[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119710-en":3,"doc-seo-119710-105":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},119710,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253",8,"Research & Report","Machine learning for discovering laws of nature - Computational model and genetic programming","A macroscopic particle obeys Newton’s law while microscopic particles follow quantum mechanics, yet the boundary between these regimes remains unresolved and is tied to the quantum measurement interpretation problem. The work argues that conventional rigorous mathematical models fail to capture natural laws in a comprehensible way and proposes an evolutionary, data-driven computational model. Entities are represented as state-value data series, and an observer learns theories via state Decision Trees and value Function Trees using only historical observations. By maximizing expected value through rewarded or punished decisions, the model rediscovers Newton’s law, the Born rule, and the efficient market hypothesis without differential equations.","Machine learning for discovering laws of nature  \nLizhi Xin1, Kevin Xin2, Houwen Xin3, *  \n1 Building 59, 96 Jinzhai Road, Hefei, Anhui, P. R. China  \n26 South Laflin Street Chicago, IL, USA  \n3 Department of Chemical physics USTC, Hefei, Anhui, P. R. China  \n*  \n [hxin@ustc.edu.cn](hxin@ustc.edu.cn)  \nABSTRACT  \nA macroscopic particle obeys Newton's law, and a microscopic particle obeys the principles of quantum mechanics-so where is the sharp boundary between the macroscopic and microscopic worlds? It was this “interpretation problem” that prompted Schrödinger to propose his famous thought experiment (a cat that is simultaneously both dead and alive) and sparked a great debate about the quantum measurement problem, and there is still no satisfactory answer yet. This is precisely the inadequacy of rigorous mathematical models in describing the laws of nature. We propose a computational model to describe and understand the laws of nature based on Darwin’s natural selection. In fact, whether it’s a macro particle, a micro electron or a security, they can all be considered as an entity, the change of this entity over time can be described by a data series composed of states and values. An observer can learn from this data series to construct theories (usually consisting of functions and differential equations) . We don’t model with the usual functions or differential equations, but with a state Decision Tree (determines the state of an entity) and a value Function Tree (determines the distance between two points of an entity) . A state Decision Tree and a value Function Tree together can reconstruct an entity's trajectory and make predictions about its future trajectory. Our proposed algorithmic model discovers laws of nature by only learning observed historical data (sequential measurement of observables) based on maximizing the observer’s expected value. There is no differential equation in our model; our model has an emphasis on machine learning, where the observer builds up his/her experience by being rewarded or punished for each decision he/she makes, and eventually leads to rediscovering Newton’s law, the Born rule (quantum mechanics) and the efficient market hypothesis (financial market) .  \nIntroduction  \n{ (0,0),(0,7), ⋯ ,(0,224),(0, 279), ⋯ ,(0, 1044),(0, 1159)} (1a)  \n{ (1, −1),(0,0), ⋯ ,(0, 1),(0,2), ⋯ ,(1, −1),(0,0)} (1b)  \n{ (0,3707),(1,3694), ⋯ ,(1, 3698),(1, 3690), ⋯ ,(1,3792),(1,3781)} (1c)  \nThe data sequences of (1a) are generated based off Newton’s equation, data sequences of (1b) are generated for Schrödinger’s cat thought experiment, and data sequences of (1c) are the observed data of rebar (contract rb1901) tradedon the Shanghai Futures Exchange.  \nA fundamental science theory usually includes three core elements: one, to describe the observed experiment data; two, to predict the future outcome; and three, to understand natural phenomena as defined by observed data. To this day, the mainstream way of discovering the laws of nature is to describe experimental observations in rigorous mathematical structure (differential equation) and use probability theory to make predictions about future outcomes. For example, Newton's differential equation for (1a); Schrödinger differential equation for (1b); Stochastic diffusion differential equation for (1c) . However, without the collapse postulate of quantum mechanics, it is difficult for Schrödinger’s equation alone to interpret the quantum measurement, and without the rational-economic person postulate it’s difficult for the stochastic differential equation alone to interpret the efficient market hypothesis. The main issue with rigorous mathematical models is that they are difficult to understand, and is not easy to calculate theoretical values to compare with actual observed results when the mathematical model becomes more complex.  \nIn 2001, Leo Breiman [1] claimed that:  \n“There are two cultures in the use of statistical modeling to reach conclusions from data. ","cbCaipvOhEAdJ3gA","https://ap.wps.com/l/cbCaipvOhEAdJ3gA","pdf",1116297,1,12,"English","en",105,"# Introduction\n## Machine learning algorithm\n## Discussion of natural law modeling\n# References","[{\"question\":\"How does the proposed model represent an entity and its evolution over time?\",\"answer\":\"An entity is encoded as a data series of states and values over time. A state Decision Tree determines the entity’s state, while a value Function Tree determines distances between points, enabling reconstruction of trajectories.\"},{\"question\":\"What problem does the paper claim traditional mathematical modeling struggles with?\",\"answer\":\"As models become more complex, they are difficult to understand and harder to calculate theoretical values for direct comparison with observed results. The paper also highlights interpretation difficulties in quantum measurement and in applying assumptions to financial-market modeling.\"},{\"question\":\"How does the model discover laws of nature without using differential equations?\",\"answer\":\"It learns from observed historical data using evolutionary algorithms and genetic programming, with machine-learning-style decision feedback. An observer maximizes expected value through being rewarded or punished for each decision, leading to rediscovered known laws.\"}]","Machine learning for discovering laws of nature - Computational model and genetic programming | PDF",1785725909,30,{"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},"machine-learning-for-discovering-laws-of-nature-computational-model-and-genetic-programming","",{"@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/machine-learning-for-discovering-laws-of-nature-computational-model-and-genetic-programming/119710/",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","2026-08-03",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},"How does the proposed model represent an entity and its evolution over time?","Question",{"text":75,"@type":76},"An entity is encoded as a data series of states and values over time. A state Decision Tree determines the entity’s state, while a value Function Tree determines distances between points, enabling reconstruction of trajectories.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What problem does the paper claim traditional mathematical modeling struggles with?",{"text":80,"@type":76},"As models become more complex, they are difficult to understand and harder to calculate theoretical values for direct comparison with observed results. The paper also highlights interpretation difficulties in quantum measurement and in applying assumptions to financial-market modeling.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the model discover laws of nature without using differential equations?",{"text":84,"@type":76},"It learns from observed historical data using evolutionary algorithms and genetic programming, with machine-learning-style decision feedback. 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