Foundations of data science (Springfield, Mo.)最新文献

{"title":"HETEROGENEOUS PERIDYNAMIC NEURAL OPERATORS: DISCOVER BIOTISSUE CONSTITUTIVE LAW AND MICROSTRUCTURE FROM DIGITAL IMAGE CORRELATION MEASUREMENTS.","authors":"Siavash Jafarzadeh, Stewart Silling, Lu Zhang, Colton Ross, Chung-Hao Lee, S M Rakibur Rahman, Shuodao Wang, Yue Yu","doi":"10.3934/fods.2024041","DOIUrl":"10.3934/fods.2024041","url":null,"abstract":"<p><p>Human tissues are highly organized structures with specific collagen fiber arrangements varying from point to point. The effects of such heterogeneity play an important role for tissue function, and hence it is of critical to discover and understand the distribution of such fiber orientations from experimental measurements, such as the digital image correlation data. To this end, we introduce the heterogeneous peridynamic neural operator (HeteroPNO) approach, for data-driven constitutive modeling of heterogeneous anisotropic materials. The goal is to learn both a nonlocal constitutive law together with the material microstructure, in the form of a heterogeneous fiber orientation field, from loading field-displacement field measurements. To this end, we propose a two-phase learning approach. Firstly, we learn a homogeneous constitutive law in the form of a neural network-based kernel function and a nonlocal bond force, to capture complex homogeneous material responses from data. Then, in the second phase we reinitialize the learnt bond force and the kernel function, and training them together with a fiber orientation field for each material point. Owing to the state-based peridynamic skeleton, our HeteroPNO-learned material models are objective and have the balance of linear and angular momentum guaranteed. Moreover, the effects from heterogeneity and nonlinear constitutive relationship are captured by the kernel function and the bond force respectively, enabling physical interpretability. As a result, our HeteroPNO architecture can learn a constitutive model for a biological tissue with anisotropic heterogeneous response undergoing large deformation regime. The anisotropy and heterogeneity of this tissue stems from collagen fibers with unknown natural orientation, resulting in a location-dependent anisotropy. To demonstrate the applicability of our approach, we apply the heterogeneous PNO in learning the material model and fiber orientation field from digital image correction (DIC) data containing the planar displacement field on the tissue and the reaction forces in a biaxial testing. We find the learnt fiber architecture consistent with observations from polarized spatial frequency domain imaging. Moreover, the framework is capable to provide displacement and stress field predictions for new and unseen loading instances.</p>","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"7 1","pages":"226-270"},"PeriodicalIF":1.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12245156/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144627886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"CHATGPT FOR COMPUTATIONAL TOPOLOGY.","authors":"Jian Liu, Li Shen, Guo-Wei Wei","doi":"10.3934/fods.2024009","DOIUrl":"10.3934/fods.2024009","url":null,"abstract":"<p><p>ChatGPT represents a significant milestone in the field of artificial intelligence (AI), finding widespread applications across diverse domains. However, its effectiveness in mathematical contexts has been somewhat constrained by its susceptibility to conceptual errors. Concurrently, topological data analysis (TDA), a relatively new discipline, has garnered substantial interest in recent years. Nonetheless, the advancement of TDA is impeded by the limited understanding of computational algorithms and coding proficiency among theoreticians. This work endeavors to bridge the gap between theoretical topological concepts and their practical implementation in computational topology through the utilization of ChatGPT. We showcase how a pure theoretician, devoid of computational experience and coding skills, can effectively transform mathematical formulations and concepts into functional codes for computational topology with the assistance of ChatGPT. Our strategy outlines a productive process wherein a mathematician trains ChatGPT on pure mathematical concepts, steers ChatGPT towards generating computational topology codes, and subsequently validates the generated codes using established examples. Our specific case studies encompass the computation of Betti numbers, Laplacian matrices, and Dirac matrices for simplicial complexes, as well as the persistence of various homologies and Laplacians. Furthermore, we explore the application of ChatGPT in computing recently developed topological theories for hypergraphs and digraphs, as well as the persistent harmonic space, which has not been computed in the literature, to the best of our knowledge. This work serves as an initial step towards effectively transforming pure mathematical theories into practical computational tools, with the ultimate goal of enabling real applications across diverse fields.</p>","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"6 2","pages":"221-250"},"PeriodicalIF":1.7,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11463974/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142395644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"PERSISTENT DIRAC OF PATHS ON DIGRAPHS AND HYPERGRAPHS.","authors":"Faisal Suwayyid, Guo-Wei Wei","doi":"10.3934/fods.2024001","DOIUrl":"10.3934/fods.2024001","url":null,"abstract":"<p><p>This work introduces the development of path Dirac and hypergraph Dirac operators, along with an exploration of their persistence. These operators excel in distinguishing between harmonic and non-harmonic spectra, offering valuable insights into the subcomplexes within these structures. The paper showcases the functionality of these operators through a series of examples in various contexts. An essential facet of this research involves examining the operators' sensitivity to filtration, emphasizing their capacity to adapt to topological changes. The paper also explores a significant application of persistent path Dirac and persistent hypergraph Dirac in molecular science, specifically in analyzing molecular structures. The study introduces strict preorders derived from molecular structures, which generate graphs and digraphs with intricate path structures. The depth of information within these path complexes reflects the complexity of different preorder classes influenced by molecular structures. This characteristic underscores the effectiveness of these tools in the realm of topological data analysis.</p>","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"6 2","pages":"124-153"},"PeriodicalIF":1.7,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11620167/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142788024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"PERSISTENT PATH LAPLACIAN.","authors":"Rui Wang,&nbsp;Guo-Wei Wei","doi":"10.3934/fods.2022015","DOIUrl":"https://doi.org/10.3934/fods.2022015","url":null,"abstract":"<p><p>Path homology proposed by S.-T.Yau and his co-workers provides a new mathematical model for directed graphs and networks. Persistent path homology (PPH) extends the path homology with filtration to deal with asymmetry structures. However, PPH is constrained to purely topological persistence and cannot track the homotopic shape evolution of data during filtration. To overcome the limitation of PPH, persistent path Laplacian (PPL) is introduced to capture the shape evolution of data. PPL's harmonic spectra fully recover PPH's topological persistence and its non-harmonic spectra reveal the homotopic shape evolution of data during filtration.</p>","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"5 1","pages":"26-55"},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10575407/pdf/nihms-1888540.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41241769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Diagnostic of the Lévy area for geophysical flow models in view of defining high order stochastic discrete-time schemes","authors":"Pierre-Marie Boulvard, Etienne Mémin","doi":"10.3934/fods.2023011","DOIUrl":"https://doi.org/10.3934/fods.2023011","url":null,"abstract":"In this paper we characterize numerically through two criteria the Lévy area related to unresolved fluctuation velocities associated to a stochastic coarse-scale representation of geophysical fluid flow dynamics. We study in particular whether or not the process associated to the random unresolved velocity components exhibits a Lévy area corresponding to a Wiener process, and if the law of this process can reasonably be approached by a centered Dirac measure. This exploration enables us to answer positively to a conjecture made for the constitution of high-order discrete time evolution schemes for stochastic representation defined from stochastic transport.","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136306282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hierarchical regularization networks for sparsification based learning on noisy datasets","authors":"P. Shekhar, M. Babu, Abani Patra","doi":"10.3934/fods.2023009","DOIUrl":"https://doi.org/10.3934/fods.2023009","url":null,"abstract":"","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70248298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Persistent hyperdigraph homology and persistent hyperdigraph Laplacians","authors":"Dong Chen, Jian Liu, Jie Wu, Guo-Wei Wei","doi":"10.3934/fods.2023010","DOIUrl":"https://doi.org/10.3934/fods.2023010","url":null,"abstract":"Hypergraphs are useful mathematical models for describing complex relationships among members of a structured graph, while hyperdigraphs serve as a generalization that can encode asymmetric relationships in the data. However, obtaining topological information directly from hyperdigraphs remains a challenge. To address this issue, we introduce hyperdigraph homology in this work. We also propose topological hyperdigraph Laplacians, which can extract both harmonic spectra and non-harmonic spectra from directed and internally organized data. Moreover, we introduce persistent hyperdigraph homology and persistent hyperdigraph Laplacians through filtration, enabling the capture of topological persistence and homotopic shape evolution of directed and structured data across multiple scales. The proposed methods offer new multiscale algebraic topology tools for topological data analysis.","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136053367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Unsupervised learning of observation functions in state space models by nonparametric moment methods","authors":"Qingci An, Yannis Kevrekidis, Fei Lu, Mauro Maggioni","doi":"10.3934/fods.2023002","DOIUrl":"https://doi.org/10.3934/fods.2023002","url":null,"abstract":"We investigate the unsupervised learning of non-invertible observation functions in nonlinear state space models. Assuming abundant data of the observation process along with the distribution of the state process, we introduce a nonparametric generalized moment method to estimate the observation function via constrained regression. The major challenge comes from the non-invertibility of the observation function and the lack of data pairs between the state and observation. We address the fundamental issue of identifiability from quadratic loss functionals and show that the function space of identifiability is the closure of a RKHS that is intrinsic to the state process. Numerical results show that the first two moments and temporal correlations, along with upper and lower bounds, can identify functions ranging from piecewise polynomials to smooth functions, leading to convergent estimators. The limitations of this method, such as non-identifiability due to symmetry and stationarity, are also discussed.","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135534595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Noise calibration for SPDEs: A case study for the rotating shallow water model","authors":"Dan Crisan, Oana Lang, Alexander Lobbe, Peter-Jan van Leeuwen, Roland Potthast","doi":"10.3934/fods.2023012","DOIUrl":"https://doi.org/10.3934/fods.2023012","url":null,"abstract":"","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"161 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134980769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weight set decomposition for weighted rank and rating aggregation: An interpretable and visual decision support tool","authors":"Tyler A. Perini, A. Langville, Glenn Kramer, Jeff Shrager, Mark Shapiro","doi":"10.3934/fods.2023001","DOIUrl":"https://doi.org/10.3934/fods.2023001","url":null,"abstract":"","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70248223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}