{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T08:15:07Z","timestamp":1783152907170,"version":"3.54.6"},"reference-count":75,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/100009110","name":"Natural Science Foundation of Xinjiang Uygur Autonomous Region","doi-asserted-by":"publisher","award":["2022D01D32"],"award-info":[{"award-number":["2022D01D32"]}],"id":[{"id":"10.13039\/100009110","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["92270109"],"award-info":[{"award-number":["92270109"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071406"],"award-info":[{"award-number":["12071406"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Communications in Nonlinear Science and Numerical Simulation"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.cnsns.2026.110110","type":"journal-article","created":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T15:35:14Z","timestamp":1778340914000},"page":"110110","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P2","title":["Self-attention enhanced physics-informed neural networks for multi-field physics"],"prefix":"10.1016","volume":"161","author":[{"given":"Zi","family":"Ye","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mengxue","family":"Lu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinlong","family":"Feng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hui","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"7","key":"10.1016\/j.cnsns.2026.110110_bib0001","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1002\/we.458","article-title":"Review of computational fluid dynamics for wind turbine wake aerodynamics","volume":"14","author":"Sanderse","year":"2011","journal-title":"Wind Energy"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110110_bib0002","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1016\/j.jweia.2011.01.023","article-title":"A preliminary study of assimilating numerical weather prediction data into computational fluid dynamics models for wind prediction","volume":"99","author":"Zajaczkowski","year":"2011","journal-title":"J Wind Eng Ind Aerodyn"},{"issue":"10","key":"10.1016\/j.cnsns.2026.110110_bib0003","doi-asserted-by":"crossref","first-page":"1569","DOI":"10.1016\/0009-2509(96)00021-8","article-title":"Computational fluid dynamics for chemical reactor engineering","volume":"51","author":"Harris","year":"1996","journal-title":"Chem Eng Sci"},{"key":"10.1016\/j.cnsns.2026.110110_bib0004","doi-asserted-by":"crossref","DOI":"10.1016\/j.csite.2024.104037","article-title":"Using different geometries on the amount of heat transfer in a shell and tube heat exchanger using the finite volume method","volume":"55","author":"Sohrabi","year":"2024","journal-title":"Case Stud Therm Eng"},{"key":"10.1016\/j.cnsns.2026.110110_bib0005","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2024.115758","article-title":"Computational study on entropy generation in casson nanofluid flow with motile gyrotactic microorganisms using finite difference method","volume":"190","author":"Raza","year":"2025","journal-title":"Chaos Solit Fractals"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110110_bib0006","doi-asserted-by":"crossref","first-page":"201","DOI":"10.63278\/1357","article-title":"Advanced finite element methods for solving fluid dynamics problems in engineering applications","volume":"31","author":"Kavitha","year":"2025","journal-title":"Metall Mater Eng"},{"key":"10.1016\/j.cnsns.2026.110110_bib0007","doi-asserted-by":"crossref","unstructured":"Knight D.. Design optimization in computational fluid dynamics.In: Floudas, C.A., Pardalos, P.M. (eds) Encyclopedia of Optimization; Springer, Boston, MA; 2001.","DOI":"10.1007\/0-306-48332-7_90"},{"key":"10.1016\/j.cnsns.2026.110110_bib0008","doi-asserted-by":"crossref","DOI":"10.1016\/j.energy.2022.126184","article-title":"Study on the slagging trends of the pre-combustion chamber in industrial pulverized coal boiler under different excess air coefficients by CFD numerical simulation","volume":"264","author":"Yuan","year":"2023","journal-title":"Energy"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110110_bib0009","doi-asserted-by":"crossref","DOI":"10.1063\/5.0087161","article-title":"Effects of wing\u2013body interaction on hawk moth aerodynamics and energetics at various flight velocities","volume":"34","author":"Xue","year":"2022","journal-title":"Phys Fluids"},{"key":"10.1016\/j.cnsns.2026.110110_bib0010","series-title":"Theoretical and numerical combustion","author":"Poinsot","year":"2005"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110110_bib0011","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1146\/annurev.fluid.30.1.539","article-title":"Direct numerical simulation: a tool in turbulence research","volume":"30","author":"Moin","year":"1998","journal-title":"Annu Rev Fluid Mech"},{"key":"10.1016\/j.cnsns.2026.110110_bib0012","doi-asserted-by":"crossref","DOI":"10.1016\/j.ijheatmasstransfer.2024.126314","article-title":"Direct numerical simulations of centrifugal convection: from gravitational to centrifugal buoyancy dominance","volume":"236","author":"Yao","year":"2025","journal-title":"Int J Heat Mass Transfer"},{"issue":"515","key":"10.1016\/j.cnsns.2026.110110_bib0013","first-page":"1","article-title":"Large-eddy simulation: a critical review of the technique","volume":"120","author":"Mason","year":"1994","journal-title":"Q J R Meteorol Soc"},{"key":"10.1016\/j.cnsns.2026.110110_bib0014","doi-asserted-by":"crossref","DOI":"10.1016\/j.applthermaleng.2024.122733","article-title":"Large Eddy simulation of hydrogen\/air MILD combustion in a cyclonic burner","volume":"244","author":"Carpenella","year":"2024","journal-title":"Appl Therm Eng"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110110_bib0015","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1090\/qam\/11999","article-title":"On velocity correlations and the solutions of the equations of turbulent fluctuation","volume":"3","author":"Chou","year":"1945","journal-title":"Q Appl Math"},{"key":"10.1016\/j.cnsns.2026.110110_bib0016","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1016\/j.ijhydene.2024.11.242","article-title":"Unsteady RANS simulations of under-expanded hydrogen jets for internal combustion engines","volume":"96","author":"Caramia","year":"2024","journal-title":"Int J Hydrogr Energy"},{"key":"10.1016\/j.cnsns.2026.110110_bib0017","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1017\/S0022112087000958","article-title":"Vortex-driven acoustically coupled combustion instabilities","volume":"177","author":"Poinsot","year":"1987","journal-title":"J Fluid Mech"},{"key":"10.1016\/j.cnsns.2026.110110_bib0018","series-title":"Turbulent reactive flows","first-page":"541","article-title":"The interaction between turbulence and chemistry in premixed turbulent flames","author":"Bray","year":"1989"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110110_bib0019","doi-asserted-by":"crossref","first-page":"1965","DOI":"10.1016\/S1540-7489(02)80239-5","article-title":"Experimental analysis and large eddy simulation to determine the response of non-premixed flames submitted to acoustic forcing","volume":"29","author":"Varoqui\u00e9","year":"2002","journal-title":"Proc Combust Inst"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110110_bib0020","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S1540-7489(02)80007-4","article-title":"Combustion dynamics and control: progress and challenges","volume":"29","author":"Candel","year":"2002","journal-title":"Proc Combust Inst"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110110_bib0021","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1146\/annurev-fluid-010719-060214","article-title":"Machine learning for fluid mechanics","volume":"52","author":"Brunton","year":"2020","journal-title":"Annu Rev Fluid Mech"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110110_bib0022","doi-asserted-by":"crossref","first-page":"1392","DOI":"10.1109\/TNNLS.2018.2868980","article-title":"Generalization and expressivity for deep nets","volume":"30","author":"Lin","year":"2018","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110110_bib0023","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/0893-6080(89)90020-8","article-title":"Multilayer feedforward networks are universal approximators","volume":"2","author":"Hornik","year":"1989","journal-title":"Neural Netw"},{"key":"10.1016\/j.cnsns.2026.110110_bib0024","series-title":"Symposium (international) on combustion","first-page":"43","article-title":"An integrated PDF\/neural network approach for simulating turbulent reacting systems","volume":"vol. 26","author":"Christo","year":"1996"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110110_bib0025","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1088\/1364-7830\/4\/1\/304","article-title":"A self-organizing-map approach to chemistry representation in combustion applications","volume":"4","author":"Blasco","year":"2000","journal-title":"Combust Theory Model"},{"key":"10.1016\/j.cnsns.2026.110110_bib0026","doi-asserted-by":"crossref","DOI":"10.1016\/j.combustflame.2022.112319","article-title":"A multi-scale sampling method for accurate and robust deep neural network to predict combustion chemical kinetics","volume":"245","author":"Zhang","year":"2022","journal-title":"Combust Flame"},{"key":"10.1016\/j.cnsns.2026.110110_bib0027","doi-asserted-by":"crossref","DOI":"10.1016\/j.egyai.2022.100221","article-title":"Deep neural network-based generation of planar CH distribution through flame chemiluminescence in premixed turbulent flame","volume":"12","author":"Han","year":"2023","journal-title":"Energy AI"},{"key":"10.1016\/j.cnsns.2026.110110_bib0028","doi-asserted-by":"crossref","DOI":"10.1016\/j.fuel.2024.131212","article-title":"Combustion chemistry acceleration with deepONets","volume":"365","author":"Kumar","year":"2024","journal-title":"Fuel"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110110_bib0029","doi-asserted-by":"crossref","DOI":"10.1063\/5.0087247","article-title":"Intelligent reconstruction of the flow field in a supersonic combustor based on deep learning","volume":"34","author":"Chen","year":"2022","journal-title":"Phys Fluids"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110110_bib0030","doi-asserted-by":"crossref","first-page":"5187","DOI":"10.1016\/j.proci.2022.07.128","article-title":"High-resolution reconstruction and a-priori modeling of turbulent flames in the context of large eddy simulation using the convolutional neural network","volume":"39","author":"Liu","year":"2023","journal-title":"Proc Combust Inst"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110110_bib0031","doi-asserted-by":"crossref","DOI":"10.1063\/5.0140443","article-title":"Reconstructing the self-luminous image of a flame in a supersonic combustor based on residual network reconstruction algorithm","volume":"35","author":"Deng","year":"2023","journal-title":"Phys Fluids"},{"key":"10.1016\/j.cnsns.2026.110110_bib0032","doi-asserted-by":"crossref","DOI":"10.1016\/j.ast.2023.108593","article-title":"2D-supervised fast neural fluid reconstruction technique for time-resolved volumetric flame reconstruction","volume":"142","author":"Zhang","year":"2023","journal-title":"Aerosp Sci Technol"},{"key":"10.1016\/j.cnsns.2026.110110_bib0033","doi-asserted-by":"crossref","DOI":"10.1016\/j.combustflame.2023.113182","article-title":"Reconstructing temperature fields from OH distribution and soot volume fraction in turbulent flames using an artificial neural network","volume":"259","author":"Nie","year":"2024","journal-title":"Combust Flame"},{"key":"10.1016\/j.cnsns.2026.110110_bib0034","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","article-title":"Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","volume":"378","author":"Raissi","year":"2019","journal-title":"J Comput Phys"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110110_bib0035","doi-asserted-by":"crossref","first-page":"A2603","DOI":"10.1137\/18M1229845","article-title":"fPINNs: fractional physics-informed neural networks","volume":"41","author":"Pang","year":"2019","journal-title":"SIAM J Sci Comput"},{"key":"10.1016\/j.cnsns.2026.110110_bib0036","doi-asserted-by":"crossref","first-page":"26328","DOI":"10.1109\/ACCESS.2019.2963390","article-title":"A physics-informed neural network framework for PDEs on 3d surfaces: time independent problems","volume":"8","author":"Fang","year":"2019","journal-title":"IEEE Access"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110110_bib0037","doi-asserted-by":"crossref","first-page":"A639","DOI":"10.1137\/19M1260141","article-title":"Learning in modal space: solving time-dependent stochastic PDEs using physics-informed neural networks","volume":"42","author":"Zhang","year":"2020","journal-title":"SIAM J Sci Comput"},{"key":"10.1016\/j.cnsns.2026.110110_bib0038","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2020.109951","article-title":"NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations","volume":"426","author":"Jin","year":"2021","journal-title":"J Comput Phys"},{"key":"10.1016\/j.cnsns.2026.110110_bib0039","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2019.112789","article-title":"Physics-informed neural networks for high-speed flows","volume":"360","author":"Mao","year":"2020","journal-title":"Comput Methods Appl Mech Eng"},{"key":"10.1016\/j.cnsns.2026.110110_bib0040","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2021.104232","article-title":"A physics-informed machine learning approach for solving heat transfer equation in advanced manufacturing and engineering applications","volume":"101","author":"Zobeiry","year":"2021","journal-title":"Eng Appl Artif Intell"},{"key":"10.1016\/j.cnsns.2026.110110_bib0041","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1007\/s11831-020-09405-5","article-title":"Multiscale modeling meets machine learning: what can we learn?","volume":"28","author":"Peng","year":"2021","journal-title":"Arch Comput Methods Eng"},{"issue":"36","key":"10.1016\/j.cnsns.2026.110110_bib0042","doi-asserted-by":"crossref","first-page":"8098","DOI":"10.1021\/acs.jpca.1c05102","article-title":"Stiff-PINN: physics-informed neural network for stiff chemical kinetics","volume":"125","author":"Ji","year":"2021","journal-title":"J Phys Chem A"},{"issue":"45","key":"10.1016\/j.cnsns.2026.110110_bib0043","doi-asserted-by":"crossref","first-page":"8534","DOI":"10.1021\/acs.jpca.2c06513","article-title":"Multiscale physics-informed neural networks for stiff chemical kinetics","volume":"126","author":"Weng","year":"2022","journal-title":"J Phys Chem A"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110110_bib0044","doi-asserted-by":"crossref","first-page":"1597","DOI":"10.1016\/j.proci.2022.08.036","article-title":"Physics-informed recurrent neural networks for linear and nonlinear flame dynamics","volume":"39","author":"Yadav","year":"2023","journal-title":"Proc Combust Inst"},{"key":"10.1016\/j.cnsns.2026.110110_bib0045","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2024.113698","article-title":"RF-PINNS: reactive flow physics-informed neural networks for field reconstruction of laminar and turbulent flames using sparse data","volume":"524","author":"Yadav","year":"2025","journal-title":"J Comput Phys"},{"key":"10.1016\/j.cnsns.2026.110110_bib0046","doi-asserted-by":"crossref","DOI":"10.1016\/j.fuel.2022.125908","article-title":"Application of a physics-informed neural network to solve the steady-state bratu equation arising from solid biofuel combustion theory","volume":"332","author":"Hosseini","year":"2023","journal-title":"Fuel"},{"key":"10.1016\/j.cnsns.2026.110110_bib0047","doi-asserted-by":"crossref","DOI":"10.1016\/j.combustflame.2023.113094","article-title":"Surrogate modeling of parameterized multi-dimensional premixed combustion with physics-informed neural networks for rapid exploration of design space","volume":"258","author":"Liu","year":"2023","journal-title":"Combust Flame"},{"issue":"10","key":"10.1016\/j.cnsns.2026.110110_bib0048","doi-asserted-by":"crossref","DOI":"10.1063\/5.0227581","article-title":"Physics-informed neural networks coupled with flamelet\/progress variable model for solving combustion physics considering detailed reaction mechanism","volume":"36","author":"Song","year":"2024","journal-title":"Phys Fluids"},{"key":"10.1016\/j.cnsns.2026.110110_bib0049","doi-asserted-by":"crossref","DOI":"10.1016\/j.combustflame.2024.113647","article-title":"CRK-PINN: a physics-informed neural network for solving combustion reaction kinetics ordinary differential equations","volume":"269","author":"Zhang","year":"2024","journal-title":"Combust Flame"},{"issue":"11","key":"10.1016\/j.cnsns.2026.110110_bib0050","doi-asserted-by":"crossref","DOI":"10.1063\/5.0235674","article-title":"Surrogate modeling of multi-dimensional premixed and non-premixed combustion using pseudo-time stepping physics-informed neural networks","volume":"36","author":"Cao","year":"2024","journal-title":"Phys Fluids"},{"key":"10.1016\/j.cnsns.2026.110110_bib0051","doi-asserted-by":"crossref","DOI":"10.1016\/j.combustflame.2025.113964","article-title":"FlamePINN-1D: physics-informed neural networks to solve forward and inverse problems of 1D laminar flames","volume":"273","author":"Wu","year":"2025","journal-title":"Combust Flame"},{"issue":"8","key":"10.1016\/j.cnsns.2026.110110_bib0052","doi-asserted-by":"crossref","DOI":"10.1063\/5.0097496","article-title":"Velocity reconstruction in puffing pool fires with physics-informed neural networks","volume":"34","author":"Sitte","year":"2022","journal-title":"Phys Fluids"},{"issue":"7","key":"10.1016\/j.cnsns.2026.110110_bib0053","article-title":"Flow-field reconstruction in rotating detonation combustor based on physics-informed neural network","volume":"35","author":"Wang","year":"2023","journal-title":"Phys Fluids"},{"issue":"7","key":"10.1016\/j.cnsns.2026.110110_bib0054","doi-asserted-by":"crossref","DOI":"10.1063\/5.0217991","article-title":"Intelligent reconstruction of unsteady combustion flow field of scramjet based on physical information constraints","volume":"36","author":"Deng","year":"2024","journal-title":"Phys Fluids"},{"key":"10.1016\/j.cnsns.2026.110110_bib0055","doi-asserted-by":"crossref","DOI":"10.1016\/j.combustflame.2023.113275","article-title":"High-resolution reconstruction of turbulent flames from sparse data with physics-informed neural networks","volume":"260","author":"Liu","year":"2024","journal-title":"Combust Flame"},{"issue":"153","key":"10.1016\/j.cnsns.2026.110110_bib0056","first-page":"1","article-title":"Automatic differentiation in machine learning: a survey","volume":"18","author":"Baydin","year":"2018","journal-title":"J Mach Learn Res"},{"key":"10.1016\/j.cnsns.2026.110110_bib0057","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0962492900000015","article-title":"Radial basis functions","volume":"9","author":"Buhmann","year":"2000","journal-title":"Acta Numer"},{"key":"10.1016\/j.cnsns.2026.110110_bib0058","article-title":"Multivariable functional interpolation and adaptive networks","volume":"2","author":"Broomhead","year":"1988","journal-title":"Complex Syst"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110110_bib0059","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1162\/neco.1989.1.2.281","article-title":"Fast learning in networks of locally-tuned processing units","volume":"1","author":"Moody","year":"1989","journal-title":"Neural Comput"},{"key":"10.1016\/j.cnsns.2026.110110_bib0060","first-page":"321","article-title":"Attention is all you need","volume":"30","author":"Vaswani","year":"2017","journal-title":"Adv Neural Inf Process Syst"},{"key":"10.1016\/j.cnsns.2026.110110_bib0061","article-title":"An image is worth 16x16 words: transformers for image recognition at scale","volume":"abs\/2010.11929","author":"Dosovitskiy","year":"2020","journal-title":","},{"key":"10.1016\/j.cnsns.2026.110110_bib0062","series-title":"Proceedings of the IEEE conference on computer vision and pattern recognition","first-page":"770","article-title":"Deep residual learning for image recognition","author":"He","year":"2016"},{"key":"10.1016\/j.cnsns.2026.110110_bib0063","series-title":"Proceedings of the thirteenth international conference on artificial intelligence and statistics","first-page":"249","article-title":"Understanding the difficulty of training deep feedforward neural networks","author":"Glorot","year":"2010"},{"key":"10.1016\/j.cnsns.2026.110110_bib0064","unstructured":"Kingma D.P.. ADAM: a method for stochastic optimization.CoRR; 2014;abs\/1412.6980, arXiv preprint arXiv: 14126980."},{"key":"10.1016\/j.cnsns.2026.110110_bib0065","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2019.109136","article-title":"Adaptive activation functions accelerate convergence in deep and physics-informed neural networks","volume":"404","author":"Jagtap","year":"2020","journal-title":"J Comput Phys"},{"key":"10.1016\/j.cnsns.2026.110110_bib0066","unstructured":"Loshchilov I., Hutter F.. SGDR: Stochastic gradient descent with warm restarts. 2016, arXiv preprint arXiv: 160803983."},{"key":"10.1016\/j.cnsns.2026.110110_bib0067","unstructured":"Paszke A.. PyTorch: an imperative style, high-performance deep learning library. 2019, arXiv preprint arXiv: 191201703."},{"key":"10.1016\/j.cnsns.2026.110110_bib0068","series-title":"Proceedings of the 26th annual international conference on machine learning","first-page":"41","article-title":"Curriculum learning","author":"Bengio","year":"2009"},{"key":"10.1016\/j.cnsns.2026.110110_bib0069","series-title":"Chemically reacting flow: theory and practice","author":"Kee","year":"2005"},{"key":"10.1016\/j.cnsns.2026.110110_bib0070","article-title":"Cantera: an object-oriented software toolkit for chemical kinetics, thermodynamics, and transport processes","volume":"abs\/1412.6980","author":"Goodwin","year":"2014","journal-title":"Zenodo"},{"key":"10.1016\/j.cnsns.2026.110110_bib0071","first-page":"7537","article-title":"Fourier features let networks learn high frequency functions in low dimensional domains","volume":"33","author":"Tancik","year":"2020","journal-title":"Adv Neural Inf Process Syst"},{"key":"10.1016\/j.cnsns.2026.110110_bib0072","article-title":"Neural tangent kernel: convergence and generalization in neural networks","volume":"abs\/1806.07572","author":"Jacot","year":"2018","journal-title":"ArXiv"},{"key":"10.1016\/j.cnsns.2026.110110_bib0073","series-title":"Proceedings of the IEEE conference on computer vision and pattern recognition","first-page":"7132","article-title":"Squeeze-and-excitation networks","author":"Hu","year":"2018"},{"key":"10.1016\/j.cnsns.2026.110110_bib0074","series-title":"Symposium (international) on combustion","first-page":"1087","article-title":"Effects of turbulence on species mass fractions in methane\/air jet flames","volume":"vol. 27","author":"Barlow","year":"1998"},{"key":"10.1016\/j.cnsns.2026.110110_bib0075","unstructured":"Launder B.E., Spalding D.B.. Lectures in mathematical models of turbulence. Academic Press;1972."}],"container-title":["Communications in Nonlinear Science and Numerical Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426004697?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426004697?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T07:16:39Z","timestamp":1783149399000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1007570426004697"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":75,"alternative-id":["S1007570426004697"],"URL":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.110110","relation":{},"ISSN":["1007-5704"],"issn-type":[{"value":"1007-5704","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Self-attention enhanced physics-informed neural networks for multi-field physics","name":"articletitle","label":"Article Title"},{"value":"Communications in Nonlinear Science and Numerical Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.110110","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"110110"}}