Chew, Joyce; Hirn, Matthew; Krishnaswamy, Smita; Needell, Deanna; Perlmutter, Michael; Steach, Holly; Viswanath, Siddharth; Wu, Hau-Tieng Geometric scattering on measure spaces. (English) Zbl 07811907 Appl. Comput. Harmon. Anal. 70, Article ID 101635, 41 p. (2024). MSC: 68-XX 92-XX PDFBibTeX XMLCite \textit{J. Chew} et al., Appl. Comput. Harmon. Anal. 70, Article ID 101635, 41 p. (2024; Zbl 07811907) Full Text: DOI arXiv
Barroso, M.; Alaíz, C. M.; Torrecilla, J. L.; Fernández, A. Functional diffusion maps. (English) Zbl 07800659 Stat. Comput. 34, No. 1, Paper No. 22, 16 p. (2024). MSC: 62-08 62R10 PDFBibTeX XMLCite \textit{M. Barroso} et al., Stat. Comput. 34, No. 1, Paper No. 22, 16 p. (2024; Zbl 07800659) Full Text: DOI arXiv OA License
Martin-Linares, Cristina P.; Psarellis, Yorgos M.; Karapetsas, George; Koronaki, Eleni D.; Kevrekidis, Ioannis G. Physics-agnostic and physics-infused machine learning for thin films flows: modelling, and predictions from small data. (English) Zbl 07774980 J. Fluid Mech. 975, Paper No. A41, 22 p. (2023). MSC: 76M99 76A20 68T05 PDFBibTeX XMLCite \textit{C. P. Martin-Linares} et al., J. Fluid Mech. 975, Paper No. A41, 22 p. (2023; Zbl 07774980) Full Text: DOI arXiv OA License
Perlmutter, Michael; Tong, Alexander; Gao, Feng; Wolf, Guy; Hirn, Matthew Understanding graph neural networks with generalized geometric scattering transforms. (English) Zbl 07768237 SIAM J. Math. Data Sci. 5, No. 4, 873-898 (2023). MSC: 68R10 68T07 05C62 05C81 42C15 42C40 PDFBibTeX XMLCite \textit{M. Perlmutter} et al., SIAM J. Math. Data Sci. 5, No. 4, 873--898 (2023; Zbl 07768237) Full Text: DOI arXiv
Owens, Katherine; Kutz, J. Nathan Data-driven discovery of governing equations for coarse-grained heterogeneous network dynamics. (English) Zbl 1528.37069 SIAM J. Appl. Dyn. Syst. 22, No. 3, 2601-2623 (2023). MSC: 37M05 34C26 34C15 37N25 PDFBibTeX XMLCite \textit{K. Owens} and \textit{J. N. Kutz}, SIAM J. Appl. Dyn. Syst. 22, No. 3, 2601--2623 (2023; Zbl 1528.37069) Full Text: DOI arXiv
Landa, Boris; Cheng, Xiuyuan Robust inference of manifold density and geometry by doubly stochastic scaling. (English) Zbl 07732334 SIAM J. Math. Data Sci. 5, No. 3, 589-614 (2023). MSC: 62R07 62Gxx PDFBibTeX XMLCite \textit{B. Landa} and \textit{X. Cheng}, SIAM J. Math. Data Sci. 5, No. 3, 589--614 (2023; Zbl 07732334) Full Text: DOI arXiv
Hummel, Felix; Ashwin, Peter; Kuehn, Christian Reduction methods in climate dynamics – a brief review. (English) Zbl 1509.86001 Physica D 448, Article ID 133678, 25 p. (2023). MSC: 86-08 86A08 86-10 PDFBibTeX XMLCite \textit{F. Hummel} et al., Physica D 448, Article ID 133678, 25 p. (2023; Zbl 1509.86001) Full Text: DOI arXiv
Patsatzis, Dimitrios G.; Russo, Lucia; Kevrekidis, Ioannis G.; Siettos, Constantinos Data-driven control of agent-based models: an equation/variable-free machine learning approach. (English) Zbl 07660326 J. Comput. Phys. 478, Article ID 111953, 25 p. (2023). MSC: 68Txx 93Cxx 65-XX PDFBibTeX XMLCite \textit{D. G. Patsatzis} et al., J. Comput. Phys. 478, Article ID 111953, 25 p. (2023; Zbl 07660326) Full Text: DOI arXiv
Gao, Yuan; Liu, Jian-Guo; Wu, Nan Data-driven efficient solvers for Langevin dynamics on manifold in high dimensions. (English) Zbl 1509.82098 Appl. Comput. Harmon. Anal. 62, 261-309 (2023). MSC: 82C31 82C41 37M21 37M05 65C30 60J05 35Q84 65M08 65M06 65N08 80M12 80M20 PDFBibTeX XMLCite \textit{Y. Gao} et al., Appl. Comput. Harmon. Anal. 62, 261--309 (2023; Zbl 1509.82098) Full Text: DOI arXiv
dos Santos, Ketson R. M.; Giovanis, Dimitris G.; Kontolati, Katiana; Loukrezis, Dimitrios; Shields, Michael D. Grassmannian diffusion maps based surrogate modeling via geometric harmonics. (English) Zbl 07768041 Int. J. Numer. Methods Eng. 123, No. 15, 3507-3529 (2022). MSC: 62Hxx 65Cxx PDFBibTeX XMLCite \textit{K. R. M. dos Santos} et al., Int. J. Numer. Methods Eng. 123, No. 15, 3507--3529 (2022; Zbl 07768041) Full Text: DOI arXiv OA License
Craig, Katy; Garciatrillos, Nicolas; Slepčev, Dejan Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation. (English) Zbl 07625088 Bellomo, Nicola (ed.) et al., Active particles. Volume 3. Advances in theory, models, and applications. Cham: Birkhäuser. Model. Simul. Sci. Eng. Technol., 105-151 (2022). MSC: 65Mxx 65Nxx 05Cxx PDFBibTeX XMLCite \textit{K. Craig} et al., in: Active particles. Volume 3. Advances in theory, models, and applications. Cham: Birkhäuser. 105--151 (2022; Zbl 07625088) Full Text: DOI arXiv
Rahman, Atta Ur; Javed, Muhammad; Ji, ZhaoXu; Ullah, Arif Probing multipartite entanglement, coherence and quantum information preservation under classical Ornstein-Uhlenbeck noise. (English) Zbl 1499.81018 J. Phys. A, Math. Theor. 55, No. 2, Article ID 025305, 27 p. (2022). MSC: 81P40 81P45 81P68 PDFBibTeX XMLCite \textit{A. U. Rahman} et al., J. Phys. A, Math. Theor. 55, No. 2, Article ID 025305, 27 p. (2022; Zbl 1499.81018) Full Text: DOI arXiv
Galaris, Evangelos; Fabiani, Gianluca; Gallos, Ioannis; Kevrekidis, Ioannis; Siettos, Constantinos Numerical bifurcation analysis of PDEs from lattice Boltzmann model simulations: a parsimonious machine learning approach. (English) Zbl 1490.65184 J. Sci. Comput. 92, No. 2, Paper No. 34, 30 p. (2022). MSC: 65M32 35R30 68T05 76M28 PDFBibTeX XMLCite \textit{E. Galaris} et al., J. Sci. Comput. 92, No. 2, Paper No. 34, 30 p. (2022; Zbl 1490.65184) Full Text: DOI arXiv
Brunton, Steven L.; Budišić, Marko; Kaiser, Eurika; Kutz, J. Nathan Modern Koopman theory for dynamical systems. (English) Zbl 1497.37105 SIAM Rev. 64, No. 2, 229-340 (2022). MSC: 37M99 37C10 37N35 47A35 47B33 34A34 PDFBibTeX XMLCite \textit{S. L. Brunton} et al., SIAM Rev. 64, No. 2, 229--340 (2022; Zbl 1497.37105) Full Text: DOI arXiv
Murphy, James M.; Polk, Sam L. A multiscale environment for learning by diffusion. (English) Zbl 07472531 Appl. Comput. Harmon. Anal. 57, 58-100 (2022). MSC: 68-XX 62-XX PDFBibTeX XMLCite \textit{J. M. Murphy} and \textit{S. L. Polk}, Appl. Comput. Harmon. Anal. 57, 58--100 (2022; Zbl 07472531) Full Text: DOI arXiv
Coifman, Ronald R.; Goldberg, Maxim J. Some extensions of E. Stein’s work on Littlewood-Paley theory applied to symmetric diffusion semigroups. (English) Zbl 1494.47079 J. Geom. Anal. 31, No. 7, 6781-6795 (2021). MSC: 47D07 60J60 41A35 26A16 PDFBibTeX XMLCite \textit{R. R. Coifman} and \textit{M. J. Goldberg}, J. Geom. Anal. 31, No. 7, 6781--6795 (2021; Zbl 1494.47079) Full Text: DOI
Burov, Dmitry; Giannakis, Dimitrios; Manohar, Krithika; Stuart, Andrew Kernel analog forecasting: multiscale test problems. (English) Zbl 1487.60088 Multiscale Model. Simul. 19, No. 2, 1011-1040 (2021). MSC: 60G25 62M20 62H30 68T05 PDFBibTeX XMLCite \textit{D. Burov} et al., Multiscale Model. Simul. 19, No. 2, 1011--1040 (2021; Zbl 1487.60088) Full Text: DOI arXiv
Tencer, John; Potter, Kevin A tailored convolutional neural network for nonlinear manifold learning of computational physics data using unstructured spatial discretizations. (English) Zbl 1511.35292 SIAM J. Sci. Comput. 43, No. 4, A2581-A2613 (2021). MSC: 35Q35 35Q68 35Q74 35Q79 92B20 68T07 PDFBibTeX XMLCite \textit{J. Tencer} and \textit{K. Potter}, SIAM J. Sci. Comput. 43, No. 4, A2581--A2613 (2021; Zbl 1511.35292) Full Text: DOI arXiv
Chu, Bryan; Farazmand, Mohammad Data-driven prediction of multistable systems from sparse measurements. (English) Zbl 1475.37095 Chaos 31, No. 6, 063118, 15 p. (2021). MSC: 37M99 35K57 PDFBibTeX XMLCite \textit{B. Chu} and \textit{M. Farazmand}, Chaos 31, No. 6, 063118, 15 p. (2021; Zbl 1475.37095) Full Text: DOI arXiv
Landa, Boris; Coifman, Ronald R.; Kluger, Yuval Doubly stochastic normalization of the Gaussian kernel is robust to heteroskedastic noise. (English) Zbl 1468.62431 SIAM J. Math. Data Sci. 3, No. 1, 388-413 (2021). MSC: 62R07 62G35 62P10 92D20 PDFBibTeX XMLCite \textit{B. Landa} et al., SIAM J. Math. Data Sci. 3, No. 1, 388--413 (2021; Zbl 1468.62431) Full Text: DOI arXiv
Cowen, Lenore; Devkota, Kapil; Hu, Xiaozhe; Murphy, James M.; Wu, Kaiyi Diffusion state distances: multitemporal analysis, fast algorithms, and applications to biological networks. (English) Zbl 1470.60231 SIAM J. Math. Data Sci. 3, No. 1, 142-170 (2021). MSC: 60J70 92C42 62H30 62M15 65C20 68T09 PDFBibTeX XMLCite \textit{L. Cowen} et al., SIAM J. Math. Data Sci. 3, No. 1, 142--170 (2021; Zbl 1470.60231) Full Text: DOI arXiv
Bittracher, Andreas; Klus, Stefan; Hamzi, Boumediene; Koltai, Péter; Schütte, Christof Dimensionality reduction of complex metastable systems via kernel embeddings of transition manifolds. (English) Zbl 1466.37068 J. Nonlinear Sci. 31, No. 1, Paper No. 3, 41 p. (2021). MSC: 37M99 68T05 68T10 PDFBibTeX XMLCite \textit{A. Bittracher} et al., J. Nonlinear Sci. 31, No. 1, Paper No. 3, 41 p. (2021; Zbl 1466.37068) Full Text: DOI arXiv
Bramburger, Jason J.; Kutz, J. Nathan Poincaré maps for multiscale physics discovery and nonlinear Floquet theory. (English) Zbl 1493.37096 Physica D 408, Article ID 132479, 12 p. (2020). MSC: 37M21 37C75 37C25 70K20 PDFBibTeX XMLCite \textit{J. J. Bramburger} and \textit{J. N. Kutz}, Physica D 408, Article ID 132479, 12 p. (2020; Zbl 1493.37096) Full Text: DOI arXiv
AlMomani, Abd AlRahman R.; Bollt, Erik Go with the flow, on Jupiter and snow. Coherence from model-free video data without trajectories. (English) Zbl 1466.37066 J. Nonlinear Sci. 30, No. 5, 2375-2404 (2020). MSC: 37M99 37N05 54H30 65D18 94A08 PDFBibTeX XMLCite \textit{A. A. R. AlMomani} and \textit{E. Bollt}, J. Nonlinear Sci. 30, No. 5, 2375--2404 (2020; Zbl 1466.37066) Full Text: DOI arXiv
Goldberg, Maxim J.; Kim, Seonja An equivalence between the limit smoothness and the rate of convergence for a general contraction operator family. (English) Zbl 1474.42095 Abstr. Appl. Anal. 2020, Article ID 8866826, 5 p. (2020). MSC: 42B35 47D07 58J65 PDFBibTeX XMLCite \textit{M. J. Goldberg} and \textit{S. Kim}, Abstr. Appl. Anal. 2020, Article ID 8866826, 5 p. (2020; Zbl 1474.42095) Full Text: DOI
Qi, Weiwei; Shen, Zhongwei; Wang, Shirou; Yi, Yingfei Towards mesoscopic ergodic theory. (English) Zbl 1508.37023 Sci. China, Math. 63, No. 9, 1853-1876 (2020). MSC: 37A30 35Q84 35J25 37B25 60J60 PDFBibTeX XMLCite \textit{W. Qi} et al., Sci. China, Math. 63, No. 9, 1853--1876 (2020; Zbl 1508.37023) Full Text: DOI
Du, Qiang; Tian, Xiaochuan Mathematics of smoothed particle hydrodynamics: a study via nonlocal Stokes equations. (English) Zbl 1448.76112 Found. Comput. Math. 20, No. 4, 801-826 (2020). MSC: 76M28 76D07 35Q35 65N12 65N75 PDFBibTeX XMLCite \textit{Q. Du} and \textit{X. Tian}, Found. Comput. Math. 20, No. 4, 801--826 (2020; Zbl 1448.76112) Full Text: DOI arXiv
Dietrich, Felix; Kooshkbaghi, Mahdi; Bollt, Erik M.; Kevrekidis, Ioannis G. Manifold learning for organizing unstructured sets of process observations. (English) Zbl 1447.37075 Chaos 30, No. 4, 043108, 9 p. (2020). MSC: 37M99 68Q32 93B47 PDFBibTeX XMLCite \textit{F. Dietrich} et al., Chaos 30, No. 4, 043108, 9 p. (2020; Zbl 1447.37075) Full Text: DOI arXiv
Banisch, Ralf; Trstanova, Zofia; Bittracher, Andreas; Klus, Stefan; Koltai, Péter Diffusion maps tailored to arbitrary non-degenerate Itô processes. (English) Zbl 1456.60198 Appl. Comput. Harmon. Anal. 48, No. 1, 242-265 (2020). MSC: 60J60 62H11 PDFBibTeX XMLCite \textit{R. Banisch} et al., Appl. Comput. Harmon. Anal. 48, No. 1, 242--265 (2020; Zbl 1456.60198) Full Text: DOI arXiv
Shnitzer, Tal; Ben-Chen, Mirela; Guibas, Leonidas; Talmon, Ronen; Wu, Hau-Tieng Recovering hidden components in multimodal data with composite diffusion operators. (English) Zbl 1499.62463 SIAM J. Math. Data Sci. 1, No. 3, 588-616 (2019). MSC: 62R30 57M50 57R40 62M15 PDFBibTeX XMLCite \textit{T. Shnitzer} et al., SIAM J. Math. Data Sci. 1, No. 3, 588--616 (2019; Zbl 1499.62463) Full Text: DOI arXiv
Gao, Tingran; Kovalsky, Shahar Z.; Boyer, Doug M.; Daubechies, Ingrid Gaussian process landmarking for three-dimensional geometric morphometrics. (English) Zbl 1499.60113 SIAM J. Math. Data Sci. 1, No. 1, 237-267 (2019). MSC: 60G15 62K05 65D18 PDFBibTeX XMLCite \textit{T. Gao} et al., SIAM J. Math. Data Sci. 1, No. 1, 237--267 (2019; Zbl 1499.60113) Full Text: DOI arXiv
Felsberger, Lukas; Koutsourelakis, Phaedon-Stelios Physics-constrained, data-driven discovery of coarse-grained dynamics. (English) Zbl 1473.62088 Commun. Comput. Phys. 25, No. 5, 1259-1301 (2019). MSC: 62F15 62H99 82C21 PDFBibTeX XMLCite \textit{L. Felsberger} and \textit{P.-S. Koutsourelakis}, Commun. Comput. Phys. 25, No. 5, 1259--1301 (2019; Zbl 1473.62088) Full Text: DOI arXiv
Michaelides, Michalis; Hillston, Jane; Sanguinetti, Guido Geometric fluid approximation for general continuous-time Markov chains. (English) Zbl 1472.60129 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2229, Article ID 20190100, 21 p. (2019). MSC: 60J27 PDFBibTeX XMLCite \textit{M. Michaelides} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2229, Article ID 20190100, 21 p. (2019; Zbl 1472.60129) Full Text: DOI arXiv Link
Dixit, Purushottam D. Introducing user-prescribed constraints in Markov chains for nonlinear dimensionality reduction. (English) Zbl 1475.62126 Neural Comput. 31, No. 5, 980-997 (2019). MSC: 62F30 60J10 PDFBibTeX XMLCite \textit{P. D. Dixit}, Neural Comput. 31, No. 5, 980--997 (2019; Zbl 1475.62126) Full Text: DOI arXiv
Talmon, Ronen; Wu, Hau-Tieng Latent common manifold learning with alternating diffusion: analysis and applications. (English) Zbl 1441.62241 Appl. Comput. Harmon. Anal. 47, No. 3, 848-892 (2019). Reviewer: Catalin Stoean (Craiova) MSC: 62M10 62R30 60J60 28-08 62P10 PDFBibTeX XMLCite \textit{R. Talmon} and \textit{H.-T. Wu}, Appl. Comput. Harmon. Anal. 47, No. 3, 848--892 (2019; Zbl 1441.62241) Full Text: DOI arXiv
DeGennaro, Anthony M.; Urban, Nathan M. Scalable extended dynamic mode decomposition using random kernel approximation. (English) Zbl 1422.37060 SIAM J. Sci. Comput. 41, No. 3, A1482-A1499 (2019). MSC: 37M10 62M15 PDFBibTeX XMLCite \textit{A. M. DeGennaro} and \textit{N. M. Urban}, SIAM J. Sci. Comput. 41, No. 3, A1482--A1499 (2019; Zbl 1422.37060) Full Text: DOI arXiv
Long, Andrew W.; Ferguson, Andrew L. Landmark diffusion maps (L-dMaps): accelerated manifold learning out-of-sample extension. (English) Zbl 1489.68228 Appl. Comput. Harmon. Anal. 47, No. 1, 190-211 (2019). MSC: 68T05 05C50 42B35 60J60 62R30 68Q25 92-10 PDFBibTeX XMLCite \textit{A. W. Long} and \textit{A. L. Ferguson}, Appl. Comput. Harmon. Anal. 47, No. 1, 190--211 (2019; Zbl 1489.68228) Full Text: DOI arXiv
Lafata, Kyle; Zhou, Zhennan; Liu, Jian-Guo; Yin, Fang-Fang Data clustering based on Langevin annealing with a self-consistent potential. (English) Zbl 1419.62154 Q. Appl. Math. 77, No. 3, 591-613 (2019). MSC: 62H30 82C31 60H10 37M25 81Q05 60J65 PDFBibTeX XMLCite \textit{K. Lafata} et al., Q. Appl. Math. 77, No. 3, 591--613 (2019; Zbl 1419.62154) Full Text: DOI arXiv
Bou-Rabee, Nawaf; Vanden-Eijnden, Eric Continuous-time random walks for the numerical solution of stochastic differential equations. (English) Zbl 1437.65002 Memoirs of the American Mathematical Society 1228. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-3181-5/pbk; 978-1-4704-4919-3/ebook). v, 124 p. (2018). Reviewer: Melvin D. Lax (Long Beach) MSC: 65-02 65C30 60H10 60J25 60J74 PDFBibTeX XMLCite \textit{N. Bou-Rabee} and \textit{E. Vanden-Eijnden}, Continuous-time random walks for the numerical solution of stochastic differential equations. Providence, RI: American Mathematical Society (AMS) (2018; Zbl 1437.65002) Full Text: DOI arXiv
Schaeffer, Hayden; Tran, Giang; Ward, Rachel Extracting sparse high-dimensional dynamics from limited data. (English) Zbl 1405.62127 SIAM J. Appl. Math. 78, No. 6, 3279-3295 (2018). MSC: 62M99 60B20 65K10 65L09 94A12 PDFBibTeX XMLCite \textit{H. Schaeffer} et al., SIAM J. Appl. Math. 78, No. 6, 3279--3295 (2018; Zbl 1405.62127) Full Text: DOI arXiv
Klus, Stefan; Nüske, Feliks; Koltai, Péter; Wu, Hao; Kevrekidis, Ioannis; Schütte, Christof; Noé, Frank Data-driven model reduction and transfer operator approximation. (English) Zbl 1396.37083 J. Nonlinear Sci. 28, No. 3, 985-1010 (2018). Reviewer: T. C. Mohan (Chennai) MSC: 37M10 37M25 37L65 34L16 68P99 37C30 PDFBibTeX XMLCite \textit{S. Klus} et al., J. Nonlinear Sci. 28, No. 3, 985--1010 (2018; Zbl 1396.37083) Full Text: DOI arXiv
Lai, Rongjie; Lu, Jianfeng Point cloud discretization of Fokker-Planck operators for committor functions. (English) Zbl 1431.65235 Multiscale Model. Simul. 16, No. 2, 710-726 (2018). Reviewer: Zhiming Chen (Beijing) MSC: 65N99 65D25 60H10 82C35 82C31 82C26 35R60 35P15 65D05 65N35 PDFBibTeX XMLCite \textit{R. Lai} and \textit{J. Lu}, Multiscale Model. Simul. 16, No. 2, 710--726 (2018; Zbl 1431.65235) Full Text: DOI arXiv
Bittracher, Andreas; Koltai, Péter; Klus, Stefan; Banisch, Ralf; Dellnitz, Michael; Schütte, Christof Transition manifolds of complex metastable systems. Theory and data-driven computation of effective dynamics. (English) Zbl 06860496 J. Nonlinear Sci. 28, No. 2, 471-512 (2018). MSC: 47B38 82C31 60H35 PDFBibTeX XMLCite \textit{A. Bittracher} et al., J. Nonlinear Sci. 28, No. 2, 471--512 (2018; Zbl 06860496) Full Text: DOI arXiv
Dsilva, Carmeline J.; Talmon, Ronen; Coifman, Ronald R.; Kevrekidis, Ioannis G. Parsimonious representation of nonlinear dynamical systems through manifold learning: a chemotaxis case study. (English) Zbl 1390.68523 Appl. Comput. Harmon. Anal. 44, No. 3, 759-773 (2018). MSC: 68T05 62H11 62H25 92C40 PDFBibTeX XMLCite \textit{C. J. Dsilva} et al., Appl. Comput. Harmon. Anal. 44, No. 3, 759--773 (2018; Zbl 1390.68523) Full Text: DOI arXiv
Lederman, Roy R.; Talmon, Ronen Learning the geometry of common latent variables using alternating-diffusion. (English) Zbl 1394.94297 Appl. Comput. Harmon. Anal. 44, No. 3, 509-536 (2018). MSC: 94A12 62-07 PDFBibTeX XMLCite \textit{R. R. Lederman} and \textit{R. Talmon}, Appl. Comput. Harmon. Anal. 44, No. 3, 509--536 (2018; Zbl 1394.94297) Full Text: DOI
Françoisse, Kevin; Kivimäki, Ilkka; Mantrach, Amin; Rossi, Fabrice; Saerens, Marco A bag-of-paths framework for network data analysis. (English) Zbl 1434.68535 Neural Netw. 90, 90-111 (2017). MSC: 68T09 62H30 68R10 PDFBibTeX XMLCite \textit{K. Françoisse} et al., Neural Netw. 90, 90--111 (2017; Zbl 1434.68535) Full Text: DOI arXiv
Banisch, Ralf; Koltai, Péter Understanding the geometry of transport: diffusion maps for Lagrangian trajectory data unravel coherent sets. (English) Zbl 1387.37011 Chaos 27, No. 3, 035804, 16 p. (2017). MSC: 37A50 60J70 82C70 PDFBibTeX XMLCite \textit{R. Banisch} and \textit{P. Koltai}, Chaos 27, No. 3, 035804, 16 p. (2017; Zbl 1387.37011) Full Text: DOI arXiv Link
Miura, Yasunari; Sugiyama, Yuki Coarse analysis of collective behaviors: bifurcation analysis of the optimal velocity model for traffic jam formation. (English) Zbl 1378.90038 Phys. Lett., A 381, No. 48, 3983-3988 (2017). MSC: 90B20 76R50 PDFBibTeX XMLCite \textit{Y. Miura} and \textit{Y. Sugiyama}, Phys. Lett., A 381, No. 48, 3983--3988 (2017; Zbl 1378.90038) Full Text: DOI
Crosskey, Miles; Maggioni, Mauro ATLAS: a geometric approach to learning high-dimensional stochastic systems near manifolds. (English) Zbl 1362.60066 Multiscale Model. Simul. 15, No. 1, 110-156 (2017). MSC: 60J20 60J35 60J60 PDFBibTeX XMLCite \textit{M. Crosskey} and \textit{M. Maggioni}, Multiscale Model. Simul. 15, No. 1, 110--156 (2017; Zbl 1362.60066) Full Text: DOI arXiv
Xing, W. W.; Triantafyllidis, V.; Shah, A. A.; Nair, P. B.; Zabaras, N. Manifold learning for the emulation of spatial fields from computational models. (English) Zbl 1373.68340 J. Comput. Phys. 326, 666-690 (2016). MSC: 68T05 35B30 60G15 62H25 68U20 PDFBibTeX XMLCite \textit{W. W. Xing} et al., J. Comput. Phys. 326, 666--690 (2016; Zbl 1373.68340) Full Text: DOI Link
Bermanis, Amit; Wolf, Guy; Averbuch, Amir Diffusion-based kernel methods on Euclidean metric measure spaces. (English) Zbl 1382.42014 Appl. Comput. Harmon. Anal. 41, No. 1, 190-213 (2016). MSC: 42B37 94A08 PDFBibTeX XMLCite \textit{A. Bermanis} et al., Appl. Comput. Harmon. Anal. 41, No. 1, 190--213 (2016; Zbl 1382.42014) Full Text: DOI
Berry, Tyrus; Sauer, Timothy Local kernels and the geometric structure of data. (English) Zbl 1376.94002 Appl. Comput. Harmon. Anal. 40, No. 3, 439-469 (2016). MSC: 94A08 62H35 62G08 PDFBibTeX XMLCite \textit{T. Berry} and \textit{T. Sauer}, Appl. Comput. Harmon. Anal. 40, No. 3, 439--469 (2016; Zbl 1376.94002) Full Text: DOI arXiv
Bermanis, Amit; Salhov, Moshe; Wolf, Guy; Averbuch, Amir Measure-based diffusion grid construction and high-dimensional data discretization. (English) Zbl 1335.94008 Appl. Comput. Harmon. Anal. 40, No. 2, 207-228 (2016). MSC: 94A08 94A12 62H30 65C60 62-07 PDFBibTeX XMLCite \textit{A. Bermanis} et al., Appl. Comput. Harmon. Anal. 40, No. 2, 207--228 (2016; Zbl 1335.94008) Full Text: DOI
Berry, Tyrus; Harlim, John Variable bandwidth diffusion kernels. (English) Zbl 1343.94020 Appl. Comput. Harmon. Anal. 40, No. 1, 68-96 (2016). MSC: 94A12 PDFBibTeX XMLCite \textit{T. Berry} and \textit{J. Harlim}, Appl. Comput. Harmon. Anal. 40, No. 1, 68--96 (2016; Zbl 1343.94020) Full Text: DOI arXiv
Williams, Matthew O.; Kevrekidis, Ioannis G.; Rowley, Clarence W. A data-driven approximation of the koopman operator: extending dynamic mode decomposition. (English) Zbl 1329.65310 J. Nonlinear Sci. 25, No. 6, 1307-1346 (2015). MSC: 65P99 37M25 37H10 47B33 PDFBibTeX XMLCite \textit{M. O. Williams} et al., J. Nonlinear Sci. 25, No. 6, 1307--1346 (2015; Zbl 1329.65310) Full Text: DOI arXiv
Liu, Ping; Siettos, C. I.; Gear, C. W.; Kevrekidis, I. G. Equation-free model reduction in agent-based computations: coarse-grained bifurcation and variable-free rare event analysis. (English) Zbl 1325.35233 Math. Model. Nat. Phenom. 10, No. 3, 71-90 (2015). MSC: 35Q91 37G10 37H20 65P30 PDFBibTeX XMLCite \textit{P. Liu} et al., Math. Model. Nat. Phenom. 10, No. 3, 71--90 (2015; Zbl 1325.35233) Full Text: DOI Link
Berry, Tyrus; Harlim, John Nonparametric uncertainty quantification for stochastic gradient flows. (English) Zbl 1339.60067 SIAM/ASA J. Uncertain. Quantif. 3, 484-508 (2015). MSC: 60H10 60G25 60G35 62M20 60J60 93E11 65C60 82C31 PDFBibTeX XMLCite \textit{T. Berry} and \textit{J. Harlim}, SIAM/ASA J. Uncertain. Quantif. 3, 484--508 (2015; Zbl 1339.60067) Full Text: DOI arXiv
Giannakis, Dimitrios Dynamics-adapted cone kernels. (English) Zbl 1370.37141 SIAM J. Appl. Dyn. Syst. 14, No. 2, 556-608 (2015). MSC: 37N10 37M10 62H11 PDFBibTeX XMLCite \textit{D. Giannakis}, SIAM J. Appl. Dyn. Syst. 14, No. 2, 556--608 (2015; Zbl 1370.37141) Full Text: DOI arXiv
Fan, Mingyu; Gu, Nannan; Qiao, Hong; Zhang, Bo Dimensionality reduction: an interpretation from manifold regularization perspective. (English) Zbl 1354.68222 Inf. Sci. 277, 694-714 (2014). MSC: 68T05 PDFBibTeX XMLCite \textit{M. Fan} et al., Inf. Sci. 277, 694--714 (2014; Zbl 1354.68222) Full Text: DOI
Wolf, Guy; Averbuch, Amir; Neittaanmäki, Pekka Parameter rating by diffusion gradient. (English) Zbl 1328.65046 Fitzgibbon, William (ed.) et al., Modeling, simulation and optimization for science and technology. Selected contributions based on the presentations at the conferences “Optimization and PDE’s with industrial applications”, Jyväskylä, Finland, June, 2012 on the occasion of the 70th birthday of Jaques Périaux and “Optimization and PDE’s with application”, Jyväskylä, Finland, June, 2012 on the occasion of the 75th birthday of Roland Glowinski. Dordrecht: Springer (ISBN 978-94-017-9053-6/hbk; 978-94-017-9054-3/ebook). Computational Methods in Applied Sciences 34, 225-248 (2014). MSC: 65C60 PDFBibTeX XMLCite \textit{G. Wolf} et al., Comput. Methods Appl. Sci. 34, 225--248 (2014; Zbl 1328.65046) Full Text: DOI
Parpas, Panos; Webster, Mort A stochastic multiscale model for electricity generation capacity expansion. (English) Zbl 1305.90405 Eur. J. Oper. Res. 232, No. 2, 359-374 (2014). MSC: 90C40 90C90 90B90 91B76 PDFBibTeX XMLCite \textit{P. Parpas} and \textit{M. Webster}, Eur. J. Oper. Res. 232, No. 2, 359--374 (2014; Zbl 1305.90405) Full Text: DOI Link
Bold, Katherine A.; Rajendran, Karthikeyan; Ráth, Balász; Kevrekidis, Ioannis G. An equation-free approach to coarse-graining the dynamics of networks. (English) Zbl 1317.68257 J. Comput. Dyn. 1, No. 1, 111-134 (2014). MSC: 68U20 05C82 37E25 65Z05 PDFBibTeX XMLCite \textit{K. A. Bold} et al., J. Comput. Dyn. 1, No. 1, 111--134 (2014; Zbl 1317.68257) Full Text: DOI arXiv
Castillo, Ismaël; Kerkyacharian, Gérard; Picard, Dominique Thomas Bayes’ walk on manifolds. (English) Zbl 1285.62028 Probab. Theory Relat. Fields 158, No. 3-4, 665-710 (2014). MSC: 62F15 62G20 62M99 62B10 62G05 PDFBibTeX XMLCite \textit{I. Castillo} et al., Probab. Theory Relat. Fields 158, No. 3--4, 665--710 (2014; Zbl 1285.62028) Full Text: DOI arXiv
Giannakis, Dimitrios; Majda, Andrew J. Nonlinear Laplacian spectral analysis: capturing intermittent and low-frequency spatiotemporal patterns in high-dimensional data. (English) Zbl 07260360 Stat. Anal. Data Min. 6, No. 3, 180-194 (2013). MSC: 62-XX 68-XX PDFBibTeX XMLCite \textit{D. Giannakis} and \textit{A. J. Majda}, Stat. Anal. Data Min. 6, No. 3, 180--194 (2013; Zbl 07260360) Full Text: DOI arXiv
Röblitz, Susanna; Weber, Marcus Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification. (English) Zbl 1273.62145 Adv. Data Anal. Classif., ADAC 7, No. 2, 147-179 (2013). MSC: 62H30 62H86 60J20 60J10 65K05 PDFBibTeX XMLCite \textit{S. Röblitz} and \textit{M. Weber}, Adv. Data Anal. Classif., ADAC 7, No. 2, 147--179 (2013; Zbl 1273.62145) Full Text: DOI
Grauman, Kristen; Fergus, Rob Learning binary hash codes for large-scale image search. (English) Zbl 1251.68268 Cipolla, Roberto (ed.) et al., Machine learning for computer vision. Selected papers based on the presentations at the international computer vision summer school (ICVSS 2012), Sicily, Italy, July 7–15, 2012. Berlin: Springer (ISBN 978-3-642-28660-5/hbk; 978-3-642-28661-2/ebook). Studies in Computational Intelligence 411, 49-87 (2013). MSC: 68T45 68P10 68P20 68T05 68U05 68P05 PDFBibTeX XMLCite \textit{K. Grauman} and \textit{R. Fergus}, Stud. Comput. Intell. 411, 49--87 (2013; Zbl 1251.68268) Full Text: DOI
Giannakis, Dimitrios; Majda, Andrew J. Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability. (English) Zbl 1256.62053 Proc. Natl. Acad. Sci. USA 109, No. 7, 2222-2227 (2012). MSC: 62M15 62M10 86A32 62P12 PDFBibTeX XMLCite \textit{D. Giannakis} and \textit{A. J. Majda}, Proc. Natl. Acad. Sci. USA 109, No. 7, 2222--2227 (2012; Zbl 1256.62053) Full Text: DOI
Fouss, François; Francoisse, Kevin; Yen, Luh; Pirotte, Alain; Saerens, Marco An experimental investigation of kernels on graphs for collaborative recommendation and semisupervised classification. (English) Zbl 1245.68155 Neural Netw. 31, 53-72 (2012). MSC: 68T05 62H30 PDFBibTeX XMLCite \textit{F. Fouss} et al., Neural Netw. 31, 53--72 (2012; Zbl 1245.68155) Full Text: DOI
Sahai, Tuhin; Speranzon, Alberto; Banaszuk, Andrzej Hearing the clusters of a graph: A distributed algorithm. (English) Zbl 1244.93016 Automatica 48, No. 1, 15-24 (2012). MSC: 93A15 94C15 93A14 PDFBibTeX XMLCite \textit{T. Sahai} et al., Automatica 48, No. 1, 15--24 (2012; Zbl 1244.93016) Full Text: DOI arXiv
Goldberg, Maxim J.; Kim, Seonja An efficient tree-based computation of a metric comparable to a natural diffusion distance. (English) Zbl 1248.68403 Appl. Comput. Harmon. Anal. 33, No. 2, 261-281 (2012). MSC: 68T05 60D99 60J60 62H30 PDFBibTeX XMLCite \textit{M. J. Goldberg} and \textit{S. Kim}, Appl. Comput. Harmon. Anal. 33, No. 2, 261--281 (2012; Zbl 1248.68403) Full Text: DOI
Salhov, Moshe; Wolf, Guy; Averbuch, Amir Patch-to-tensor embedding. (English) Zbl 1243.68249 Appl. Comput. Harmon. Anal. 33, No. 2, 182-203 (2012). MSC: 68T05 62H25 PDFBibTeX XMLCite \textit{M. Salhov} et al., Appl. Comput. Harmon. Anal. 33, No. 2, 182--203 (2012; Zbl 1243.68249) Full Text: DOI
Yu, Jun; Seah, Hock-Soon Fuzzy diffusion distance learning for cartoon similarity estimation. (English) Zbl 1280.68231 J. Comput. Sci. Technol. 26, No. 2, 203-216 (2011). MSC: 68T10 68T37 68T05 PDFBibTeX XMLCite \textit{J. Yu} and \textit{H.-S. Seah}, J. Comput. Sci. Technol. 26, No. 2, 203--216 (2011; Zbl 1280.68231) Full Text: DOI
Singer, Amit; Wu, Hau-Tieng Orientability and diffusion maps. (English) Zbl 1218.68131 Appl. Comput. Harmon. Anal. 31, No. 1, 44-58 (2011). MSC: 68T05 68U05 PDFBibTeX XMLCite \textit{A. Singer} and \textit{H.-T. Wu}, Appl. Comput. Harmon. Anal. 31, No. 1, 44--58 (2011; Zbl 1218.68131) Full Text: DOI arXiv Link
Mémoli, Facundo A spectral notion of Gromov-Wasserstein distance and related methods. (English) Zbl 1219.53046 Appl. Comput. Harmon. Anal. 30, No. 3, 363-401 (2011). Reviewer: Witold Mozgawa (Lublin) MSC: 53C23 58J05 58J50 58J35 68U10 PDFBibTeX XMLCite \textit{F. Mémoli}, Appl. Comput. Harmon. Anal. 30, No. 3, 363--401 (2011; Zbl 1219.53046) Full Text: DOI
Goldberg, Maxim J.; Kim, Seonja Some remarks on diffusion distances. (English) Zbl 1218.60074 J. Appl. Math. 2010, Article ID 464815, 17 p. (2010). MSC: 60J99 42B35 46N30 PDFBibTeX XMLCite \textit{M. J. Goldberg} and \textit{S. Kim}, J. Appl. Math. 2010, Article ID 464815, 17 p. (2010; Zbl 1218.60074) Full Text: DOI EuDML
Zou, Yu; Kavousanakis, Michail E.; Kevrekidis, Ioannis G.; Fox, Rodney O. Coarse-grained computation for particle coagulation and sintering processes by linking quadrature method of moments with Monte-Carlo. (English) Zbl 1346.82037 J. Comput. Phys. 229, No. 14, 5299-5314 (2010). MSC: 82C80 65C05 82B80 92E20 PDFBibTeX XMLCite \textit{Y. Zou} et al., J. Comput. Phys. 229, No. 14, 5299--5314 (2010; Zbl 1346.82037) Full Text: DOI
Schütte, Christof; Jahnke, Tobias Towards effective dynamics in complex systems by Markov kernel approximation. (English) Zbl 1168.60358 ESAIM, Math. Model. Numer. Anal. 43, No. 4, 721 (2009). MSC: 60J22 60J25 60J35 62M05 65C40 PDFBibTeX XMLCite \textit{C. Schütte} and \textit{T. Jahnke}, ESAIM, Math. Model. Numer. Anal. 43, No. 4, 721 (2009; Zbl 1168.60358) Full Text: DOI EuDML
Ahuja, Sunil; Yakhot, Victor; Kevrekidis, Ioannis G. Computational coarse graining of a randomly forced one-dimensional Burgers equation. (English) Zbl 1182.76008 Phys. Fluids 20, No. 3, Paper No. 035111, 10 p. (2008). MSC: 76-XX PDFBibTeX XMLCite \textit{S. Ahuja} et al., Phys. Fluids 20, No. 3, Paper No. 035111, 10 p. (2008; Zbl 1182.76008) Full Text: DOI arXiv
Runolfsson, Thordur Towards hybrid system modeling of uncertain complex dynamical systems. (English) Zbl 1155.93422 Nonlinear Anal., Hybrid Syst. 2, No. 2, 383-393 (2008). MSC: 93E03 93C55 60J05 93A30 PDFBibTeX XMLCite \textit{T. Runolfsson}, Nonlinear Anal., Hybrid Syst. 2, No. 2, 383--393 (2008; Zbl 1155.93422) Full Text: DOI
Singer, Amit; Coifman, Ronald R. Non-linear independent component analysis with diffusion maps. (English) Zbl 1144.62044 Appl. Comput. Harmon. Anal. 25, No. 2, 226-239 (2008). MSC: 62H25 60J70 62M99 60H30 PDFBibTeX XMLCite \textit{A. Singer} and \textit{R. R. Coifman}, Appl. Comput. Harmon. Anal. 25, No. 2, 226--239 (2008; Zbl 1144.62044) Full Text: DOI
Kolpas, Allison; Moehlis, Jeff; Frewen, Thomas A.; Kevrekidis, Ioannis G. Coarse analysis of collective motion with different communication mechanisms. (English) Zbl 1143.92043 Math. Biosci. 214, No. 1-2, 49-57 (2008). MSC: 92D50 60J70 94A99 PDFBibTeX XMLCite \textit{A. Kolpas} et al., Math. Biosci. 214, No. 1--2, 49--57 (2008; Zbl 1143.92043) Full Text: DOI
Bold, Katherine A.; Zou, Yu; Kevrekidis, Ioannis G.; Henson, Michael A. An equation-free approach to analyzing heterogeneous cell population dynamics. (English) Zbl 1123.37051 J. Math. Biol. 55, No. 3, 331-352 (2007). MSC: 37N25 34C15 92D25 92C17 37D45 93D15 PDFBibTeX XMLCite \textit{K. A. Bold} et al., J. Math. Biol. 55, No. 3, 331--352 (2007; Zbl 1123.37051) Full Text: DOI
Shay, M. A.; Drake, J. F.; Dorland, B. Equation free projective integration: a multiscale method applied to a plasma ion acoustic wave. (English) Zbl 1310.76132 J. Comput. Phys. 226, No. 1, 571-585 (2007). MSC: 76M25 76X05 PDFBibTeX XMLCite \textit{M. A. Shay} et al., J. Comput. Phys. 226, No. 1, 571--585 (2007; Zbl 1310.76132) Full Text: DOI
Owhadi, Houman; Zhang, Lei Metric-based upscaling. (English) Zbl 1190.35070 Commun. Pure Appl. Math. 60, No. 5, 675-723 (2007). MSC: 35J25 35B65 65N06 74Q05 76M50 PDFBibTeX XMLCite \textit{H. Owhadi} and \textit{L. Zhang}, Commun. Pure Appl. Math. 60, No. 5, 675--723 (2007; Zbl 1190.35070) Full Text: DOI arXiv
Coifman, Ronald R.; Lafon, Stéphane Diffusion maps. (English) Zbl 1095.68094 Appl. Comput. Harmon. Anal. 21, No. 1, 5-30 (2006). MSC: 68T05 68T30 05C50 PDFBibTeX XMLCite \textit{R. R. Coifman} and \textit{S. Lafon}, Appl. Comput. Harmon. Anal. 21, No. 1, 5--30 (2006; Zbl 1095.68094) Full Text: DOI
Erban, Radek; Kevrekidis, Ioannis G.; Othmer, Hans G. An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal. (English) Zbl 1094.35127 Physica D 215, No. 1, 1-24 (2006). MSC: 35Q80 60J70 92D25 92C17 82C80 PDFBibTeX XMLCite \textit{R. Erban} et al., Physica D 215, No. 1, 1--24 (2006; Zbl 1094.35127) Full Text: DOI arXiv