{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T04:03:14Z","timestamp":1784520194945,"version":"3.55.0"},"reference-count":70,"publisher":"Springer Science and Business Media LLC","issue":"13","license":[{"start":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T00:00:00Z","timestamp":1782172800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T00:00:00Z","timestamp":1782172800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100005714","name":"Office of Experimental Program to Stimulate Competitive Research","doi-asserted-by":"publisher","award":["FA9550-22-1-0303"],"award-info":[{"award-number":["FA9550-22-1-0303"]}],"id":[{"id":"10.13039\/100005714","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-23-1-0033"],"award-info":[{"award-number":["FA9550-23-1-0033"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014072","name":"National Coordination Office","doi-asserted-by":"publisher","award":["1937460 and 2234919"],"award-info":[{"award-number":["1937460 and 2234919"]}],"id":[{"id":"10.13039\/100014072","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Air Force Research Laboratory (AFRL) Regional Network \u2013 Midwest"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2026,7]]},"DOI":"10.1007\/s00521-026-12289-4","type":"journal-article","created":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T08:16:50Z","timestamp":1782202610000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Topology-informed deep learning estimation using feedforward attention layer for high-rate state estimation"],"prefix":"10.1007","volume":"38","author":[{"given":"Arman","family":"Razmarashooli","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Metrid","family":"Okumu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel","family":"Salazar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yang Kang","family":"Chua","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Simon","family":"Laflamme","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chao","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paul T.","family":"Schrader","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Erik","family":"Blasch","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,23]]},"reference":[{"key":"12289_CR1","doi-asserted-by":"crossref","unstructured":"Dodson J, Downey A, Laflamme S, Todd MD, Moura AG, Wang Y, Mao Z, Avitabile P, Blasch E (2022) High-rate structural health monitoring and prognostics: An overview. Data science in engineering, Volume 9: proceedings of the 39th IMAC, a conference and exposition on structural dynamics 2021. Springer, pp 213\u2013217","DOI":"10.1007\/978-3-030-76004-5_23"},{"key":"12289_CR2","doi-asserted-by":"publisher","first-page":"108201","DOI":"10.1016\/j.ymssp.2021.108201","volume":"164","author":"V Barzegar","year":"2022","unstructured":"Barzegar V, Laflamme S, Hu C, Dodson J (2022) Ensemble of recurrent neural networks with long short-term memory cells for high-rate structural health monitoring. Mech Syst Signal Process 164:108201","journal-title":"Mech Syst Signal Process"},{"issue":"10","key":"12289_CR3","doi-asserted-by":"publisher","first-page":"103001","DOI":"10.1088\/1361-6501\/ae3abb","volume":"37","author":"S Laflamme","year":"2026","unstructured":"Laflamme S, Blasch E, Ubertini F, Liu Z, Wertz J, Knott C, Cherry M, Lindgren E, Chang FK, Kumar A et al (2026) Roadmap: Integrating artificial intelligence in structural health monitoring systems. Meas Sci Technol 37(10):103001","journal-title":"Meas Sci Technol"},{"key":"12289_CR4","doi-asserted-by":"publisher","first-page":"106551","DOI":"10.1016\/j.ymssp.2019.106551","volume":"138","author":"A Downey","year":"2020","unstructured":"Downey A, Hong J, Dodson J, Carroll M, Scheppegrell J (2020) Millisecond model updating for structures experiencing unmodeled high-rate dynamic events. Mech Syst Signal Process 138:106551","journal-title":"Mech Syst Signal Process"},{"key":"12289_CR5","doi-asserted-by":"publisher","first-page":"5015","DOI":"10.1007\/s00521-018-3927-x","volume":"32","author":"J Hong","year":"2020","unstructured":"Hong J, Laflamme S, Cao L, Dodson J, Joyce B (2020) Variable input observer for nonstationary high-rate dynamic systems. Neural Comput Appl 32:5015\u20135026","journal-title":"Neural Comput Appl"},{"key":"12289_CR6","doi-asserted-by":"publisher","first-page":"109536","DOI":"10.1016\/j.ymssp.2022.109536","volume":"182","author":"M Nelson","year":"2023","unstructured":"Nelson M, Barzegar V, Laflamme S, Hu C, Downey AR, Bakos JD, Thelen A, Dodson J (2023) Multi-step ahead state estimation with hybrid algorithm for high-rate dynamic systems. Mech Syst Signal Process 182:109536","journal-title":"Mech Syst Signal Process"},{"key":"12289_CR7","first-page":"1","volume":"2","author":"F Darema","year":"2023","unstructured":"Darema F, Blasch EP, Ravela S, Aved AJ (2023) The dynamic data driven applications systems (dddas) paradigm and emerging directions. Handbook Dyn Data Driven Appl Syst 2:1\u201351","journal-title":"Handbook Dyn Data Driven Appl Syst"},{"key":"12289_CR8","doi-asserted-by":"crossref","unstructured":"Diligenti M, Roychowdhury S, Gori M (2017) Integrating prior knowledge into deep learning. 16th IEEE International Conference on Machine Learning and Applications (ICMLA). IEEE, pp 920\u2013923","DOI":"10.1109\/ICMLA.2017.00-37"},{"key":"12289_CR9","doi-asserted-by":"crossref","unstructured":"Daw A, Karpatne A, Watkins WD, Read JS, Kumar V (2022) Physics-guided neural networks (pgnn): An application in lake temperature modeling. Knowledge guided machine learning. Chapman and Hall\/CRC, Boca Raton, pp 353\u2013372","DOI":"10.1201\/9781003143376-15"},{"key":"12289_CR10","doi-asserted-by":"crossref","unstructured":"Blasch E (2018) Dddas advantages from high-dimensional simulation. Winter simulation conference (WSC). IEEE, pp 1418\u20131429","DOI":"10.1109\/WSC.2018.8632336"},{"key":"12289_CR11","doi-asserted-by":"crossref","unstructured":"Ahmed SF, Alam MSB, Hassan M, Rozbu MR, Ishtiak T, Rafa N, Mofijur M, Shawkat Ali A, Gandomi AH (2023) Deep learning modelling techniques: current progress, applications, advantages, and challenges. Artif Intell Rev 56(11):13521\u201313617","DOI":"10.1007\/s10462-023-10466-8"},{"issue":"6","key":"12289_CR12","doi-asserted-by":"publisher","first-page":"7833","DOI":"10.1109\/JSEN.2019.2923982","volume":"21","author":"Z Han","year":"2019","unstructured":"Han Z, Zhao J, Leung H, Ma KF, Wang W (2019) A review of deep learning models for time series prediction. IEEE Sens J 21(6):7833\u20137848","journal-title":"IEEE Sens J"},{"key":"12289_CR13","doi-asserted-by":"crossref","unstructured":"Fan Z, Shen D, Bao Y, Pham K, Blasch E, Chen G (2024) Rnn-ukf: enhancing hyperparameter auto-tuning in unscented kalman filters through recurrent neural networks. In: 2024 27th international conference on information fusion (FUSION). IEEE, pp 1\u20138","DOI":"10.23919\/FUSION59988.2024.10706523"},{"key":"12289_CR14","doi-asserted-by":"publisher","first-page":"112995","DOI":"10.1016\/j.enconman.2020.112995","volume":"217","author":"H Liu","year":"2020","unstructured":"Liu H, Yang R, Duan Z (2020) Wind speed forecasting using a new multi-factor fusion and multi-resolution ensemble model with real-time decomposition and adaptive error correction. Energy Convers Manage 217:112995","journal-title":"Energy Convers Manage"},{"issue":"2","key":"12289_CR15","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1162\/neco.1994.6.2.181","volume":"6","author":"MI Jordan","year":"1994","unstructured":"Jordan MI, Jacobs RA (1994) Hierarchical mixtures of experts and the em algorithm. Neural Comput 6(2):181\u2013214","journal-title":"Neural Comput"},{"key":"12289_CR16","unstructured":"Zeevi A, Meir R, Adler R (1996) Time series prediction using mixtures of experts. Adv Neural Inf Process Syst 9"},{"key":"12289_CR17","unstructured":"Shazeer N, Mirhoseini A, Maziarz K, Davis A, Le Q, Hinton G, Dean J (2017) Outrageously large neural networks: the sparsely-gated mixture-of-experts layer. arXiv preprint arXiv:1701.06538"},{"key":"12289_CR18","unstructured":"Ni R, Lin Z, Wang S, Fanti G (2024) Mixture-of-linear-experts for long-term time series forecasting. In: International Conference on Artificial Intelligence and Statistics. pp 4672\u20134680. PMLR"},{"key":"12289_CR19","unstructured":"Ortigossa ES, Lutsker G, Segal E (2026) Mohets: long-term time series forecasting with mixture-of-heterogeneous-experts. arXiv preprint arXiv:2601.21866"},{"key":"12289_CR20","doi-asserted-by":"crossref","unstructured":"Qiu X, Wu X, Lin Y, Guo C, Hu J, Yang B (2025) Duet: dual clustering enhanced multivariate time series forecasting. In: Proceedings of the 31st ACM SIGKDD conference on knowledge discovery and data mining V. 1. pp 1185\u20131196","DOI":"10.1145\/3690624.3709325"},{"key":"12289_CR21","unstructured":"Liu X, Liu J, Woo G, Aksu T, Liang Y, Zimmermann R, Liu C, Savarese S, Xiong C, Sahoo D (2024) Moirai-moe: empowering time series foundation models with sparse mixture of experts. arXiv preprint arXiv:2410.10469"},{"key":"12289_CR22","unstructured":"Chen P, Zhang Y, Cheng Y, Shu Y, Wang Y, Wen Q, Yang B, Guo C (2024) Pathformer: multi-scale transformers with adaptive pathways for time series forecasting. arXiv preprint arXiv:2402.05956"},{"issue":"3","key":"12289_CR23","doi-asserted-by":"publisher","first-page":"1658","DOI":"10.1109\/TII.2020.2991796","volume":"17","author":"M Ma","year":"2020","unstructured":"Ma M, Mao Z (2020) Deep-convolution-based lstm network for remaining useful life prediction. IEEE Trans Indust Inform 17(3):1658\u20131667","journal-title":"IEEE Trans Indust Inform"},{"key":"12289_CR24","doi-asserted-by":"crossref","unstructured":"Todisco M, Mao Z (2025) High-rate damage classification and lifecycle prediction. Data science in engineering, Volume 9: proceedings of the 39th IMAC, a conference and exposition on structural dynamics 2021. CRC Press, pp 225-[object Object]","DOI":"10.1007\/978-3-030-76004-5_25"},{"key":"12289_CR25","doi-asserted-by":"crossref","unstructured":"Du S, Li T, Yang Y, Horng S-J (2020) Multivariate time series forecasting via attention-based encoder-decoder framework. Neurocomputing 388:269\u2013279","DOI":"10.1016\/j.neucom.2019.12.118"},{"key":"12289_CR26","unstructured":"Keles FD, Wijewardena PM, Hegde C (2023) On the computational complexity of self-attention. In: International conference on algorithmic learning theory. pp 597\u2013619. PMLR"},{"key":"12289_CR27","doi-asserted-by":"crossref","unstructured":"Wang D, Chen C (2023) Spatiotemporal self-attention-based lstnet for multivariate time series prediction. Int J Intell Syst 2023(1):9523230","DOI":"10.1155\/2023\/9523230"},{"key":"12289_CR28","doi-asserted-by":"crossref","unstructured":"Cheng H, Tan P-N, Gao J, Scripps J (2006) Multistep-ahead time series prediction. In: Advances in knowledge discovery and data mining: 10th Pacific-Asia conference, PAKDD 2006, Singapore, 2006. Proceedings 10, pp. 765\u2013774. Springer","DOI":"10.1007\/11731139_89"},{"issue":"1","key":"12289_CR29","doi-asserted-by":"publisher","first-page":"6","DOI":"10.3390\/tomography11010006","volume":"11","author":"Y Singh","year":"2025","unstructured":"Singh Y, Quaia E (2025) Unraveling the invisible: Topological data analysis as the new frontier in radiology\u2019s diagnostic arsenal. Tomography 11(1):6","journal-title":"Tomography"},{"key":"12289_CR30","doi-asserted-by":"crossref","unstructured":"Conti F, Moroni D, Pascali MA (2022) A topological machine learning pipeline for classification. Mathematics 10(17):3086","DOI":"10.3390\/math10173086"},{"key":"12289_CR31","doi-asserted-by":"crossref","unstructured":"Majumdar S, Laha AK (2020) Clustering and classification of time series using topological data analysis with applications to finance. Expert Syst Appl 162:113868","DOI":"10.1016\/j.eswa.2020.113868"},{"key":"12289_CR32","doi-asserted-by":"publisher","DOI":"10.1017\/9781108975704","volume-title":"Topological Data Analysis with Applications","author":"G Carlsson","year":"2021","unstructured":"Carlsson G, Vejdemo-Johansson M (2021) Topological Data Analysis with Applications. Cambridge University Press, Cambridge, UK"},{"key":"12289_CR33","first-page":"228","volume":"12","author":"Y Umeda","year":"2017","unstructured":"Umeda Y (2017) Time series classification via topological data analysis. Inform Media Technol 12:228\u2013239","journal-title":"Inform Media Technol"},{"issue":"1","key":"12289_CR34","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1137\/22M1476848","volume":"22","author":"A Myers","year":"2023","unstructured":"Myers A, Khasawneh FA, Munch E (2023) Persistence of weighted ordinal partition networks for dynamic state detection. SIAM J Appl Dyn Syst 22(1):65\u201389","journal-title":"SIAM J Appl Dyn Syst"},{"issue":"3","key":"12289_CR35","doi-asserted-by":"publisher","first-page":"1955","DOI":"10.3150\/24-BEJ1793","volume":"31","author":"F Chazal","year":"2025","unstructured":"Chazal F, Michel B, Reise W (2025) Topological signatures of periodic-like signals. Bernoulli 31(3):1955\u20131990","journal-title":"Bernoulli"},{"key":"12289_CR36","unstructured":"Tanweer S, Mamis K, Khasawneh FA (2025) Use of Topological Data Analysis for the Detection of Phenomenological Bifurcations in Stochastic Epidemiological Models. arXiv:2504.13215 (submitted)"},{"key":"12289_CR37","doi-asserted-by":"publisher","first-page":"112048","DOI":"10.1016\/j.ymssp.2024.112048","volume":"224","author":"A Razmarashooli","year":"2025","unstructured":"Razmarashooli A, Chua YK, Barzegar V, Salazar D, Laflamme S, Hu C, Downey AR, Dodson J, Schrader PT (2025) Real-time state estimation of nonstationary systems through dominant fundamental frequency using topological data analysis features. Mech Syst Signal Process 224:112048","journal-title":"Mech Syst Signal Process"},{"key":"12289_CR38","doi-asserted-by":"publisher","first-page":"112319","DOI":"10.1016\/j.ymssp.2025.112319","volume":"227","author":"YK Chua","year":"2025","unstructured":"Chua YK, Coble D, Razmarashooli A, Paul S, Martinez DAS, Hu C, Downey AR, Laflamme S (2025) Probabilistic machine learning pipeline using topological descriptors for real-time state estimation of high-rate dynamic systems. Mech Syst Signal Process 227:112319","journal-title":"Mech Syst Signal Process"},{"key":"12289_CR39","doi-asserted-by":"crossref","unstructured":"Martinez DAS, Chua YK, Razmarashooli A, Okumu M, Laflamme S, Hu C, Schrader PT, Comert G, Begashaw N, Dodson J (2025) Investigation of fast topological data analysis feature extraction for high-rate dynamic prediction. In: 2025 AIAA DATC\/IEEE 44th digital avionics systems conference (DASC). IEEE, pp 1\u20139","DOI":"10.1109\/DASC66011.2025.11257270"},{"key":"12289_CR40","unstructured":"Martinez DAS, Razmarashooli A, Chua YK, Laflamme S, Hu C, Schrader PT, Downey ARJ, Bakos JD, Comert G, Begashaw N, Dodson J (2024) Fast topological data analysis feature for nonstationary time series. p 1551"},{"issue":"2","key":"12289_CR41","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1088\/0256-307X\/17\/2\/004","volume":"17","author":"J-S Zhang","year":"2000","unstructured":"Zhang J-S, Xiao X-C (2000) Predicting chaotic time series using recurrent neural network. Chin Phys Lett 17(2):88","journal-title":"Chin Phys Lett"},{"key":"12289_CR42","doi-asserted-by":"crossref","unstructured":"Tan E, Algar S, Corr\u00eaa D, Small M, Stemler T, Walker D (2023) Selecting embedding delays: an overview of embedding techniques and a new method using persistent homology. An Interdisciplinary J Nonlinear Sci 33(3)","DOI":"10.1063\/5.0137223"},{"key":"12289_CR43","doi-asserted-by":"publisher","first-page":"110045","DOI":"10.1016\/j.chaos.2020.110045","volume":"139","author":"M Sangiorgio","year":"2020","unstructured":"Sangiorgio M, Dercole F (2020) Robustness of lstm neural networks for multi-step forecasting of chaotic time series. Chaos Solit Fract 139:110045","journal-title":"Chaos Solit Fract"},{"key":"12289_CR44","doi-asserted-by":"crossref","unstructured":"Kim W, Goyal B, Chawla K, Lee J, Kwon K (2018) Attention-based ensemble for deep metric learning. In: Proceedings of the european conference on computer vision (ECCV). pp 736\u2013751","DOI":"10.1007\/978-3-030-01246-5_45"},{"key":"12289_CR45","unstructured":"Zhang C, Song Q, Zhou H, Ou Y, Deng H, Yang LT (2021) Revisiting recursive least squares for training deep neural networks. arXiv preprint arXiv:2109.03220"},{"key":"12289_CR46","doi-asserted-by":"publisher","first-page":"650","DOI":"10.1016\/j.procir.2021.03.088","volume":"99","author":"B Lindemann","year":"2021","unstructured":"Lindemann B, M\u00fcller T, Vietz H, Jazdi N, Weyrich M (2021) A survey on long short-term memory networks for time series prediction. Procedia Cirp 99:650\u2013655","journal-title":"Procedia Cirp"},{"issue":"8","key":"12289_CR47","doi-asserted-by":"publisher","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","volume":"9","author":"S Hochreiter","year":"1997","unstructured":"Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735\u20131780","journal-title":"Neural Comput"},{"issue":"2","key":"12289_CR48","first-page":"47","volume":"4","author":"E Munch","year":"2017","unstructured":"Munch E (2017) A user\u2019s guide to topological data analysis. J Learn Anal 4(2):47\u201361","journal-title":"J Learn Anal"},{"key":"12289_CR49","volume-title":"A topology-based approach for nonlinear time series with applications in computer performance analysis","author":"Z Alexander","year":"2012","unstructured":"Alexander Z (2012) A topology-based approach for nonlinear time series with applications in computer performance analysis. Boulder, CO, USA"},{"key":"12289_CR50","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511755798","volume-title":"Nonlinear Time Series Analysis","author":"H Kantz","year":"2003","unstructured":"Kantz H, Schreiber T (2003) Nonlinear Time Series Analysis. Cambridge University Press, Cambridge, UK"},{"key":"12289_CR51","doi-asserted-by":"crossref","unstructured":"Deshmukh V, Bradley E, Garland J, Meiss JD (2020) Using curvature to select the time lag for delay reconstruction. Chaos An Interdisciplinary J Nonlinear Sci 30(6)","DOI":"10.1063\/5.0005890"},{"issue":"6","key":"12289_CR52","doi-asserted-by":"publisher","first-page":"066220","DOI":"10.1103\/PhysRevE.81.066220","volume":"81","author":"DJ Cross","year":"2010","unstructured":"Cross DJ, Gilmore R (2010) Differential embedding of the lorenz attractor. Phys Rev E Stat Nonlinear Soft Matter Phys 81(6):066220","journal-title":"Phys Rev E Stat Nonlinear Soft Matter Phys"},{"key":"12289_CR53","doi-asserted-by":"publisher","first-page":"1149","DOI":"10.1016\/S0098-1354(97)00204-4","volume":"21","author":"C Rhodes","year":"1997","unstructured":"Rhodes C, Morari M (1997) The false nearest neighbors algorithm: An overview. Comput Chem Eng 21:1149\u20131154","journal-title":"Comput Chem Eng"},{"key":"12289_CR54","doi-asserted-by":"crossref","unstructured":"Takens F (1981) Detecting strange attractors in turbulence. In: Lecture notes in mathematics, pp. 366\u2013381. Springer, Berlin","DOI":"10.1007\/BFb0091924"},{"key":"12289_CR55","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s003329900072","volume":"9","author":"J Stark","year":"1999","unstructured":"Stark J (1999) Delay embeddings for forced systems. i. deterministic forcing. J Nonlinear Sci 9:255\u2013332","journal-title":"J Nonlinear Sci"},{"key":"12289_CR56","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1007\/s00332-003-0534-4","volume":"13","author":"J Stark","year":"2003","unstructured":"Stark J, Broomhead DS, Davies ME, Huke J (2003) Delay embeddings for forced systems. ii. stochastic forcing. J Nonlinear Sci 13:519\u2013577","journal-title":"J Nonlinear Sci"},{"issue":"2","key":"12289_CR57","doi-asserted-by":"publisher","first-page":"022314","DOI":"10.1103\/PhysRevE.100.022314","volume":"100","author":"A Myers","year":"2019","unstructured":"Myers A, Munch E, Khasawneh FA (2019) Persistent homology of complex networks for dynamic state detection. Phys Rev E 100(2):022314","journal-title":"Phys Rev E"},{"issue":"15\u201316","key":"12289_CR58","doi-asserted-by":"publisher","first-page":"6026","DOI":"10.1016\/j.eswa.2015.04.010","volume":"42","author":"CM Pereira","year":"2015","unstructured":"Pereira CM, Mello RF (2015) Persistent homology for time series and spatial data clustering. Expert Syst Appl 42(15\u201316):6026\u20136038","journal-title":"Expert Syst Appl"},{"key":"12289_CR59","doi-asserted-by":"publisher","first-page":"108","DOI":"10.3389\/frai.2021.667963","volume":"4","author":"F Chazal","year":"2021","unstructured":"Chazal F, Michel B (2021) An introduction to topological data analysis: fundamental and practical aspects for data scientists. Front Artif Intell 4:108","journal-title":"Front Artif Intell"},{"key":"12289_CR60","doi-asserted-by":"crossref","unstructured":"Cohen-Steiner D, Edelsbrunner H, Harer J (2005) Stability of persistence diagrams. In: Proceedings of the twenty-first annual symposium on computational geometry. pp 263\u2013271","DOI":"10.1145\/1064092.1064133"},{"key":"12289_CR61","volume-title":"Computational Topology: an Introduction","author":"H Edelsbrunner","year":"2022","unstructured":"Edelsbrunner H, Harer JL (2022) Computational Topology: an Introduction. American Mathematical Society, Providence, RI, USA"},{"key":"12289_CR62","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1016\/j.neucom.2015.11.059","volume":"177","author":"W Pan","year":"2016","unstructured":"Pan W (2016) A survey of transfer learning for collaborative recommendation with auxiliary data. Neurocomputing 177:447\u2013453","journal-title":"Neurocomputing"},{"key":"12289_CR63","volume-title":"Applied Nonlinear Time Series Analysis: Applications in Physics, Physiology and Finance","author":"M Small","year":"2005","unstructured":"Small M (2005) Applied Nonlinear Time Series Analysis: Applications in Physics, Physiology and Finance, vol 52. World Scientific, Singapore"},{"key":"12289_CR64","doi-asserted-by":"crossref","unstructured":"An NH, Anh DT (2015) Comparison of strategies for multi-step-ahead prediction of time series using neural network. In: 2015 international conference on advanced computing and applications (ACOMP), pp. 142\u2013149. IEEE","DOI":"10.1109\/ACOMP.2015.24"},{"key":"12289_CR65","doi-asserted-by":"publisher","DOI":"10.1017\/9781316761403","volume-title":"Advanced Structural Dynamics","author":"E Kausel","year":"2017","unstructured":"Kausel E (2017) Advanced Structural Dynamics. Cambridge University Press, Cambridge, UK"},{"key":"12289_CR66","doi-asserted-by":"crossref","unstructured":"Arai K, Eto K, da M (2024) Method for prediction of motion based on recursive least squares method with time warp parameter and its application to physical therapy. International J Adv Comput Sci & Appl 15(7)","DOI":"10.14569\/IJACSA.2024.0150714"},{"issue":"4","key":"12289_CR67","doi-asserted-by":"publisher","first-page":"044401","DOI":"10.1088\/2633-1357\/aca0d2","volume":"3","author":"M Nelson","year":"2022","unstructured":"Nelson M, Laflamme S, Hu C, Moura AG, Hong J, Downey A, Lander P, Wang Y, Blasch E, Dodson J (2022) Generated datasets from dynamic reproduction of projectiles in ballistic environments for advanced research (dropbear) testbed. IOP SciNotes 3(4):044401","journal-title":"IOP SciNotes"},{"key":"12289_CR68","doi-asserted-by":"crossref","unstructured":"Zeng A, Chen M, Zhang L, Xu Q (2023) Are transformers effective for time series forecasting? In Proceedings of the AAAI Conference on Artificial Intelligence 37:11121\u201311128","DOI":"10.1609\/aaai.v37i9.26317"},{"key":"12289_CR69","doi-asserted-by":"crossref","unstructured":"Li Z, Qi S, Li Y, Xu Z (2026) Revisiting long-term time series forecasting: an investigation on affine mapping. Academia AI and Applications 2(2)","DOI":"10.20935\/AcadAI8236"},{"key":"12289_CR70","doi-asserted-by":"crossref","unstructured":"Zhou H, Zhang S, Peng J, Zhang S, Li J, Xiong H, Zhang W (2021) Informer: beyond efficient transformer for long sequence time-series forecasting. In Proceedings of the AAAI Conference on Artificial Intelligence 35:11106\u201311115","DOI":"10.1609\/aaai.v35i12.17325"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-026-12289-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-026-12289-4","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-026-12289-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T03:38:49Z","timestamp":1784518729000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-026-12289-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,23]]},"references-count":70,"journal-issue":{"issue":"13","published-print":{"date-parts":[[2026,7]]}},"alternative-id":["12289"],"URL":"https:\/\/doi.org\/10.1007\/s00521-026-12289-4","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,23]]},"assertion":[{"value":"16 September 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 May 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 June 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":1,"name":"Ethics","label":"Competing interests","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"531"}}