Lin, Yen Ting; Tian, Yifeng; Perez, Danny; Livescu, Daniel Regression-based projection for learning Mori-Zwanzig operators. (English) Zbl 07773373 SIAM J. Appl. Dyn. Syst. 22, No. 4, 2890-2926 (2023). MSC: 37M99 46N55 62M10 PDFBibTeX XMLCite \textit{Y. T. Lin} et al., SIAM J. Appl. Dyn. Syst. 22, No. 4, 2890--2926 (2023; Zbl 07773373) Full Text: DOI arXiv
Crabtree, Ellis R.; Bello-Rivas, Juan M.; Kevrekidis, Ioannis G. Micro-Macro Consistency in Multiscale Modeling: Score-Based Model Assisted Sampling of Fast/Slow Dynamical Systems. arXiv:2312.05715 Preprint, arXiv:2312.05715 [cs.LG] (2023). MSC: 82C32 37M05 60H10 68T07 82-08 BibTeX Cite \textit{E. R. Crabtree} et al., ``Micro-Macro Consistency in Multiscale Modeling: Score-Based Model Assisted Sampling of Fast/Slow Dynamical Systems'', Preprint, arXiv:2312.05715 [cs.LG] (2023) Full Text: arXiv OA License
Levine, Matthew E.; Stuart, Andrew M. A framework for machine learning of model error in dynamical systems. (English) Zbl 07750994 Commun. Am. Math. Soc. 2, 283-344 (2022). MSC: 65L05 68T30 37A30 37M10 37M25 41A30 PDFBibTeX XMLCite \textit{M. E. Levine} and \textit{A. M. Stuart}, Commun. Am. Math. Soc. 2, 283--344 (2022; Zbl 07750994) Full Text: DOI arXiv
Yin, H. M.; Pan, Q.; Chow, K. W. The Fermi-Pasta-Ulam-Tsingou recurrence for discrete systems: cascading mechanism and machine learning for the Ablowitz-Ladik equation. (English) Zbl 1504.35506 Commun. Nonlinear Sci. Numer. Simul. 114, Article ID 106664, 13 p. (2022). MSC: 35Q55 35Q51 35Q53 35C08 35B10 37K40 82C20 65L06 68T07 PDFBibTeX XMLCite \textit{H. M. Yin} et al., Commun. Nonlinear Sci. Numer. Simul. 114, Article ID 106664, 13 p. (2022; Zbl 1504.35506) Full Text: DOI
Brunton, Steven L.; Kutz, J. Nathan Data-driven science and engineering. Machine learning, dynamical systems, and control. 2nd edition. (English) Zbl 1487.68001 Cambridge: Cambridge University Press (ISBN 978-1-00-909848-9/hbk; 978-1-00-908951-7/ebook). xxiv, 590 p. (2022). MSC: 68-01 62-01 93-01 37N35 62R07 68T05 68T09 93B28 93B30 93C95 94A16 PDFBibTeX XMLCite \textit{S. L. Brunton} and \textit{J. N. Kutz}, Data-driven science and engineering. Machine learning, dynamical systems, and control. 2nd edition. Cambridge: Cambridge University Press (2022; Zbl 1487.68001) Full Text: DOI
Yoon, Ryeongkyung; Bhat, Harish S.; Osting, Braxton A nonautonomous equation discovery method for time signal classification. (English) Zbl 1489.37097 SIAM J. Appl. Dyn. Syst. 21, No. 1, 33-59 (2022). MSC: 37M99 68T07 62L10 PDFBibTeX XMLCite \textit{R. Yoon} et al., SIAM J. Appl. Dyn. Syst. 21, No. 1, 33--59 (2022; Zbl 1489.37097) Full Text: DOI arXiv
Brunton, Steven L.; Kutz, J. Nathan Data-driven science and engineering. Machine learning, dynamical systems, and control. (English) Zbl 1407.68002 Cambridge: Cambridge University Press (ISBN 978-1-108-42209-3/hbk; 978-1-108-38069-0/ebook). xxii, 472 p. (2019). Reviewer: Bülent Karasözen (Ankara) MSC: 68-01 62-01 93-01 37N35 62R07 68T05 68T09 93B28 93B30 93C95 94A16 PDFBibTeX XMLCite \textit{S. L. Brunton} and \textit{J. N. Kutz}, Data-driven science and engineering. Machine learning, dynamical systems, and control. Cambridge: Cambridge University Press (2019; Zbl 1407.68002) Full Text: DOI
Ram, Mangey (ed.); Frenkel, Ilia B. (ed.); Gupta, Arpan (ed.) Preface: Applied mathematical techniques in engineering applications and related topics. I. (English) Zbl 1298.00342 Math. Eng. Sci. Aerosp. MESA 5, No. 2, 135-136 (2014). MSC: 00B25 34A08 34K37 35G31 37N25 41A05 60G25 62N05 65D05 65M70 65Z05 68M15 68Q32 68T05 68T27 68U10 74F05 76D05 76E25 76F10 76Sxx 76Wxx 82C32 90B25 92B05 92B20 92C37 94A08 PDFBibTeX XMLCite \textit{M. Ram} (ed.) et al., Math. Eng. Sci. Aerosp. MESA 5, No. 2, 135--136 (2014; Zbl 1298.00342) Full Text: Link
Chen, Jie; Sun, Jian; Liu, G. P.; Rees, D. New delay-dependent stability criteria for neural networks with time-varying interval delay. (English) Zbl 1238.82027 Phys. Lett., A 374, No. 43, 4397-4405 (2010). MSC: 82C32 68T05 15A39 37B25 PDFBibTeX XMLCite \textit{J. Chen} et al., Phys. Lett., A 374, No. 43, 4397--4405 (2010; Zbl 1238.82027) Full Text: DOI
Lu, Hongtao; van Leeuwen, C. Synchronization of chaotic neural networks via output or state coupling. (English) Zbl 1144.37377 Chaos Solitons Fractals 30, No. 1, 166-176 (2006). MSC: 37D45 34K20 82C32 93D15 68T05 PDFBibTeX XMLCite \textit{H. Lu} and \textit{C. van Leeuwen}, Chaos Solitons Fractals 30, No. 1, 166--176 (2006; Zbl 1144.37377) Full Text: DOI
Ho, Ming-Chung; Hung, Yao-Chen; Jiang, I-Min Stochastic coupling of two random Boolean networks. (English) Zbl 1194.82075 Phys. Lett., A 344, No. 1, 36-42 (2005). MSC: 82C32 37N99 68T05 PDFBibTeX XMLCite \textit{M.-C. Ho} et al., Phys. Lett., A 344, No. 1, 36--42 (2005; Zbl 1194.82075) Full Text: DOI
Boikov, I. V. Stability of Hopfield neural networks. (English. Russian original) Zbl 1107.34333 Autom. Remote Control 64, No. 9, 1474-1487 (2003); translation from Avtom. Telemekh. 2003, No. 9, 124-140 (2003). MSC: 34D20 37N25 68T05 82C32 92B20 93D15 PDFBibTeX XMLCite \textit{I. V. Boikov}, Autom. Remote Control 64, No. 9, 1474--1487 (2003; Zbl 1107.34333); translation from Avtom. Telemekh. 2003, No. 9, 124--140 (2003) Full Text: DOI
Xu, Bingji; Liu, Xinzhi; Liao, Xiaoxin Global asymptotic stability of high-order Hopfield type neural networks with time delays. (English) Zbl 1045.37056 Comput. Math. Appl. 45, No. 10-11, 1729-1737 (2003). MSC: 37N20 34D23 82C32 68T05 94A08 94A12 PDFBibTeX XMLCite \textit{B. Xu} et al., Comput. Math. Appl. 45, No. 10--11, 1729--1737 (2003; Zbl 1045.37056) Full Text: DOI
Garliauskas, Algis Some aspects of neural networks chaos modeling. I: Double-mode model of chaos. (English) Zbl 1046.82026 Int. J. Comput. Numer. Anal. Appl. 4, No. 1, 1-21 (2003). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 82C32 68T05 92B20 37N25 PDFBibTeX XMLCite \textit{A. Garliauskas}, Int. J. Comput. Numer. Anal. Appl. 4, No. 1, 1--21 (2003; Zbl 1046.82026)
Slavova, Angela Cellular neural networks: dynamics and modelling. (English) Zbl 1049.37001 Mathematical Modelling: Theory and Applications 16. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1192-X/hbk). x, 220 p. (2003). Reviewer: Yuri V. Rogovchenko (Famagusta) MSC: 37-01 37N25 92B20 82C32 68T05 34C60 34D20 34K60 PDFBibTeX XMLCite \textit{A. Slavova}, Cellular neural networks: dynamics and modelling. Dordrecht: Kluwer Academic Publishers (2003; Zbl 1049.37001)
Potapov, A. B.; Ali, M. K. Nonlinear dynamics of information processing by neural networks. (Russian) Zbl 1051.94006 Izv. Vyssh. Uchebn. Zaved., Prikl. Nelinejn. Din. 9, No. 6, 3-44 (2001). Reviewer: Andrei Zemskov (Moskva) MSC: 94A15 68T05 82C32 37D45 PDFBibTeX XMLCite \textit{A. B. Potapov} and \textit{M. K. Ali}, Izv. Vyssh. Uchebn. Zaved., Prikl. Nelineĭn. Din. 9, No. 6, 3--44 (2001; Zbl 1051.94006)
Thiran, Patrick; Setti, Gianluca; Hasler, Martin An approach to information propagation in 1-D cellular neural networks. I: Local diffusion. (English) Zbl 0951.92001 IEEE Trans. Circuits Syst., I, Fundam. Theory Appl. 45, No. 8, 777-789 (1998). MSC: 92B20 37B15 37N25 68Q80 68T05 82C32 PDFBibTeX XMLCite \textit{P. Thiran} et al., IEEE Trans. Circuits Syst., I, Fundam. Theory Appl. 45, No. 8, 777--789 (1998; Zbl 0951.92001) Full Text: DOI
Setti, Gianluca; Thiran, Patrick; Serpico, Claudio An approach to information propagation in 1-D cellular neural networks. II: Global propagation. (English) Zbl 0951.92002 IEEE Trans. Circuits Syst., I, Fundam. Theory Appl. 45, No. 8, 790-811 (1998). MSC: 92B20 37B15 37N25 68Q80 68T05 82C32 PDFBibTeX XMLCite \textit{G. Setti} et al., IEEE Trans. Circuits Syst., I, Fundam. Theory Appl. 45, No. 8, 790--811 (1998; Zbl 0951.92002) Full Text: DOI
Bastolla, U.; Parisi, G. Relevant elements, magnetization and dynamical properties in Kauffman networks: A numerical study. (English) Zbl 0938.82043 Physica D 115, No. 3-4, 203-218 (1998). MSC: 82C32 37B15 68Q80 68T05 PDFBibTeX XMLCite \textit{U. Bastolla} and \textit{G. Parisi}, Physica D 115, No. 3--4, 203--218 (1998; Zbl 0938.82043) Full Text: DOI arXiv