[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119705-en":3,"doc-seo-119705-105":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},119705,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253",8,"Research & Report","Optimal Active Particle Navigation meets Machine Learning","Active agents such as insects, microorganisms, and future colloidal robots must steer efficiently to reach or discover targets in complex environments, including odor sources, food, or cancer cells. The work reviews optimal navigation problems from microscale to macroscale and highlights emerging approaches that use machine learning to uncover highly efficient strategies. It emphasizes that learning can solve challenging settings with chaotic, high-dimensional, or unknown environments where analytical or simulation-based methods struggle.","epl draft  \nOptimal Active Particle Navigation meets Machine Learning  \nMahdi Nasiri 1 , Hartmut Lwen2 and Benno Liebchen 1 (a)  \n1 Institute of Condensed Matter Physics, Technische Universit􀁿at Darmstadt - D-64289 Darmstadt, Germany  \n2 Institut f􀁿ur Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universit􀁿at D􀁿usseldorf, D-40225 D􀁿usseldorf, Germany  \n-mat .soft] 9 Mar 2023  \nPACS 82 .70 .Dd { Colloids  \nPACS 05 .40 .Jc { Brownian motion  \nAbstract { The question of how \\smart\" active agents, like insects, microorganisms, or future colloidal robots need to steer to optimally reach or discover a target, such as an odor source, food, or a cancer cell in a complex environment has recently attracted great interest. Here, we provide an overview of recent developments, regarding such optimal navigation problems, from the microto the macroscale, and give a perspective by discussing some of the challenges which are ahead of us. Besides exemplifying an elementary approach to optimal navigation problems, the article focuses on works utilizing machine learning-based methods. Such learning-based approaches can uncover highly e􀀎cient navigation strategies even for problems that involve e.g. chaotic, highdimensional, or unknown environments and are hardly solvable based on conventional analytical or simulation methods.  \nIntroduction. { Before the start of an airplane, the conductor often runs a software to plan a path to a target  \nlar patterns that can even be chaotic due to turbulent air streams [6{9] .  \n[cond  \ninformation into a desired action (motion command) and sends it to an actuator, which initiates the motion. In the animal kingdom, the ability to develop e􀀎cient navigation strategies can assist the survival of species. To reach their breeding grounds, some turtles, for example, have to 􀀌nd an e􀀎cient path through the ocean over hundreds of kilometers [4, 5] . Similarly, insects need strategies to 􀀌nd odor sources by navigating through complex molecu-  \n(a) E-mail: [benno.liebchen@pkm.tu-darmstadt.de](benno.liebchen@pkm.tu-darmstadt.de)  \nSmart microswimmers { Besides macroscale agents, even microorganisms can perceive information from their environment and use it for navigation. For example, the ability of sperm cells to sense gradients in the concentration of those chemicals which are emitted by the egg cell [10,11] is crucial for the survival of many species. Similarly, bacteria possess a remarkable spectrum of biochemical sensors which allow them e.g. to measure gradients in oxygen, nutrient, or autoinducer concentration [12{14] and to use them for navigation.  \nBesides biological microswimmers, since almost two decades [15] also synthetic microswimmers have become available, and are currently studied together in the research 􀀌eld of active matter [16{35] . Synthetic microswimmers can be steered by external 􀀌elds [36{53](or even with feedback control systems [54{56]) and can react to their environment through various forms of taxis [57, 58], which may be used in the future to help them navigate through our blood vessels to detect and perhaps repair mutated cells [59, 60], transport drugs to cancer cells [61{63] or perform microsurgery [64] .  \nWhile optimal navigation problems at the macroscale have been studied for decades [65,66], based on methods such as optimal control theory and dynamic programming [67{70], and more recently reinforcement learning [71, 72], at the  \nmicroscale corresponding explorations have started only recently. Here, the smallness of the particles leads to various new challenges: (i) Microswimmers are subject to signi􀀌cant 􀀍uctuations due to Brownian motion (or errors and delays in the steering protocol), hence they cannot accurately predict the outcome of their navigational maneuvers. (ii) Microswimmers interact hydrodynamically with walls, obstacles, and other microswimmers, which can qualitatively change the required navigation strategy to reach a target fastest [73] . (iii) The displace","cbCairlxFsgXUDeE","https://ap.wps.com/l/cbCairlxFsgXUDeE","pdf",3405855,1,7,"English","en",105,"# Abstract\n# Introduction\n# Smart microswimmers\n# Optimal point-to-point navigation\n# Elementary calculation of exact optimal trajectories","[{\"question\":\"What navigation problem does the document focus on?\",\"answer\":\"It focuses on how active agents steer optimally to reach or discover targets fastest or most efficiently in complex environments.\"},{\"question\":\"How does machine learning contribute to solving optimal navigation?\",\"answer\":\"Machine learning-based methods can reveal highly efficient navigation strategies even for chaotic, high-dimensional, or unknown environments where conventional analytical or simulation methods are difficult.\"},{\"question\":\"Why are navigation challenges at the microscale different from the macroscale?\",\"answer\":\"Microswimmers face significant fluctuations from Brownian motion, complex hydrodynamic interactions, environment-driven displacement that can exceed self-propulsion speed, and limited local information requiring transferable strategies.\"}]","Optimal Active Particle Navigation meets Machine Learning | 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navigation problem does the document focus on?","Question",{"text":75,"@type":76},"It focuses on how active agents steer optimally to reach or discover targets fastest or most efficiently in complex environments.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does machine learning contribute to solving optimal navigation?",{"text":80,"@type":76},"Machine learning-based methods can reveal highly efficient navigation strategies even for chaotic, high-dimensional, or unknown environments where conventional analytical or simulation methods are difficult.",{"name":82,"@type":73,"acceptedAnswer":83},"Why are navigation challenges at the microscale different from the macroscale?",{"text":84,"@type":76},"Microswimmers face significant fluctuations from Brownian motion, complex hydrodynamic interactions, environment-driven displacement that can exceed self-propulsion speed, and limited local information requiring transferable 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