sabine Andergassen  \n3. Berichterstatter: Prof. Dr. Martin Oettel  \nSummary  \nIn this thesis, we examine the dynamics of many-body systems within both quantum and classical contexts. When dealing with many-body systems, the focus is typically on what are known as order parameters. These parameters indicate whether the physical system is in an ordered phase or not. Order parameters often correspond to the expectation values of local observables, or to the averages of the microscopic degrees of freedom within the system’s configuration. Specifically, we leverage machine learning methodologies to develop an interpretable and physically consistent theoretical framework for describing local and macroscopic degrees of freedom within both quantum and classical contexts. In the case of quantum system, we develop a method that is able to approximate a “dynamical generator,” that is, an operator which is able to evolve in time few body observables of the system. In particular, this generator preserves some important physical quantities of the state representing the system under investigation, such as its probabilistic interpretation. We explore the capabilities of this method in our first and second scientific paper. In the first work, we provide full access to the dynamics through the coherence vector, a representation of the quantum state. In our second work, more akin to actual experimental conditions, we supply the variational method with data obtained via state tomography through projective measurements, a routine approach in retrieving the state of quantum devices using qubits. Here, we further develop the methods used in our fist work to address the problem of learning the dynamical generator in the presence of projection noise. Given that projective measurements introduce noise into the dynamics, we naturally consider how to represent physical noise in a machine learning routine. To better understand how noise could be managed by a machine learning routine, we studied the reduced degrees of freedom of classical systems composed of many ”binary”spin degrees of freedom whose evolution is probabilistic in our third scientific paper. Average quantities of these spin variables are inherently stochastic. By taking the expectation values over numerous stochastic trajectories, order parameters emerge. Specifically, we model the dynamics of this order parameter using a stochastic di!erential equation of It type. Such equations are first-order di!erential equations in time that include a directed force term, known asthe “drift coe”cient,” and a noisy force term called the “di!usion coe”cient.” We con-  \ncentrate on encoding the di!usion term and the drift term of this stochastic di!erential equation into two separate neural networks. This method proves robust in reproducing the dynamics and allows us to extract valuable information about the system, such asthe critical point and the critical exponent.  \nZusammenfassung  \nIn dieser Arbeit untersuchen wir die Dynamik von Vielkrpersystemen sowohlim quantenmechanischen als auch im klassischen Kontext. Bei der Betrachtung von Vielkrpersystemen liegt der Fokus typischerweise auf sogenannten Ordnungsparametern. Diese Parameter zeigen an, ob sich das physikalische System in einer geordneten Phase befindet oder nicht. Ordnungsparameter entsprechen oft den Erwartungswerten lokaler Observablenoderden Mitte","cbCaikW3npbFIs1n","https://ap.wps.com/l/cbCaikW3npbFIs1n","pdf",31312622,1,126,"English","en",105,"# Summary\n## Quantum systems and dynamical generators\n## Projection noise and learning from tomography data\n## Classical binary-spin systems and stochastic dynamics\n## Neural network encoding of drift and diffusion terms","[{\"question\":\"What is the main goal of the dissertation’s machine learning approach?\",\"answer\":\"To develop an interpretable and physically consistent framework that describes local and macroscopic degrees of freedom in both quantum and classical many-body systems using machine learning.\"},{\"question\":\"How does the method for quantum systems work?\",\"answer\":\"It learns a “dynamical generator” that approximates an operator evolving in time few-body observables, while preserving important physical quantities of the state, such as its probabilistic interpretation.\"},{\"question\":\"How is noise handled across the different system settings?\",\"answer\":\"For quantum systems, the learning problem is addressed in the presence of projection noise introduced by projective measurements. For classical binary-spin dynamics, the order-parameter evolution is modeled using an Itô stochastic differential equation, where noise is represented through the diffusion term learned by neural networks.\"}]","Modeling Dynamics of Classical and Quantum Systems Using Machine Learning Techniques - Dissertation | PDF",1785896697,318,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"modeling-dynamics-of-classical-and-quantum-systems-using-machine-learning-techniques-dissertation","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/modeling-dynamics-of-classical-and-quantum-systems-using-machine-learning-techniques-dissertation/125110/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is the main goal of the dissertation’s machine learning approach?","Question",{"text":75,"@type":76},"To develop an interpretable and physically consistent framework that describes local and macroscopic degrees of freedom in both quantum and classical many-body systems using machine learning.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the method for quantum systems work?",{"text":80,"@type":76},"It learns a “dynamical generator” that approximates an operator evolving in time few-body observables, while preserving important physical quantities of the state, such as its probabilistic interpretation.",{"name":82,"@type":73,"acceptedAnswer":83},"How is noise handled across the different system settings?",{"text":84,"@type":76},"For quantum systems, the learning problem is addressed in the presence of projection noise introduced by projective measurements. For classical binary-spin dynamics, the order-parameter evolution is modeled using an Itô stochastic differential equation, where noise is represented through the diffusion term learned by neural networks.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]