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Machine learning for metal additive manufacturing: predicting temperature and melt pool fluid dynamics using physics-informed neural networks

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Abstract

The recent explosion of machine learning (ML) and artificial intelligence (AI) shows great potential in the breakthrough of metal additive manufacturing (AM) process modeling, which is an indispensable step to derive the process-structure-property relationship. However, the success of conventional machine learning tools in data science is primarily attributed to the unprecedented large amount of labeled data-sets (big data), which can be either obtained by experiments or first-principle simulations. Unfortunately, these labeled data-sets are expensive to obtain in AM due to the high expense of the AM experiments and prohibitive computational cost of high-fidelity simulations, hindering the direct applications of big-data based ML tools to metal AM problems. To fully exploit the power of machine learning for metal AM while alleviating the dependence on “big data”, we put forth a physics-informed neural network (PINN) framework that fuses both data and first physical principles, including conservation laws of momentum, mass, and energy, into the neural network to inform the learning processes. To the best knowledge of the authors, this is the first application of physics-informed deep learning to three dimensional AM processes modeling. Besides, we propose a hard-type approach for Dirichlet boundary conditions (BCs) based on a Heaviside function, which can not only exactly enforce the BCs but also accelerate the learning process. The PINN framework is applied to two representative metal manufacturing problems, including the 2018 NIST AM-Benchmark test series. We carefully assess the performance of the PINN model by comparing the predictions with available experimental data and high-fidelity simulation results, using finite element based variational multi-scale formulation method. The investigations show that the PINN, owed to the additional physical knowledge, can accurately predict the temperature and melt pool dynamics during metal AM processes with only a moderate amount of labeled data-sets. The foray of PINN to metal AM shows the great potential of physics-informed deep learning for broader applications to advanced manufacturing. All the data-sets and the PINN code will be made open-sourced in https://yan.cee.illinois.edu/ once the paper is published.

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References

  1. Zhao C, Fezzaa K, Cunningham R, Wen H, De Carlo F, Chen L, Rollett A, Sun T (2017) Real-time monitoring of laser powder bed fusion process using high-speed x-ray imaging and diffraction. Sci Rep 7(1):1–11

    Google Scholar 

  2. Cunningham R, Zhao C, Parab N, Kantzos C, Pauza J, Fezzaa K, Sun T, Rollett A (2019) Keyhole threshold and morphology in laser melting revealed by ultrahigh-speed x-ray imaging. Science 363(6429):849–852

    Article  Google Scholar 

  3. Guo Q, Zhao C, Qu M, Xiong L, Hojjatzadeh S, Escano L, Parab N, Fezzaa K, Sun T, Chen L (2020) In-situ full-field mapping of melt flow dynamics in laser metal additive manufacturing. Addit Manuf 31:100939

    Google Scholar 

  4. NIST Additive Manufacturing Benchmark Test Series (AM-BENCH) (2020). https://www.nist.gov/ambench. Accessed 03 Aug 2020

  5. AFRL Additive Manufacturing Modeling Challenge Series (2020). https://www.americamakes.us/america-makes-and-afrl-announce-am-modeling-challenge/. Accessed 07 July 2020

  6. Noble C, Anderson A, Barton N, Bramwell J, Capps A, Chang M, Chou J, Dawson D, Diana E, Dunn T (2017) Ale3d: an arbitrary Lagrangian–Eulerian multi-physics code. Techical report, Lawrence Livermore National Lab.(LLNL), Livermore, CA (United States)

  7. Khairallah S, Anderson A, Rubenchik A, King W (2016) Laser powder-bed fusion additive manufacturing: physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Mater 108:36–45

    Article  Google Scholar 

  8. Roehling TT, Wu SS, Khairallah SA, Roehling JD, Soezeri SS, Crumb MF, Matthews MJ (2017) Modulating laser intensity profile ellipticity for microstructural control during metal additive manufacturing. Acta Mater 128:197–206

    Article  Google Scholar 

  9. Khairallah S, Martin A, Lee J, Guss G, Calta N, Hammons J, Nielsen M, Chaput K, Schwalbach E, Shah M, Chapman G, Willey T, Rubenchik A, Anderson A, Wang Y, Matthews M, King W (2020) Controlling interdependent meso-nanosecond dynamics and defect generation in metal 3d printing. Science 368(6491):660–665

    Article  Google Scholar 

  10. Knapp G, Mukherjee T, Zuback J, Wei H, Palmer T, De A, DebRoy T (2017) Building blocks for a digital twin of additive manufacturing. Acta Mater 135:390–399

    Article  Google Scholar 

  11. Mukherjee T, Wei H, De A, DebRoy T (2018) Heat and fluid flow in additive manufacturing-part i: modeling of powder bed fusion. Comput Mater Sci 150:304–313

    Article  Google Scholar 

  12. Mukherjee T, Wei H, De A, DebRoy T (2018) Heat and fluid flow in additive manufacturing-part ii: Powder bed fusion of stainless steel, and titanium, nickel and aluminum base alloys. Comput Mater Sci 150:369–380

    Article  Google Scholar 

  13. Lin S (2019) Numerical methods and high performance computing for modeling metallic additive manufacturing processes at multiple scales. Ph.D. thesis, Northwestern University

  14. Lin S, Gan Z, Yan J, Wagner G (2020) A conservative level set method on unstructured meshes for modeling multiphase thermo-fluid flow in additive manufacturing processes. Comput Methods Appl Mech Eng 372:113348

    Article  MathSciNet  Google Scholar 

  15. Attar E, Körner C (2011) Lattice Boltzmann model for thermal free surface flows with liquid–solid phase transition. Int J Heat Fluid Flow 32(1):156–163

    Article  Google Scholar 

  16. Körner C, Attar E, Heinl P (2011) Mesoscopic simulation of selective beam melting processes. J Mater Process Technol 211(6):978–987

    Article  Google Scholar 

  17. Körner C, Bauereiß A, Attar E (2013) Fundamental consolidation mechanisms during selective beam melting of powders. Model Simul Mater Sci Eng 21(8):085011

    Article  Google Scholar 

  18. Zohdi TI (2014) Additive particle deposition and selective laser processing-a computational manufacturing framework. Comput Mech 54(1):171–191

    Article  Google Scholar 

  19. Zohdi T (2014) A direct particle-based computational framework for electrically enhanced thermo-mechanical sintering of powdered materials. Math Mech Solids 19(1):93–113

    Article  MATH  Google Scholar 

  20. Ganeriwala R, Zohdi TI (2014) Multiphysics modeling and simulation of selective laser sintering manufacturing processes. Procedia Cirp 14:299–304

    Article  Google Scholar 

  21. Yan W, Ge W, Qian Y, Lin S, Zhou B, Liu WK, Lin F, Wagner GJ (2017) Multi-physics modeling of single/multiple-track defect mechanisms in electron beam selective melting. Acta Mater 134:324–333

    Article  Google Scholar 

  22. Yan W, Qian Y, Ge W, Lin S, Liu WK, Lin F, Wagner GJ (2018) Meso-scale modeling of multiple-layer fabrication process in selective electron beam melting: inter-layer/track voids formation. Mater Des 141:210–219

    Article  Google Scholar 

  23. Yan W, Lin S, Kafka O, Lian Y, Yu C, Liu Z, Yan J, Wolff S, Wu H, Ndip-Agbor E, Mozaffar M, Ehmann K, Cao J, Wagner G, Liu W (2018) Data-driven multi-scale multi-physics models to derive process-structure-property relationships for additive manufacturing. Comput Mech 61(5):521–541

    Article  MATH  Google Scholar 

  24. Yan W, Ge W, Smith J, Lin S, Kafka O, Lin F, Liu W (2016) Multi-scale modeling of electron beam melting of functionally graded materials. Acta Mater 115:403–412

    Article  Google Scholar 

  25. Chen H, Yan W (2020) Spattering and denudation in laser powder bed fusion process: multiphase flow modelling. Acta Mater 196:154–167

    Article  Google Scholar 

  26. Panwisawas C, Qiu C, Anderson MJ, Sovani Y, Turner RP, Attallah MM, Brooks JW, Basoalto HC (2017) Mesoscale modelling of selective laser melting: thermal fluid dynamics and microstructural evolution. Comput Mater Sci 126:479–490

    Article  Google Scholar 

  27. Li X, Zhao C, Sun T, Tan W (2020) Revealing transient powder-gas interaction in laser powder bed fusion process through multi-physics modeling and high-speed synchrotron x-ray imaging. Addit Manuf 35:101362

    Google Scholar 

  28. Megahed M, Mindt H-W, Shula B, Peralta A, Neumann J (2016) Powder bed models-numerical assessment of as-built quality. In: 57th AIAA/ASCE/AHS/ASC structures, structural dynamics, and materials conference, p 1657

  29. Mindt H-W, Desmaison O, Megahed M, Peralta A, Neumann J (2018) Modeling of powder bed manufacturing defects. J Mater Eng Perform 27(1):32–43

    Article  Google Scholar 

  30. Yan J, Yan W, Lin S, Wagner G (2018) A fully coupled finite element formulation for liquid–solid–gas thermo-fluid flow with melting and solidification. Comput Methods Appl Mech Eng 336:444–470

    Article  MathSciNet  MATH  Google Scholar 

  31. Fan Z, Li B (2019) Meshfree simulations for additive manufacturing process of metals. Integrat Mater Manuf Innov 8(2):144–153

    Article  Google Scholar 

  32. Gan Z, Lian Y, Lin SE, Jones KK, Liu WK, Wagner GJ (2019) Benchmark study of thermal behavior, surface topography, and dendritic microstructure in selective laser melting of inconel 625. Integrat Mater Manuf Innov 8(2):178–193

    Article  Google Scholar 

  33. Liu Z, Wu C, Koishi M (2019) Transfer learning of deep material network for seamless structure-property predictions. Comput Mech 64(2):451–465

    Article  MathSciNet  MATH  Google Scholar 

  34. Liu Z, Wu C, Koishi M (2019) A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials. Comput Methods Appl Mech Eng 345:1138–1168

    Article  MathSciNet  MATH  Google Scholar 

  35. Liu Z, Wu C (2019) Exploring the 3d architectures of deep material network in data-driven multiscale mechanics. J Mech Phys Solids 127:20–46

    Article  MathSciNet  Google Scholar 

  36. Liu Z, Kafka O, Yu C, Liu W (2018) Data-driven self-consistent clustering analysis of heterogeneous materials with crystal plasticity. In: Oñate E, Peric D, de Souza Neto E, Chiumenti M (eds) Advances in computational plasticity. Springer, pp 221–242

  37. Liu Z, Fleming M, Liu W (2018) Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials. Comput Methods Appl Mech Eng 330:547–577

    Article  MathSciNet  MATH  Google Scholar 

  38. Liu Z, Bessa M, Liu W (2016) Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials. Comput Methods Appl Mech Eng 306:319–341

    Article  MathSciNet  MATH  Google Scholar 

  39. Abadi M, Barham P, Chen J., Chen Z, Davis A, Dean J, Devin M, Ghemawat S, Irving G, Isard M, et al (2016) Tensorflow: a system for large-scale machine learning. In: 12th \(\{\)USENIX\(\}\) symposium on operating systems design and implementation (\(\{\)OSDI\(\}\) 16), pp 265–283

  40. Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G, Killeen T, Lin Z, Gimelshein N, Antiga L, et al (2019) Pytorch: an imperative style, high-performance deep learning library. In: Wallach H, Larochelle H, Beygelzimer A, d’Alché-Buc F, Fox E, Garnett R (eds) Advances in neural information processing systems, pp 8024–8035

  41. Bastien F, Lamblin P, Pascanu R, Bergstra J, Goodfellow I, Bergeron A, Bouchard N, Warde-Farley D, Bengio Y Theano: new features and speed improvements. arXiv:1211.5590

  42. Jia Y, Shelhamer E, Donahue J, Karayev S, Long J, Girshick R, Guadarrama S, Darrell T (2014)Caffe: convolutional architecture for fast feature embedding. In: Proceedings of the 22nd ACM international conference on multimedia, pp 675–678

  43. Yang X, Barajas-Solano D, Tartakovsky G, Tartakovsky A (2019) Physics-informed Cokriging: a Gaussian-process-regression-based multifidelity method for data-model convergence. J Comput Phys 395:410–431

    Article  MathSciNet  Google Scholar 

  44. Raissi M, Perdikaris P, Karniadakis GE (2017) Machine learning of linear differential equations using Gaussian processes. J Comput Phys 348:683–693

    Article  MathSciNet  MATH  Google Scholar 

  45. Lagaris I, Likas A, Fotiadis D (1998) Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans Neural Netw 9(5):987–1000

    Article  Google Scholar 

  46. Raissi M, Yazdani A, Karniadakis G (2020) Hidden fluid mechanics: learning velocity and pressure fields from flow visualizations. Science 367(6481):1026–1030

    Article  Google Scholar 

  47. Sun L, Gao H, Pan S, Wang J-X (2020) Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data. Comput Methods Appl Mech Eng 361:112732

    Article  MathSciNet  MATH  Google Scholar 

  48. Zissis D, Xidias EK, Lekkas D (2015) A cloud based architecture capable of perceiving and predicting multiple vessel behaviour. Appl Soft Comput 35:652–661

    Article  Google Scholar 

  49. Raissi M, Perdikaris P, Karniadakis GE Physics informed deep learning (part i): data-driven solutions of nonlinear partial differential equations. arXiv:1711.10561

  50. He Q, Tartakovsky G, Barajas-Solano D, Tartakovsky A (2019) Physics-informed deep neural networks for multiphysics data assimilation in subsurface transport problems. AGUFM 2019:H34B–02

  51. Tartakovsky A, Marrero C, Perdikaris P, Tartakovsky G, Barajas-Solano D (2020) Physics-informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems. Water Resour Res 56(5):e2019WR026731

    Article  Google Scholar 

  52. Lu L, Dao M, Kumar P, Ramamurty U, Karniadakis GE, Suresh S (2020) Extraction of mechanical properties of materials through deep learning from instrumented indentation. Proc Nat Acad Sci 117(13):7052–7062

    Article  Google Scholar 

  53. He Q, Chen J (2020) A physics-constrained data-driven approach based on locally convex reconstruction for noisy database. Comput Methods Appl Mech Eng 363:112791

    Article  MathSciNet  MATH  Google Scholar 

  54. Raissi M, Perdikaris P, Karniadakis G (2019) Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys 378:686–707

    Article  MathSciNet  MATH  Google Scholar 

  55. Kissas G, Yang Y, Hwuang E, Witschey W, Detre J, Perdikaris P (2020) Machine learning in cardiovascular flows modeling: predicting arterial blood pressure from non-invasive 4d flow mri data using physics-informed neural networks. Comput Methods Appl Mech Eng 358:112623

    Article  MathSciNet  MATH  Google Scholar 

  56. Dantzig JA, Rappaz M (2016) Solidification: revised & expanded. EPFL Press, Lausanne

    Google Scholar 

  57. Khan P, Debroy T (1984) Alloying element vaporization and weld pool temperature during laser welding of alsl 202 stainless steel. Metall Trans B 15(4):641–644

    Article  Google Scholar 

  58. Collur M, Paul A, Debroy T (1987) Mechanism of alloying element vaporization during laser welding. Metall Trans B 18(4):733–740

    Article  Google Scholar 

  59. Voller V, Swaminathan C (1991) Eral source-based method for solidification phase change. Numer Heat Transf Part B Fundam 19(2):175–189

    Article  Google Scholar 

  60. Liu W, Wang Z, Liu X, Zeng N, Liu Y, Alsaadi F (2017) A survey of deep neural network architectures and their applications. Neurocomputing 234:11–26

    Article  Google Scholar 

  61. Schwing AG, Urtasun R Fully connected deep structured networks. arXiv:1503.02351

  62. Lawrence S, Giles CL, Tsoi AC, Back AD (1997) Face recognition: a convolutional neural-network approach. IEEE Trans Neural Netw 8(1):98–113

    Article  Google Scholar 

  63. Mikolov T, Karafiát M, Burget L, Černockỳ J, Khudanpur S (2010)Recurrent neural network based language model. In: Eleventh annual conference of the international speech communication association

  64. Sengupta N, Sahidullah M, Saha G (2016) Lung sound classification using cepstral-based statistical features. Comput Biol Med 75:118–129

    Article  Google Scholar 

  65. Bishop CM (2006) Pattern recognition and machine learning. Springer, Berlin

    MATH  Google Scholar 

  66. Choy CB, Xu D, Gwak J, Chen K, Savarese S (2016) 3d-r2n2: a unified approach for single and multi-view 3d object reconstruction. In: European conference on computer vision. Springer, pp 628–644

  67. Han J, Pei J, Kamber M (2011) Data mining: concepts and techniques. Elsevier, Amsterdam

    MATH  Google Scholar 

  68. Liang S, Srikant R Why deep neural networks for function approximation? arXiv:1610.04161

  69. Sibi P, Jones SA, Siddarth P (2013) Analysis of different activation functions using back propagation neural networks. J Theor Appl Inf Technol 47(3):1264–1268

    Google Scholar 

  70. Maas A, Hannun A, Ng A (2013) Rectifier nonlinearities improve neural network acoustic models. In: Proceedings ICML, vol 30, p 3

  71. Eger S, Youssef P, Gurevych I Is it time to swish? comparing deep learning activation functions across nlp tasks. arXiv:1901.02671

  72. Ruder S An overview of gradient descent optimization algorithms. arXiv:1609.04747

  73. Kingma DP, Ba J Adam: a method for stochastic optimization. arXiv:1412.6980

  74. Baydin A, Pearlmutter B, Radul A, Siskind J (2017) Automatic differentiation in machine learning: a survey. J Mach Learn Res 18(1):5595–5637

    MathSciNet  MATH  Google Scholar 

  75. Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28:1–44. https://doi.org/10.1016/S0065-2156(08)70153-4

    Article  MathSciNet  MATH  Google Scholar 

  76. Takizawa K, Tezduyar TE (2011) Multiscale space-time fluid-structure interaction techniques. Comput Mech 48:247–267. https://doi.org/10.1007/s00466-011-0571-z

    Article  MathSciNet  MATH  Google Scholar 

  77. Takizawa K, Tezduyar TE (2012) Space-time fluid-structure interaction methods. Math Models Methods Appl Sci 22(supp02):1230001. https://doi.org/10.1142/S0218202512300013

    Article  MathSciNet  MATH  Google Scholar 

  78. Takizawa K, Tezduyar TE, Kuraishi T (2015) Multiscale ST methods for thermo-fluid analysis of a ground vehicle and its tires. Math Models Methods Appl Sci 25:2227–2255. https://doi.org/10.1142/S0218202515400072

    Article  MathSciNet  MATH  Google Scholar 

  79. Saad Y, Schultz MH (1986) Gmres: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7(3):856–869

    Article  MathSciNet  MATH  Google Scholar 

  80. Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37

    Article  MathSciNet  MATH  Google Scholar 

  81. Takizawa K, Bazilevs Y, Tezduyar TE (2012) Space-time and ALE-VMS techniques for patient-specific cardiovascular fluid-structure interaction modeling. Arch Comput Methods Eng 19:171–225. https://doi.org/10.1007/s11831-012-9071-3

    Article  MathSciNet  MATH  Google Scholar 

  82. Masud A, Calderer R (2009) A variational multiscale stabilized formulation for the incompressible Navier–Stokes equations. Comput Mech 44(2):145–160

    Article  MathSciNet  MATH  Google Scholar 

  83. Zhu L, Goraya S, Masud A (2019) Interface-capturing method for free-surface plunging and breaking waves. J Eng Mech 145(11):04019088

    Google Scholar 

  84. Calderer R, Zhu L, Gibson R, Masud A (2015) Residual-based turbulence models and arbitrary Lagrangian–Eulerian framework for free surface flows. Math Models Methods Appl Sci 25(12):2287–2317

    Article  MathSciNet  MATH  Google Scholar 

  85. Masud A, Calderer R (2013) Residual-based turbulence models for moving boundary flows: hierarchical application of variational multiscale method and three-level scale separation. Int J Numer Meth Fluids 73(3):284–305

    Article  MathSciNet  Google Scholar 

  86. Takizawa K, Tezduyar TE (2012) Computational methods for parachute fluid-structure interactions. Arch Comput Methods Eng 19:125–169. https://doi.org/10.1007/s11831-012-9070-4

    Article  MathSciNet  MATH  Google Scholar 

  87. Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid–structure interaction: methods and applications. Wiley, London. https://doi.org/10.1002/9781118483565

    Book  MATH  Google Scholar 

  88. Takizawa K, Fritze M, Montes D, Spielman T, Tezduyar TE (2012) Fluid-structure interaction modeling of ringsail parachutes with disreefing and modified geometric porosity. Comput Mech 50:835–854. https://doi.org/10.1007/s00466-012-0761-3

    Article  Google Scholar 

  89. Takizawa K, Tezduyar TE, Boben J, Kostov N, Boswell C, Buscher A (2013) Fluid–structure interaction modeling of clusters of spacecraft parachutes with modified geometric porosity. Comput Mech 52:1351–1364. https://doi.org/10.1007/s00466-013-0880-5

    Article  MATH  Google Scholar 

  90. Takizawa K, Tezduyar TE, Boswell C, Tsutsui Y, Montel K (2015) Special methods for aerodynamic-moment calculations from parachute FSI modeling. Comput Mech 55:1059–1069. https://doi.org/10.1007/s00466-014-1074-5

    Article  Google Scholar 

  91. Takizawa K, Bazilevs Y, Tezduyar TE, Korobenko A (2020) Computational flow analysis in aerospace, energy and transportation technologies with the variational multiscale methods. J Adv Eng Comput 4(2):83–117

    Article  MATH  Google Scholar 

  92. Ravensbergen M, Helgedagsrud T, Bazilevs YY, Korobenko A (2020) A variational multiscale framework for atmospheric turbulent flows over complex environmental terrains. Comput Methods Appl Mech Eng 368:113182

    Article  MathSciNet  Google Scholar 

  93. Bazilevs Y, Hsu M-C, Akkerman I, Wright S, Takizawa K, Henicke B, Spielman T, Tezduyar TE (2011) 3D simulation of wind turbine rotors at full scale. Part I: geometry modeling and aerodynamics. Int J Numer Methods Fluids 65:207–235. https://doi.org/10.1002/fld.2400

    Article  MATH  Google Scholar 

  94. Takizawa K, Henicke B, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48:333–344. https://doi.org/10.1007/s00466-011-0589-2

    Article  MATH  Google Scholar 

  95. Takizawa K, Henicke B, Montes D, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Numerical-performance studies for the stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48:647–657. https://doi.org/10.1007/s00466-011-0614-5

    Article  MATH  Google Scholar 

  96. Takizawa K, Tezduyar TE, McIntyre S, Kostov N, Kolesar R, Habluetzel C (2014) Space-time VMS computation of wind-turbine rotor and tower aerodynamics. Comput Mech 53:1–15. https://doi.org/10.1007/s00466-013-0888-x

    Article  MATH  Google Scholar 

  97. Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C, Øiseth O, Mathisen KM, Kostov N, McIntyre S (2014) Engineering analysis and design with ALE-VMS and space-time methods. Arch Comput Methods Eng 21:481–508. https://doi.org/10.1007/s11831-014-9113-0

    Article  MathSciNet  MATH  Google Scholar 

  98. Takizawa K (2014) Computational engineering analysis with the new-generation space-time methods. Comput Mech 54:193–211. https://doi.org/10.1007/s00466-014-0999-z

    Article  MathSciNet  Google Scholar 

  99. Bazilevs Y, Takizawa K, Tezduyar TE, Hsu M-C, Kostov N, McIntyre S (2014) Aerodynamic and FSI analysis of wind turbines with the ALE-VMS and ST-VMS methods. Arch Comput Methods Eng 21:359–398. https://doi.org/10.1007/s11831-014-9119-7

    Article  MathSciNet  MATH  Google Scholar 

  100. Takizawa K, Tezduyar TE, Mochizuki H, Hattori H, Mei S, Pan L, Montel K (2015) Space-time VMS method for flow computations with slip interfaces (ST-SI). Math Models Methods Appl Sci 25:2377–2406. https://doi.org/10.1142/S0218202515400126

    Article  MathSciNet  MATH  Google Scholar 

  101. Korobenko A, Bazilevs Y, Takizawa K, Tezduyar TE (2018) Recent advances in ALE-VMS and ST-VMS computational aerodynamic and FSI analysis of wind turbines. In: Tezduyar TE (ed) Frontiers in computational fluid-structure interaction and flow simulation: research from lead investigators under forty–2018, modeling and simulation in science, engineering and technology. Springer, Berlin, pp 253–336. https://doi.org/10.1007/978-3-319-96469-0_7

    Chapter  Google Scholar 

  102. Otoguro Y, Mochizuki H, Takizawa K, Tezduyar T (2020) Space-time variational multiscale isogeometric analysis of a tsunami-shelter vertical-axis wind turbine. Comput Mech 66(6):1443–1460

    Article  MathSciNet  Google Scholar 

  103. Ravensbergen M, Mohamed A, Korobenko A (2020) The actuator line method for wind turbine modelling applied in a variational multiscale framework. Comput Fluids 201:104465

    Article  MathSciNet  MATH  Google Scholar 

  104. Mohamed A, Bear C, Bear M, Korobenko A (2020) Performance analysis of two vertical-axis hydrokinetic turbines using variational multiscale method. Comput Fluids 200:104432

    Article  MathSciNet  MATH  Google Scholar 

  105. Bayram A, Korobenko A (2020) Variational multiscale framework for cavitating flows. Comput Mech 66:49–67

    Article  MathSciNet  MATH  Google Scholar 

  106. Takizawa K, Tezduyar TE, Buscher A, Asada S (2014) Space-time fluid mechanics computation of heart valve models. Comput Mech 54(4):973–986

    Article  MATH  Google Scholar 

  107. Terahara T, Takizawa K, Tezduyar T, Bazilevs Y, Hsu M (2020) Heart valve isogeometric sequentially-coupled fsi analysis with the space-time topology change method. Comput Mech 65:1167–1187

    Article  MathSciNet  MATH  Google Scholar 

  108. Terahara T, Takizawa K, Tezduyar T, Tsushima A, Shiozaki K (2020) Ventricle-valve-aorta flow analysis with the space-time isogeometric discretization and topology change. Comput Mech 65:1343–1363

    Article  MathSciNet  MATH  Google Scholar 

  109. Bazilevs Y, Takizawa K, Wu M, Kuraishi T, Avsar R, Xu Z, Tezduyar T (2020) Gas turbine computational flow and structure analysis with isogeometric discretization and a complex-geometry mesh generation method. Comput Mech. https://doi.org/10.1007/s00466-020-01919-w

    Article  Google Scholar 

  110. Bazilevs Y, Takizawa K, Tezduyar T, Hsu M, Otoguro Y, Mochizuki H, Wu M (2020) Wind turbine and turbomachinery computational analysis with the ale and space-time variational multiscale methods and isogeometric discretization. J Adv Eng Comput 4(1):1–32

    Article  MATH  Google Scholar 

  111. Kozak N, Rajanna M, Wu M, Murugan M, Bravo L, Ghoshal A, Hsu M, Bazilevs Y (2020) Optimizing gas turbine performance using the surrogate management framework and high-fidelity flow modeling. Energies 13(17):4283

    Article  Google Scholar 

  112. Otoguro Y, Takizawa K, Tezduyar TE, Nagaoka K, Avsar R, Zhang Y (2019) Space-time vms flow analysis of a turbocharger turbine with isogeometric discretization: computations with time-dependent and steady-inflow representations of the intake/exhaust cycle. Comput Mech 64(5):1403–1419

    Article  MathSciNet  MATH  Google Scholar 

  113. Otoguro Y, Takizawa K, Tezduyar TE, Nagaoka K, Mei S (2019) Turbocharger turbine and exhaust manifold flow computation with the space-time variational multiscale method and isogeometric analysis. Comput Fluids 179:764–776. https://doi.org/10.1016/j.compfluid.2018.05.019

    Article  MathSciNet  MATH  Google Scholar 

  114. Kuraishi T, Takizawa K, Tezduyar T (2019) Space-time computational analysis of tire aerodynamics with actual geometry, road contact, tire deformation, road roughness and fluid film. Comput Mech 64(6):1699–1718

    Article  MATH  Google Scholar 

  115. Kuraishi T, Takizawa K, Tezduyar TE (2019) Tire aerodynamics with actual tire geometry, road contact and tire deformation. Comput Mech 63:1165–1185. https://doi.org/10.1007/s00466-018-1642-1

    Article  MathSciNet  MATH  Google Scholar 

  116. Levine L, Lane B, Heigel J, Migler K, Stoudt M, Phan T, Ricker R, Strantza M, Hill M, Zhang F, Seppala J, Garboczi E, Bain E, Cole D, Allen A, Fox J, Campbell C (2020) Outcomes and conclusions from the 2018 am-bench measurements, challenge problems, modeling submissions, and conference. Integr Mater Manuf Innov 9(1):1–15

    Article  Google Scholar 

  117. Heigel J, Lane B, Levine L (2020) In situ measurements of melt-pool length and cooling rate during 3d builds of the metal am-bench artifacts. Integr Mater Manuf Innov 9(1):31–53

    Article  Google Scholar 

  118. Brandon L, Jarred H, Richard R, Ivan Z, Vladimir K, Jordan W, Thien P, Mark S, Sergey M, Lyle L (2020) Measurements of melt pool geometry and cooling rates of individual laser traces on in625 bare plates. Integr Mater Manuf Innov 9:16–30

    Article  Google Scholar 

  119. Heigel J, Lane B (2018) Measurement of the melt pool length during single scan tracks in a commercial laser powder bed fusion process. J Manuf Sci Eng 140(5):5–12

    Article  Google Scholar 

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Acknowledgements

J. Yan is partially supported by ASME Robert M. and Mary Haythornthwaite Research Initiation Award and Singapore National Research Foundation (NRF2018-ITS004-0011). The PINN models were trained at the Texas Advanced Computing Center (Tacc) through a startup allocation on Frontera (CTS20014). These supports are greatly acknowledged.

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  1. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Champaign, IL, USA

    Qiming Zhu & Jinhui Yan

  2. Livermore Software Technology, An ANSYS Company, Livermore, CA, USA

    Zeliang Liu

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  1. Qiming Zhu
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  2. Zeliang Liu
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Correspondence to Jinhui Yan.

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Zhu, Q., Liu, Z. & Yan, J. Machine learning for metal additive manufacturing: predicting temperature and melt pool fluid dynamics using physics-informed neural networks. Comput Mech 67, 619–635 (2021). https://doi.org/10.1007/s00466-020-01952-9

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