[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120770-en":3,"doc-seo-120770-105":30,"detail-sidebar-cat-0-en-105":92},{"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":20,"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},120770,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories - Perspective Overview","Machine-learning methods for diffusive time series aim to infer the stochastic mechanism behind measured single-particle trajectories and to identify diffusion types and system parameters. The perspective reviews recently introduced approaches, highlighting uncertainty estimates and feature-based strategies that improve interpretability and reveal what the learning process captures. It also discusses performance on out-of-distribution data and outlines expected future developments for analyzing anomalous diffusion from single-particle tracking.","Machine-Learning Solutions for the Analysis of Single-Particle Di􀀛usion Trajectories  \narXiv :2308 .09414v1 [ cond-mat .stat-mech] 18 Aug 2023  \nHenrik Seckler, 1 Janusz Szwabiński,2 and Ralf Metzler 1, 3, 􀀃  \n1 Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany  \n2 Hugo Steinhaus Center, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland  \n3 Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea (Dated: August 21, 2023)  \nSingle-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics is vital in understanding the observed systems. Typically, the task is to decipher the exact type of diffusion and/or to determine system parameters. The tools used in this endeavor are currently revolutionized by modern machine-learning techniques. In this Perspective we provide an overview over recently introduced methods in machine-learning for diffusive time series, most notably, those successfully competing in the Anomalous-DiffusionChallenge. As such methods are often criticized for their lack of interpretability, we focus on means to include uncertainty estimates and feature-based approaches, both improving interpretability and providing concrete insight into the learning process of the machine. We expand the discussion by examining predictions on different out-of-distribution data. We also comment on expected future developments.  \nSingle Particle Tracking (SPT) refers to the observation of the microscopic motion of molecules. In 1828 Robert Brown used SPT to observe the movement of granular particles, laying the foundations of Brownian Motion [1] . After advancements in theory spearheaded by Einstein, Smoluchowski, Sutherland, and Langevin, Jean Perrin was able to give a first estimate of Avogadro’s number by observing particle motion in a colloid [2] . While SPT applies mainly to observing the movement of molecules or micron-sized tracer particles [3–15], similar SPT data are also garnered in systems ranging from the movement of animals [16–18] to eye movement [19, 20] or stock dynamics [21, 22] . Understanding such trajectories and developing techniques for their analysis is thereby of vital importance in a multitude of different fields [9, 16 , 17 , 21 , 23–26] . Mathematically such a motion is described by a random walk as introduced by Karl Pearson [27] . Here the position xi of a particle at time ti is obtained via a sequence of random steps 􀀁xi (i = 1 , ..., T − 1), such that xn = x0 + P 􀀁xi (n = 0 , ..., T − 1) . In the simplest case called \"Wiener process\", whose steps 􀀁xi are independent and identically distributed according to (2πσ2 )􀀀1/2 exp 􀀀−􀀁x2i/[2σ2]􀀁 with constant waiting time ti −ti􀀀1 = 􀀁t, will lead to a Gaussian probability density function (PDF)  \nf (x, t) = √41πK1t exp 􀀒 − 4xK21t 􀀓 , (1)  \nwhere K1 = σ 2 /􀀁t. Due to the action of the Central Limit Theorem, the same PDF is reached as long as the increments are independent and identically distributed with finite variance and finite mean waiting time [28, 29] .  \n􀀃 Electronic address: [rmetzler@uni-potsdam.de](rmetzler@uni-potsdam.de)  \nIn particular this entails a linear growth of the mean squared displacement (MSD) [30–32]  \nhx2 (t)i ∼ 2K1t. (2)  \nThis type of behavior is referred to as normal diffusion, the most well-known example being the aforementioned Brownian Motion as described by Einstein, Smoluchowski, Sutherland and Langevin when analyzing the motion of small particles suspended in liquids or gases [33–36] .  \nIn practice however one often observes a non-Gaussian probability density function and/or an MSD that grows non-linearly in time [5–8, 37–48] . Here we focus on the frequent case of power-law growth of the MSD,  \nhx2 (t)i ∼ 2K􀀋 t􀀋 , (3)  \nreferred to","cbCaidnoMlFulawZ","https://ap.wps.com/l/cbCaidnoMlFulawZ","pdf",1006572,1,25,"English","en",105,"# Introduction\n## Single Particle Tracking and Diffusion Models\n## Normal vs Anomalous Diffusion\n# Machine Learning Perspectives on Diffusive Time Series\n## Uncertainty Estimates and Feature-Based Approaches\n## Out-of-Distribution Predictions and Future Outlook","[{\"question\":\"What problem does the document address in analyzing diffusion trajectories?\",\"answer\":\"It addresses deciphering the stochastic mechanism behind recorded diffusive dynamics, including identifying the diffusion type and estimating system parameters from time series.\"},{\"question\":\"How does the document distinguish normal diffusion from anomalous diffusion?\",\"answer\":\"Normal diffusion exhibits Gaussian statistics and linear growth of the mean squared displacement, while anomalous diffusion shows non-Gaussian behavior and nonlinear MSD growth characterized by an exponent.\"},{\"question\":\"Why does the document emphasize interpretability in machine-learning approaches?\",\"answer\":\"Many machine-learning methods are criticized for limited interpretability, so the document focuses on uncertainty estimates and feature-based approaches to make learning outcomes more understandable.\"}]","Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories - 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