Wang, Ziheng; Sirignano, Justin Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations. (English) Zbl 07818732 Math. Finance 34, No. 2, 348-424 (2024). MSC: 93E20 60H30 68T05 PDFBibTeX XMLCite \textit{Z. Wang} and \textit{J. Sirignano}, Math. Finance 34, No. 2, 348--424 (2024; Zbl 07818732) Full Text: DOI arXiv
Freeman, David C.; Giannakis, Dimitrios; Slawinska, Joanna Quantum mechanics for closure of dynamical systems. (English) Zbl 07813977 Multiscale Model. Simul. 22, No. 1, 283-333 (2024). MSC: 37M10 37A50 62M20 68U20 82C10 PDFBibTeX XMLCite \textit{D. C. Freeman} et al., Multiscale Model. Simul. 22, No. 1, 283--333 (2024; Zbl 07813977) Full Text: DOI arXiv OA License
Lang, Quanjun; Lu, Fei Identifiability of interaction kernels in mean-field equations of interacting particles. (English) Zbl 07805152 Found. Data Sci. 5, No. 4, 480-502 (2023). MSC: 35R30 68Q32 PDFBibTeX XMLCite \textit{Q. Lang} and \textit{F. Lu}, Found. Data Sci. 5, No. 4, 480--502 (2023; Zbl 07805152) Full Text: DOI arXiv
Berner, Rico; Gross, Thilo; Kuehn, Christian; Kurths, Jürgen; Yanchuk, Serhiy Adaptive dynamical networks. (English) Zbl 07740142 Phys. Rep. 1031, 1-59 (2023). MSC: 81P68 68M10 68T05 62M45 91D30 PDFBibTeX XMLCite \textit{R. Berner} et al., Phys. Rep. 1031, 1--59 (2023; Zbl 07740142) Full Text: DOI arXiv
Miller, Jason; Tang, Sui; Zhong, Ming; Maggioni, Mauro Learning theory for inferring interaction kernels in second-order interacting agent systems. (English) Zbl 1519.62009 Sampl. Theory Signal Process. Data Anal. 21, No. 1, Paper No. 21, 58 p. (2023). MSC: 62G08 65D07 65L60 68T05 70F17 PDFBibTeX XMLCite \textit{J. Miller} et al., Sampl. Theory Signal Process. Data Anal. 21, No. 1, Paper No. 21, 58 p. (2023; Zbl 1519.62009) Full Text: DOI arXiv
Li, Xiantao; Wang, Chunhao Succinct description and efficient simulation of non-Markovian open quantum systems. (English) Zbl 07700881 Commun. Math. Phys. 401, No. 1, 147-183 (2023). MSC: 68Qxx 81Pxx 68Nxx PDFBibTeX XMLCite \textit{X. Li} and \textit{C. Wang}, Commun. Math. Phys. 401, No. 1, 147--183 (2023; Zbl 07700881) Full Text: DOI arXiv
Strahan, John; Finkel, Justin; Dinner, Aaron R.; Weare, Jonathan Predicting rare events using neural networks and short-trajectory data. (English) Zbl 07696951 J. Comput. Phys. 488, Article ID 112152, 16 p. (2023). MSC: 68Txx 60Hxx 65Cxx PDFBibTeX XMLCite \textit{J. Strahan} et al., J. Comput. Phys. 488, Article ID 112152, 16 p. (2023; Zbl 07696951) Full Text: DOI arXiv
Venturi, Daniele; Li, Xiantao The Mori-Zwanzig formulation of deep learning. (English) Zbl 07696874 Res. Math. Sci. 10, No. 2, Paper No. 23, 47 p. (2023). MSC: 68-XX 92-XX PDFBibTeX XMLCite \textit{D. Venturi} and \textit{X. Li}, Res. Math. Sci. 10, No. 2, Paper No. 23, 47 p. (2023; Zbl 07696874) Full Text: DOI arXiv
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
Mishra, Swapnil; Flaxman, Seth; Berah, Tresnia; Zhu, Harrison; Pakkanen, Mikko; Bhatt, Samir \(\pi\) VAE: a stochastic process prior for Bayesian deep learning with MCMC. (English) Zbl 1499.62027 Stat. Comput. 32, No. 6, Paper No. 96, 16 p. (2022). MSC: 62-08 62F15 68T07 PDFBibTeX XMLCite \textit{S. Mishra} et al., Stat. Comput. 32, No. 6, Paper No. 96, 16 p. (2022; Zbl 1499.62027) Full Text: DOI arXiv
Pang, Bo; Cui, Leilei; Jiang, Zhong-Ping Human motor learning is robust to control-dependent noise. (English) Zbl 1495.92014 Biol. Cybern. 116, No. 3, 307-325 (2022). MSC: 92B20 68T07 PDFBibTeX XMLCite \textit{B. Pang} et al., Biol. Cybern. 116, No. 3, 307--325 (2022; Zbl 1495.92014) Full Text: DOI
Liu, Shu; Li, Wuchen; Zha, Hongyuan; Zhou, Haomin Neural parametric Fokker-Planck equation. (English) Zbl 1493.65132 SIAM J. Numer. Anal. 60, No. 3, 1385-1449 (2022). Reviewer: Bülent Karasözen (Ankara) MSC: 65M06 65L12 49Q22 68T07 65M15 65M12 60H30 35A24 35R02 35R60 35Q84 PDFBibTeX XMLCite \textit{S. Liu} et al., SIAM J. Numer. Anal. 60, No. 3, 1385--1449 (2022; Zbl 1493.65132) Full Text: DOI arXiv
Brolly, Martin T.; Maddison, James R.; Teckentrup, Aretha L.; Vanneste, Jacques Bayesian comparison of stochastic models of dispersion. (English) Zbl 1505.76048 J. Fluid Mech. 944, Paper No. A2, 21 p. (2022). MSC: 76F25 76F55 76M99 68T05 PDFBibTeX XMLCite \textit{M. T. Brolly} et al., J. Fluid Mech. 944, Paper No. A2, 21 p. (2022; Zbl 1505.76048) Full Text: DOI arXiv
Al-Aradi, Ali; Correia, Adolfo; Jardim, Gabriel; de Freitas Naiff, Danilo; Saporito, Yuri Extensions of the deep Galerkin method. (English) Zbl 1510.65010 Appl. Math. Comput. 430, Article ID 127287, 18 p. (2022). MSC: 65C30 60H30 60H35 68T07 65M99 65M70 PDFBibTeX XMLCite \textit{A. Al-Aradi} et al., Appl. Math. Comput. 430, Article ID 127287, 18 p. (2022; Zbl 1510.65010) Full Text: DOI arXiv
Tang, Kejun; Wan, Xiaoliang; Liao, Qifeng Adaptive deep density approximation for Fokker-Planck equations. (English) Zbl 1515.65265 J. Comput. Phys. 457, Article ID 111080, 19 p. (2022). MSC: 65M99 35Q84 62-08 62G07 68T07 PDFBibTeX XMLCite \textit{K. Tang} et al., J. Comput. Phys. 457, Article ID 111080, 19 p. (2022; Zbl 1515.65265) Full Text: DOI arXiv
Leimkuhler, Benedict; Sachs, Matthias Efficient numerical algorithms for the generalized Langevin equation. (English) Zbl 07482209 SIAM J. Sci. Comput. 44, No. 1, A364-A388 (2022). MSC: 68Q25 68R10 68U05 PDFBibTeX XMLCite \textit{B. Leimkuhler} and \textit{M. Sachs}, SIAM J. Sci. Comput. 44, No. 1, A364--A388 (2022; Zbl 07482209) Full Text: DOI arXiv
Hoffmann, Franca; Hosseini, Bamdad; Oberai, Assad A.; Stuart, Andrew M. Spectral analysis of weighted Laplacians arising in data clustering. (English) Zbl 07432352 Appl. Comput. Harmon. Anal. 56, 189-249 (2022). MSC: 47A75 62H30 68T10 35B20 05C50 PDFBibTeX XMLCite \textit{F. Hoffmann} et al., Appl. Comput. Harmon. Anal. 56, 189--249 (2022; Zbl 07432352) Full Text: DOI arXiv Link
San, Omer; Rasheed, Adil; Kvamsdal, Trond Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution. (English) Zbl 07778826 GAMM-Mitt. 44, No. 2, Article ID 202100007, 32 p. (2021). MSC: 65M99 65-02 68Q32 68T07 92B20 78A55 PDFBibTeX XMLCite \textit{O. San} et al., GAMM-Mitt. 44, No. 2, Article ID 202100007, 32 p. (2021; Zbl 07778826) Full Text: DOI arXiv
Chen, Zhen; Xiu, Dongbin On generalized residual network for deep learning of unknown dynamical systems. (English) Zbl 07505957 J. Comput. Phys. 438, Article ID 110362, 16 p. (2021). MSC: 68Txx 35Qxx 37Mxx PDFBibTeX XMLCite \textit{Z. Chen} and \textit{D. Xiu}, J. Comput. Phys. 438, Article ID 110362, 16 p. (2021; Zbl 07505957) Full Text: DOI arXiv
Crommelin, Daan; Edeling, Wouter Resampling with neural networks for stochastic parameterization in multiscale systems. (English) Zbl 1511.37096 Physica D 422, Article ID 132894, 12 p. (2021). MSC: 37M05 62H30 62M45 65L05 68T05 PDFBibTeX XMLCite \textit{D. Crommelin} and \textit{W. Edeling}, Physica D 422, Article ID 132894, 12 p. (2021; Zbl 1511.37096) Full Text: DOI arXiv
Zhang, He; Harlim, John; Li, Xiantao Error bounds of the invariant statistics in machine learning of ergodic Itô diffusions. (English) Zbl 1482.60108 Physica D 427, Article ID 133022, 28 p. (2021). MSC: 60J60 62G08 68T07 PDFBibTeX XMLCite \textit{H. Zhang} et al., Physica D 427, Article ID 133022, 28 p. (2021; Zbl 1482.60108) Full Text: DOI arXiv
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
Krishnamurthy, Vikram; Yin, George Langevin dynamics for adaptive inverse reinforcement learning of stochastic gradient algorithms. (English) Zbl 07370638 J. Mach. Learn. Res. 22, Paper No. 121, 49 p. (2021). MSC: 68T05 PDFBibTeX XMLCite \textit{V. Krishnamurthy} and \textit{G. Yin}, J. Mach. Learn. Res. 22, Paper No. 121, 49 p. (2021; Zbl 07370638) Full Text: arXiv Link
Azmi, Behzad; Kalise, Dante; Kunisch, Karl Optimal feedback law recovery by gradient-augmented sparse polynomial regression. (English) Zbl 07370565 J. Mach. Learn. Res. 22, Paper No. 48, 32 p. (2021). MSC: 68T05 PDFBibTeX XMLCite \textit{B. Azmi} et al., J. Mach. Learn. Res. 22, Paper No. 48, 32 p. (2021; Zbl 07370565) Full Text: arXiv Link
Lim, Soon Hoe Understanding recurrent neural networks using nonequilibrium response theory. (English) Zbl 07370564 J. Mach. Learn. Res. 22, Paper No. 47, 48 p. (2021). MSC: 68T05 PDFBibTeX XMLCite \textit{S. H. Lim}, J. Mach. Learn. Res. 22, Paper No. 47, 48 p. (2021; Zbl 07370564) Full Text: arXiv Link
Kovachki, Nikola B.; Stuart, Andrew M. Continuous time analysis of momentum methods. (English) Zbl 07370534 J. Mach. Learn. Res. 22, Paper No. 17, 40 p. (2021). MSC: 68T05 PDFBibTeX XMLCite \textit{N. B. Kovachki} and \textit{A. M. Stuart}, J. Mach. Learn. Res. 22, Paper No. 17, 40 p. (2021; Zbl 07370534) Full Text: arXiv Link
Goudenège, Ludovic; Molent, Andrea; Zanette, Antonino Machine learning for pricing American options in high-dimensional Markovian and non-Markovian models. (English) Zbl 1466.91339 Quant. Finance 20, No. 4, 573-591 (2020). MSC: 91G20 60G40 68T05 PDFBibTeX XMLCite \textit{L. Goudenège} et al., Quant. Finance 20, No. 4, 573--591 (2020; Zbl 1466.91339) Full Text: DOI arXiv
Vulpiani, Angelo; Baldovin, Marco Effective equations in complex systems: from Langevin to machine learning. (English) Zbl 1459.82246 J. Stat. Mech. Theory Exp. 2020, No. 1, Article ID 014003, 18 p. (2020). MSC: 82C31 68T05 PDFBibTeX XMLCite \textit{A. Vulpiani} and \textit{M. Baldovin}, J. Stat. Mech. Theory Exp. 2020, No. 1, Article ID 014003, 18 p. (2020; Zbl 1459.82246) Full Text: DOI arXiv
Pozharskiy, Dmitry; Wichrowski, Noah J.; Duncan, Andrew B.; Pavliotis, Grigorios A.; Kevrekidis, Ioannis G. Manifold learning for accelerating coarse-grained optimization. (English) Zbl 1450.37082 J. Comput. Dyn. 7, No. 2, 511-536 (2020). MSC: 37M99 37N40 68U01 68T05 90C56 PDFBibTeX XMLCite \textit{D. Pozharskiy} et al., J. Comput. Dyn. 7, No. 2, 511--536 (2020; Zbl 1450.37082) Full Text: DOI arXiv
Fan, Yuwei; Orozco Bohorquez, Cindy; Ying, Lexing BCR-net: A neural network based on the nonstandard wavelet form. (English) Zbl 1451.65244 J. Comput. Phys. 384, 1-15 (2019). MSC: 65T60 68T07 35J15 PDFBibTeX XMLCite \textit{Y. Fan} et al., J. Comput. Phys. 384, 1--15 (2019; Zbl 1451.65244) Full Text: DOI arXiv
Eigel, Martin; Schneider, Reinhold; Trunschke, Philipp; Wolf, Sebastian Variational Monte Carlo – bridging concepts of machine learning and high-dimensional partial differential equations. (English) Zbl 1435.68258 Adv. Comput. Math. 45, No. 5-6, 2503-2532 (2019). MSC: 68T05 15A69 35R60 62J02 65C05 65D15 65N22 65N30 PDFBibTeX XMLCite \textit{M. Eigel} et al., Adv. Comput. Math. 45, No. 5--6, 2503--2532 (2019; Zbl 1435.68258) Full Text: DOI arXiv
Tang, Shaoqiang; Zhang, Lei; Liu, Wing Kam From virtual clustering analysis to self-consistent clustering analysis: a mathematical study. (English) Zbl 1471.74079 Comput. Mech. 62, No. 6, 1443-1460 (2018). MSC: 74S99 74Q99 68T05 PDFBibTeX XMLCite \textit{S. Tang} et al., Comput. Mech. 62, No. 6, 1443--1460 (2018; Zbl 1471.74079) Full Text: DOI
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
Ni, Wei; Zhao, Dongya; Ni, Yuanhua; Wang, Xiaoli Stochastic averaging approach to leader-following consensus of linear multi-agent systems. (English) Zbl 1347.93024 J. Franklin Inst. 353, No. 12, 2650-2669 (2016). MSC: 93A14 68T42 93C05 PDFBibTeX XMLCite \textit{W. Ni} et al., J. Franklin Inst. 353, No. 12, 2650--2669 (2016; Zbl 1347.93024) Full Text: DOI
Feuillet, Mathieu; Robert, Philippe A scaling analysis of a transient stochastic network. (English) Zbl 1303.60085 Adv. Appl. Probab. 46, No. 2, 516-535 (2014). Reviewer: Vyacheslav Abramov (Melbourne) MSC: 60K25 60F05 68M14 90B05 PDFBibTeX XMLCite \textit{M. Feuillet} and \textit{P. Robert}, Adv. Appl. Probab. 46, No. 2, 516--535 (2014; Zbl 1303.60085) Full Text: DOI arXiv Euclid