{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T22:27:25Z","timestamp":1782944845544,"version":"3.54.5"},"reference-count":52,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T00:00:00Z","timestamp":1764201600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T00:00:00Z","timestamp":1764201600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Evolving Systems"],"published-print":{"date-parts":[[2026,2]]},"DOI":"10.1007\/s12530-025-09765-y","type":"journal-article","created":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T05:42:20Z","timestamp":1764222140000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A hybrid PINNs approach to capture interest rate dynamics in short-rate model"],"prefix":"10.1007","volume":"17","author":[{"given":"Indu","family":"Rani","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chandan Kumar","family":"Verma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,11,27]]},"reference":[{"issue":"4","key":"9765_CR1","doi-asserted-by":"publisher","first-page":"52","DOI":"10.2469\/faj.v47.n4.52","volume":"47","author":"F Black","year":"1991","unstructured":"Black F, Karasinski P (1991) Bond and option pricing when short rates are lognormal. Financ Anal J 47(4):52\u201359. https:\/\/doi.org\/10.2469\/faj.v47.n4.52","journal-title":"Financ Anal J"},{"key":"9765_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-34604-3","volume-title":"Interest rate models-theory and practice: with smile, inflation and credit","author":"D Brigo","year":"2006","unstructured":"Brigo D, Mercurio F (2006) Interest rate models-theory and practice: with smile, inflation and credit, vol 2. Springer, Berlin. https:\/\/doi.org\/10.1007\/978-3-540-34604-3"},{"key":"9765_CR3","doi-asserted-by":"publisher","DOI":"10.1002\/9781118182635.efm0126","author":"GW Buetow Jr","year":"2012","unstructured":"Buetow GW Jr, Fabozzi FJ, Sochacki J (2012) A review of no arbitrage interest rate models. Encycl Financ Models. https:\/\/doi.org\/10.1002\/9781118182635.efm0126","journal-title":"Encycl Financ Models"},{"key":"9765_CR4","doi-asserted-by":"publisher","unstructured":"Burgess N (2014) An overview of the vasicek short rate model. Available at SSRN 2479671. https:\/\/doi.org\/10.2139\/ssrn.2479671","DOI":"10.2139\/ssrn.2479671"},{"issue":"1","key":"9765_CR5","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1504\/IJFMD.2024.140636","volume":"10","author":"S Chaudhuri","year":"2024","unstructured":"Chaudhuri S, Pandey A (2024) Equilibrium interest rate models for the Indian government security market. Int J Financ Mark Deriv 10(1):70\u201386. https:\/\/doi.org\/10.1504\/IJFMD.2024.140636","journal-title":"Int J Financ Mark Deriv"},{"key":"9765_CR6","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.ins.2019.05.048","volume":"498","author":"MR Chen","year":"2019","unstructured":"Chen MR, Zeng GQ, Lu KD (2019) A many-objective population extremal optimization algorithm with an adaptive hybrid mutation operation. Inf Sci 498:62\u201390. https:\/\/doi.org\/10.1016\/j.ins.2019.05.048","journal-title":"Inf Sci"},{"issue":"8","key":"9765_CR7","doi-asserted-by":"publisher","first-page":"11618","DOI":"10.1364\/OE.384875","volume":"28","author":"Y Chen","year":"2020","unstructured":"Chen Y, Lu L, Karniadakis GE et al (2020) Physics-informed neural networks for inverse problems in nano-optics and metamaterials. Opt Express 28(8):11618\u201311633. https:\/\/doi.org\/10.1364\/OE.384875","journal-title":"Opt Express"},{"key":"9765_CR8","doi-asserted-by":"publisher","DOI":"10.1142\/9789812701022_0005","author":"JC Cox","year":"2005","unstructured":"Cox JC, Ingersoll JE Jr, Ross SA (2005) A theory of the term structure of interest rates. Theory Valuat. https:\/\/doi.org\/10.1142\/9789812701022_0005","journal-title":"Theory Valuat"},{"issue":"2","key":"9765_CR9","first-page":"61","volume":"16","author":"A Dixit","year":"2023","unstructured":"Dixit A, Jain S (2023) Contemporary approaches to analyze non-stationary time-series: some solutions and challenges. Recent Adva Comput Sci Commu (Formerly: Recent Patents on Computer Science) 16(2):61\u201380","journal-title":"Recent Adva Comput Sci Commu (Formerly: Recent Patents on Computer Science)"},{"issue":"7","key":"9765_CR10","doi-asserted-by":"publisher","first-page":"872","DOI":"10.1007\/s42979-024-03190-9","volume":"5","author":"A Dixit","year":"2024","unstructured":"Dixit A, Jain S (2024) A novel approach for optimal cluster identification and n-order hesitation based time series forecasting. SN Comput Sci 5(7):872. https:\/\/doi.org\/10.1007\/s42979-024-03190-9","journal-title":"SN Comput Sci"},{"issue":"10","key":"9765_CR11","doi-asserted-by":"publisher","first-page":"5859","DOI":"10.1109\/TNNLS.2021.3071603","volume":"33","author":"M Fan","year":"2021","unstructured":"Fan M, Zhang X, Hu J et al (2021) Adaptive data structure regularized multiclass discriminative feature selection. IEEE Trans Neural Netw Learn Syst 33(10):5859\u20135872. https:\/\/doi.org\/10.1109\/TNNLS.2021.3071603","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"9765_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.heliyon.2024.e30206","author":"Y Guan","year":"2024","unstructured":"Guan Y, Fang Z, Wang X et al (2024) Dynamic characteristics of expectations of short-term interest rate and a generalized vasicek model. Heliyon. https:\/\/doi.org\/10.1016\/j.heliyon.2024.e30206","journal-title":"Heliyon"},{"issue":"17","key":"9765_CR13","doi-asserted-by":"publisher","first-page":"5917","DOI":"10.3390\/app10175917","volume":"10","author":"Y Guo","year":"2020","unstructured":"Guo Y, Cao X, Liu B et al (2020) Solving partial differential equations using deep learning and physical constraints. Appl Sci 10(17):5917. https:\/\/doi.org\/10.3390\/app10175917","journal-title":"Appl Sci"},{"key":"9765_CR14","doi-asserted-by":"publisher","DOI":"10.2307\/2951677","author":"D Heath","year":"1992","unstructured":"Heath D, Jarrow R, Morton A (1992) Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econom J Econ Soc. https:\/\/doi.org\/10.2307\/2951677","journal-title":"Econom J Econ Soc"},{"issue":"01","key":"9765_CR15","doi-asserted-by":"publisher","first-page":"1650004","DOI":"10.1142\/S2010495216500044","volume":"11","author":"LY Hin","year":"2016","unstructured":"Hin LY, Dokuchaev N (2016) Short rate forecasting based on the inference from the cir model for multiple yield curve dynamics. Ann Financ Econ 11(01):1650004. https:\/\/doi.org\/10.1142\/S2010495216500044","journal-title":"Ann Financ Econ"},{"issue":"5","key":"9765_CR16","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.1111\/j.1540-6261.1986.tb02528.x","volume":"41","author":"TS Ho","year":"1986","unstructured":"Ho TS, Lee SB (1986) Term structure movements and pricing interest rate contingent claims. J Financ 41(5):1011\u20131029. https:\/\/doi.org\/10.1111\/j.1540-6261.1986.tb02528.x","journal-title":"J Financ"},{"key":"9765_CR18","volume-title":"Options, futures, and other derivatives","author":"JC Hull","year":"2016","unstructured":"Hull JC, Basu S (2016) Options, futures, and other derivatives. Pearson Education, Chennai"},{"issue":"4","key":"9765_CR19","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1093\/rfs\/3.4.573","volume":"3","author":"J Hull","year":"1990","unstructured":"Hull J, White A (1990) Pricing interest-rate-derivative securities. Rev Financ Stud 3(4):573\u2013592. https:\/\/doi.org\/10.1093\/rfs\/3.4.573","journal-title":"Rev Financ Stud"},{"issue":"2","key":"9765_CR20","doi-asserted-by":"publisher","first-page":"235","DOI":"10.2307\/2331288","volume":"28","author":"J Hull","year":"1993","unstructured":"Hull J, White A (1993) One-factor interest-rate models and the valuation of interest-rate derivative securities. J Financ Quant Anal 28(2):235\u2013254. https:\/\/doi.org\/10.2307\/2331288","journal-title":"J Financ Quant Anal"},{"key":"9765_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2020.113028","volume":"365","author":"AD Jagtap","year":"2020","unstructured":"Jagtap AD, Kharazmi E, Karniadakis GE (2020) Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems. Comput Methods Appl Mech Eng 365:113028. https:\/\/doi.org\/10.1016\/j.cma.2020.113028","journal-title":"Comput Methods Appl Mech Eng"},{"key":"9765_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109951","volume":"426","author":"X Jin","year":"2021","unstructured":"Jin X, Cai S, Li H et al (2021) Nsfnets (Navier\u2013Stokes flow nets): physics-informed neural networks for the incompressible Navier\u2013Stokes equations. J Comput Phys 426:109951. https:\/\/doi.org\/10.1016\/j.jcp.2020.109951","journal-title":"J Comput Phys"},{"issue":"3","key":"9765_CR23","doi-asserted-by":"publisher","first-page":"42","DOI":"10.15611\/eada.2021.3.03","volume":"25","author":"D Josheski","year":"2021","unstructured":"Josheski D, Apostolov M (2021) Equilibrium short-rate models vs no-arbitrage models: literature review and computational examples. Econometrics 25(3):42\u201371. https:\/\/doi.org\/10.15611\/eada.2021.3.03","journal-title":"Econometrics"},{"issue":"2","key":"9765_CR24","first-page":"37","volume":"5","author":"S Kozp\u0131nar","year":"2021","unstructured":"Kozp\u0131nar S (2021) A brief look at ou, vasicek, cir and hull-white models through their actuarial applications. Ba\u015fkent \u00dcniversitesi Ticari Bilimler Fak\u00fcltesi Dergisi 5(2):37\u201349","journal-title":"Ba\u015fkent \u00dcniversitesi Ticari Bilimler Fak\u00fcltesi Dergisi"},{"key":"9765_CR25","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2022.108836","volume":"122","author":"R Kumar","year":"2022","unstructured":"Kumar R (2022) A lyapunov-stability-based context-layered recurrent pi-sigma neural network for the identification of nonlinear systems. Appl Soft Comput 122:108836. https:\/\/doi.org\/10.1016\/j.asoc.2022.108836","journal-title":"Appl Soft Comput"},{"issue":"22","key":"9765_CR26","doi-asserted-by":"publisher","first-page":"17313","DOI":"10.1007\/s00500-023-08061-8","volume":"27","author":"R Kumar","year":"2023","unstructured":"Kumar R (2023) Double internal loop higher-order recurrent neural network-based adaptive control of the nonlinear dynamical system. Soft Comput 27(22):17313\u201317331. https:\/\/doi.org\/10.1007\/s00500-023-08061-8","journal-title":"Soft Comput"},{"key":"9765_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2024.127524","volume":"580","author":"R Kumar","year":"2024","unstructured":"Kumar R (2024) Recurrent context layered radial basis function neural network for the identification of nonlinear dynamical systems. Neurocomputing 580:127524. https:\/\/doi.org\/10.1016\/j.neucom.2024.127524","journal-title":"Neurocomputing"},{"key":"9765_CR28","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.jedc.2018.07.004","volume":"94","author":"E Lehrer","year":"2018","unstructured":"Lehrer E, Light B (2018) The effect of interest rates on consumption in an income fluctuation problem. J Econ Dyn Control 94:63\u201371. https:\/\/doi.org\/10.1016\/j.jedc.2018.07.004","journal-title":"J Econ Dyn Control"},{"key":"9765_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2023.110558","volume":"145","author":"X Li","year":"2023","unstructured":"Li X, Fu Q, Li Q et al (2023) Multi-objective binary grey wolf optimization for feature selection based on guided mutation strategy. Appl Soft Comput 145:110558. https:\/\/doi.org\/10.1016\/j.asoc.2023.110558","journal-title":"Appl Soft Comput"},{"issue":"2","key":"9765_CR30","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/0304-405X(89)90056-1","volume":"23","author":"FA Longstaff","year":"1989","unstructured":"Longstaff FA (1989) A nonlinear general equilibrium model of the term structure of interest rates. J Financ Econ 23(2):195\u2013224. https:\/\/doi.org\/10.1016\/0304-405X(89)90056-1","journal-title":"J Financ Econ"},{"key":"9765_CR31","volume-title":"An extension of the hull white model for interest rate modeling","author":"X Lu","year":"2014","unstructured":"Lu X (2014) An extension of the hull white model for interest rate modeling. Rochester Institute of Technology, Rochester"},{"issue":"3","key":"9765_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10489-024-06195-2","volume":"55","author":"K Luo","year":"2025","unstructured":"Luo K, Liao S, Guan Z et al (2025) An enhanced hybrid adaptive physics-informed neural network for forward and inverse pde problems. Appl Intell 55(3):1\u201320. https:\/\/doi.org\/10.1007\/s10489-024-06195-2","journal-title":"Appl Intell"},{"issue":"2","key":"9765_CR33","doi-asserted-by":"publisher","first-page":"114","DOI":"10.3390\/math9020114","volume":"9","author":"V Maltsev","year":"2021","unstructured":"Maltsev V, Pokojovy M (2021) Applying heath-jarrow-morton model to forecasting the us treasury daily yield curve rates. Mathematics 9(2):114. https:\/\/doi.org\/10.3390\/math9020114","journal-title":"Mathematics"},{"key":"9765_CR34","doi-asserted-by":"publisher","DOI":"10.18576\/jsap\/130202","author":"CP Ogbogbo","year":"2024","unstructured":"Ogbogbo CP (2024) Modeling interest rate dynamics for the bank of ghana rates using the hull-white model. Appl Math Inf Sci An Int J. https:\/\/doi.org\/10.18576\/jsap\/130202","journal-title":"Appl Math Inf Sci An Int J"},{"key":"9765_CR35","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1016\/j.neucom.2021.04.021","volume":"454","author":"E Olivares","year":"2021","unstructured":"Olivares E, Ye H, Herrero A et al (2021) Applications of information channels to physics-informed neural networks for wifi signal propagation simulation at the edge of the industrial internet of things. Neurocomputing 454:405\u2013416. https:\/\/doi.org\/10.1016\/j.neucom.2021.04.021","journal-title":"Neurocomputing"},{"issue":"8","key":"9765_CR36","doi-asserted-by":"publisher","first-page":"1566","DOI":"10.1002\/for.2783","volume":"40","author":"G Orlando","year":"2021","unstructured":"Orlando G, Bufalo M (2021) Interest rates forecasting: between hull and white and the cir#\u2014how to make a single-factor model work. J Forecast 40(8):1566\u20131580. https:\/\/doi.org\/10.1002\/for.2783","journal-title":"J Forecast"},{"issue":"4","key":"9765_CR37","doi-asserted-by":"publisher","first-page":"569","DOI":"10.1002\/for.2642","volume":"39","author":"G Orlando","year":"2020","unstructured":"Orlando G, Mininni RM, Bufalo M (2020) Forecasting interest rates through vasicek and cir models: a partitioning approach. J Forecast 39(4):569\u2013579","journal-title":"J Forecast"},{"issue":"4","key":"9765_CR38","doi-asserted-by":"publisher","first-page":"A2603","DOI":"10.1137\/18M1229845","volume":"41","author":"G Pang","year":"2019","unstructured":"Pang G, Lu L, Karniadakis GE (2019) fpinns: Fractional physics-informed neural networks. SIAM J Sci Comput 41(4):A2603\u2013A2626. https:\/\/doi.org\/10.1137\/18M1229845","journal-title":"SIAM J Sci Comput"},{"issue":"6481","key":"9765_CR39","doi-asserted-by":"publisher","first-page":"1026","DOI":"10.1126\/science.aaw474","volume":"367","author":"M Raissi","year":"2020","unstructured":"Raissi M, Yazdani A, Karniadakis GE (2020) Hidden fluid mechanics: learning velocity and pressure fields from flow visualizations. Science 367(6481):1026\u20131030. https:\/\/doi.org\/10.1126\/science.aaw474","journal-title":"Science"},{"issue":"3","key":"9765_CR40","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s43069-024-00351-7","volume":"5","author":"I Rani","year":"2024","unstructured":"Rani I, Verma CK (2024) Analyzing short-rate models for efficient bond option pricing: a review. Oper Res Forum 5(3):1\u201326. https:\/\/doi.org\/10.1007\/s43069-024-00351-7","journal-title":"Oper Res Forum"},{"key":"9765_CR41","doi-asserted-by":"publisher","DOI":"10.1016\/j.enganabound.2025.106396","volume":"179","author":"I Rani","year":"2025","unstructured":"Rani I, Verma CK (2025) G-pinns: a Bayesian-optimized gru-enhanced physics-informed neural network for advancing short rate model predictions. Eng Anal Bound Elem 179:106396. https:\/\/doi.org\/10.1016\/j.enganabound.2025.106396","journal-title":"Eng Anal Bound Elem"},{"key":"9765_CR42","doi-asserted-by":"publisher","unstructured":"Rani I, Verma N, Verma CK (2025) A rigorous statistical comparison of deep learning models for us treasury yield prediction. In: Operations research forum. Springer, pp 103. https:\/\/doi.org\/10.1007\/s43069-025-00497-y","DOI":"10.1007\/s43069-025-00497-y"},{"key":"9765_CR43","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2021.114399","volume":"389","author":"P Ren","year":"2022","unstructured":"Ren P, Rao C, Liu Y et al (2022) Phycrnet: physics-informed convolutional-recurrent network for solving spatiotemporal pdes. Comput Methods Appl Mech Eng 389:114399. https:\/\/doi.org\/10.1016\/j.cma.2021.114399","journal-title":"Comput Methods Appl Mech Eng"},{"key":"9765_CR44","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110683","volume":"447","author":"K Shukla","year":"2021","unstructured":"Shukla K, Jagtap AD, Karniadakis GE (2021) Parallel physics-informed neural networks via domain decomposition. J Comput Phys 447:110683. https:\/\/doi.org\/10.1016\/j.jcp.2021.110683","journal-title":"J Comput Phys"},{"issue":"1","key":"9765_CR45","first-page":"1","volume":"5","author":"E Thompson","year":"2016","unstructured":"Thompson E, Engmann GM, Butorac A et al (2016) Short-term interest rate model: Calibration of the vasicek process to ghana\u2019s treasury rate. J Financ Investig Anal 5(1):1\u20134","journal-title":"J Financ Investig Anal"},{"issue":"2","key":"9765_CR46","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/0304-405X(77)90016-2","volume":"5","author":"O Vasicek","year":"1977","unstructured":"Vasicek O (1977) An equilibrium characterization of the term structure. J Financ Econ 5(2):177\u2013188. https:\/\/doi.org\/10.1016\/0304-405X(77)90016-2","journal-title":"J Financ Econ"},{"issue":"4","key":"9765_CR47","doi-asserted-by":"publisher","first-page":"2441","DOI":"10.1007\/s00362-023-01494-1","volume":"65","author":"C Wei","year":"2024","unstructured":"Wei C (2024) Least squares estimation for a class of uncertain vasicek model and its application to interest rates. Stat Pap 65(4):2441\u20132459. https:\/\/doi.org\/10.1007\/s00362-023-01494-1","journal-title":"Stat Pap"},{"issue":"1","key":"9765_CR48","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1007\/s10915-022-01980-y","volume":"93","author":"W Wu","year":"2022","unstructured":"Wu W, Feng X, Xu H (2022) Improved deep neural networks with domain decomposition in solving partial differential equations. J Sci Comput 93(1):20. https:\/\/doi.org\/10.1007\/s10915-022-01980-y","journal-title":"J Sci Comput"},{"issue":"6","key":"9765_CR49","doi-asserted-by":"publisher","first-page":"2532","DOI":"10.2514\/1.J064926","volume":"63","author":"Y Yan","year":"2025","unstructured":"Yan Y, Lu Z (2025) Adaptive physics-informed neural network based directional sampling method for efficient reliability analysis. AIAA J 63(6):2532\u20132544. https:\/\/doi.org\/10.2514\/1.J064926","journal-title":"AIAA J"},{"issue":"4","key":"9765_CR50","doi-asserted-by":"publisher","first-page":"3299","DOI":"10.1007\/s40747-022-00670-4","volume":"8","author":"N Yang","year":"2022","unstructured":"Yang N, Tang Z, Cai X et al (2022) Cooperative multi-population harris hawks optimization for many-objective optimization. Complex Intell Syst 8(4):3299\u20133332. https:\/\/doi.org\/10.1007\/s40747-022-00670-4","journal-title":"Complex Intell Syst"},{"key":"9765_CR51","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2020.113603","volume":"375","author":"M Yin","year":"2021","unstructured":"Yin M, Zheng X, Humphrey JD et al (2021) Non-invasive inference of thrombus material properties with physics-informed neural networks. Comput Methods Appl Mech Eng 375:113603. https:\/\/doi.org\/10.1016\/j.cma.2020.113603","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"2","key":"9765_CR52","doi-asserted-by":"publisher","first-page":"41","DOI":"10.3390\/risks7020041","volume":"7","author":"F Zeddouk","year":"2019","unstructured":"Zeddouk F, Devolder P (2019) Pricing of longevity derivatives and cost of capital. Risks 7(2):41. https:\/\/doi.org\/10.3390\/risks7020041","journal-title":"Risks"},{"issue":"2","key":"9765_CR53","doi-asserted-by":"publisher","first-page":"A639","DOI":"10.48550\/arXiv.1905.01205","volume":"42","author":"D Zhang","year":"2020","unstructured":"Zhang D, Guo L, Karniadakis GE (2020) Learning in modal space: Solving time-dependent stochastic pdes using physics-informed neural networks. SIAM J Sci Comput 42(2):A639\u2013A665. https:\/\/doi.org\/10.48550\/arXiv.1905.01205","journal-title":"SIAM J Sci Comput"}],"container-title":["Evolving Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12530-025-09765-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12530-025-09765-y","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12530-025-09765-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T05:17:22Z","timestamp":1773119842000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12530-025-09765-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,27]]},"references-count":52,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["9765"],"URL":"https:\/\/doi.org\/10.1007\/s12530-025-09765-y","relation":{},"ISSN":["1868-6478","1868-6486"],"issn-type":[{"value":"1868-6478","type":"print"},{"value":"1868-6486","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,27]]},"assertion":[{"value":"16 May 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 October 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 November 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors report no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}],"article-number":"2"}}