Advertisement

Novel applications of intelligent computing paradigms for the analysis of nonlinear reactive transport model of the fluid in soft tissues and microvessels

  • Iftikhar Ahmad
  • Hira Ilyas
  • Aysha Urooj
  • Muhammad Saeed AslamEmail author
  • Muhammad Shoaib
  • Muhammad Asif Zahoor Raja
Original Article
  • 43 Downloads

Abstract

This article presents a methodology to solve a one-dimensional steady-state nonlinear reactive transport model (RTM) that is meant for fluid and solute transport model of soft tissues and microvessels. The methodology integrates the artificial neural network (ANN), genetic algorithms (GAs), and pattern search (PS) aided by active-set technique (AST) and interior-point technique (IPT). The RTM is represented with nonlinear second-order system based on the boundary value problem of ordinary differential equation. The ANN modeling is used for governing expression of RTM to form a fitness function in mean square sense, and optimization solvers based on the GA, PS, GA-AST, GA-IPT, PS-AST, PS-IPT are used for viable learning of weights. Proposed techniques are applied to different nonlinear RTMs based on variation in the characteristic reaction rate and half-saturation concentration. The proposed stochastic numerical solutions are compared with state-of-the-art solvers in order to check the accuracy and convergence based on sufficient large multiple runs of the algorithms.

Keywords

Nonlinear reactive transport model Artificial neural networks Genetic algorithms Pattern search Interior-point technique Active-set technique 

Notes

Compliance with ethical standards

Conflict of interest

All the authors of the manuscript declared that there are no potential conflicts of interest.

Human and animal rights

All the authors of the manuscript declared that there is no research involving human participants and/or animal.

Informed consent

All the authors of the manuscript declared that there is no material that required informed consent.

References

  1. 1.
    Shivanian E (2014) On the multiplicity of solutions of the nonlinear reactive transport model. Ain Shams Eng J 5(2):637–645Google Scholar
  2. 2.
    Clement TP, Sun Y, Hooker BS, Petersen JN (1998) Modeling multispecies reactive transport in ground water. Groundw Monit Remediat 18(2):79–92Google Scholar
  3. 3.
    Steefel CI, DePaolo DJ, Lichtner PC (2005) Reactive transport modeling: an essential tool and a new research approach for the Earth sciences. Earth Planet Sci Lett 240(3–4):539–558Google Scholar
  4. 4.
    MacQuarrie KT, Mayer KU (2005) Reactive transport modeling in fractured rock: a state-of-the-science review. Earth Sci Rev 72(3–4):189–227Google Scholar
  5. 5.
    Steefel CI, Appelo CAJ, Arora B, Jacques D, Kalbacher T, Kolditz O, Lagneau V, Lichtner PC, Mayer KU, Meeussen JCL, Molins S (2015) Reactive transport codes for subsurface environmental simulation. Comput Geosci 19(3):445–478MathSciNetzbMATHGoogle Scholar
  6. 6.
    Pabst T, Molson J, Aubertin M, Bussière B (2017) Reactive transport modelling of the hydro-geochemical behaviour of partially oxidized acid-generating mine tailings with a monolayer cover. Appl Geochem 78:219–233Google Scholar
  7. 7.
    Regnier P, Jourabchi P, Slomp CP (2003) Reactive-transport modeling as a technique for understanding coupled biogeochemical processes in surface and subsurface environments. Neth J Geosci 82(1):5–18Google Scholar
  8. 8.
    Vilcáez J, Li L, Wu D, Hubbard SS (2013) Reactive transport modeling of induced selective plugging by Leuconostoc mesenteroides in carbonate formations. Geomicrobiol J 30(9):813–828Google Scholar
  9. 9.
    Ellery AJ, Simpson MJ (2011) An analytical method to solve a general class of nonlinear reactive transport models. Chem Eng J 169(1–3):313–318Google Scholar
  10. 10.
    Lu Y, Wang W (2010) Multiscale modeling of fluid and solute transport in soft tissues and microvessels. J Multiscale Model 2(01n02):127–145Google Scholar
  11. 11.
    Van Genuchten MT, Alves WJ (1982) Analytical solutions of the one-dimensional convective-dispersive solute transport equation (No. 157268). United States Department of Agriculture, Economic Research ServiceGoogle Scholar
  12. 12.
    Toride N, Leij FJ, Van Genuchten MT (1995) The CXTFIT code for estimating transport parameters from laboratory or field tracer experiments, vol 137, version 2.0, research reportGoogle Scholar
  13. 13.
    Donea J (1984) A Taylor–Galerkin method for convective transport problems. Int J Numer Meth Eng 20(1):101–119MathSciNetzbMATHGoogle Scholar
  14. 14.
    Wazwaz AM, Rach R, Bougoffa L (2016) Dual solutions for nonlinear boundary value problems by the Adomian decomposition method. Int J Numer Meth Heat Fluid Flow 26(8):2393–2409Google Scholar
  15. 15.
    Miah MM, Ali HS, Akbar MA, Wazwaz AM (2017) Some applications of the (G′/G, 1/G)-expansion method to find new exact solutions of NLEEs. Eur Phys J Plus 132(6):252Google Scholar
  16. 16.
    Rach R, Duan JS, Wazwaz AM (2015) On the solution of non-isothermal reaction-diffusion model equations in a spherical catalyst by the modified Adomian method. Chem Eng Commun 202(8):1081–1088Google Scholar
  17. 17.
    Wazwaz AM, Rach R, Duan JS (2014) A study on the systems of the Volterra integral forms of the Lane–Emden equations by the Adomian decomposition method. Math Methods Appl Sci 37(1):10–19MathSciNetzbMATHGoogle Scholar
  18. 18.
    Kuzmin D (2010) A guide to numerical methods for transport equations. University Erlangen-Nuremberg, ErlangenGoogle Scholar
  19. 19.
    Abo-Hammour Z, Abu Arqub O, Momani S, Shawagfeh N (2014) Optimization solution of Troesch’s and Bratu’s problems of ordinary type using novel continuous genetic algorithm. Discrete Dyn Nat Soc 2014:401696.  https://doi.org/10.1155/2014/401696 MathSciNetGoogle Scholar
  20. 20.
    Al-Smadi M, Arqub OA (2019) Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates. Appl Math Comput 342:280–294MathSciNetGoogle Scholar
  21. 21.
    Arqub OA, Maayah B (2018) Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana–Baleanu fractional operator. Chaos Solitons Fractals 117:117–124MathSciNetGoogle Scholar
  22. 22.
    Raja MAZ, Shah Z, Manzar MA, Ahmad I, Awais M, Baleanu D (2018) A new stochastic computing paradigm for nonlinear Painlevé II systems in applications of random matrix theory. Eur Phys J Plus 133(7):254Google Scholar
  23. 23.
    MolaAbasi H, Shooshpasha I (2016) Prediction of zeolite-cement-sand unconfined compressive strength using polynomial neural network. Eur Phys J Plus 131(4):108Google Scholar
  24. 24.
    Ahmad I et al (2018) Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics. Eur Phys J Plus 133(5):184Google Scholar
  25. 25.
    Sabir Z et al (2018) Neuro-heuristics for nonlinear singular Thomas–Fermi systems. Appl Soft Comput 65:152–169Google Scholar
  26. 26.
    Raja MAZ, Shah FH, Alaidarous ES, Syam MI (2017) Design of bio-inspired heuristic technique integrated with interior-point algorithm to analyze the dynamics of heartbeat model. Appl Soft Comput 52:605–629Google Scholar
  27. 27.
    Raja MAZ, Shah FH, Khan AA, Khan NA (2016) Design of bio-inspired computational intelligence technique for solving steady thin film flow of Johnson–Segalman fluid on vertical cylinder for drainage problems. J Taiwan Inst Chem Eng 60:59–75Google Scholar
  28. 28.
    Raja MAZ, Mehmood A, ur Rehman A, Khan A, Zameer A (2018) Bio-inspired computational heuristics for Sisko fluid flow and heat transfer models. Appl Soft Comput 71:622–648Google Scholar
  29. 29.
    Munir A, Manzar MA, Khan NA, Raja MAZ (2019) Intelligent computing approach to analyze the dynamics of wire coating with Oldroyd 8-constant fluid. Neural Comput Appl 31(3):751–775Google Scholar
  30. 30.
    Raja MAZ, Manzar MA, Shah FH, Shah FH (2018) Intelligent computing for Mathieu’s systems for parameter excitation, vertically driven pendulum and dusty plasma models. Appl Soft Comput 62:359–372Google Scholar
  31. 31.
    Raja MAZ, Ahmad I, Khan I, Syam MI, Wazwaz AM (2017) Neuro-heuristic computational intelligence for solving nonlinear pantograph systems. Front Inf Technol Electron Eng 18(4):464–484Google Scholar
  32. 32.
    Raja MAZ, Niazi SA, Butt SA (2017) An intelligent computing technique to analyze the vibrational dynamics of rotating electrical machine. Neurocomputing 219:280–299Google Scholar
  33. 33.
    Raja MAZ (2014) Solution of the one-dimensional Bratu equation arising in the fuel ignition model using ANN optimised with PSO and SQP. Connect Sci 26(3):195–214MathSciNetGoogle Scholar
  34. 34.
    Raja MAZ, Manzar MA, Samar R (2015) An efficient computational intelligence approach for solving fractional order Riccati equations using ANN and SQP. Appl Math Model 39(10–11):3075–3093MathSciNetGoogle Scholar
  35. 35.
    Raja MAZ, Samar R, Manzar MA, Shah SM (2017) Design of unsupervised fractional neural network model optimized with interior point algorithm for solving Bagley–Torvik equation. Math Comput Simul 132:139–158MathSciNetGoogle Scholar
  36. 36.
    Ahmad I et al (2016) Bio-inspired computational heuristics to study Lane–Emden systems arising in astrophysics model. SpringerPlus 5(1):1866Google Scholar
  37. 37.
    Raja MAZ, Zameer A, Khan AU, Wazwaz AM (2016) A new numerical approach to solve Thomas–Fermi model of an atom using bio-inspired heuristics integrated with sequential quadratic programming. SpringerPlus 5(1):1400Google Scholar
  38. 38.
    Raja MAZ, Shah FH, Tariq M, Ahmad I (2018) Design of artificial neural network models optimized with sequential quadratic programming to study the dynamics of nonlinear Troesch’s problem arising in plasma physics. Neural Comput Appl 29(6):83–109Google Scholar
  39. 39.
    Mehmood A, Zameer A, Ling SH, Raja MAZ (2018) Design of neuro-computing paradigms for nonlinear nanofluidic systems of MHD Jeffery-Hamel flow. J Taiwan Inst Chem Eng 91:57–85Google Scholar
  40. 40.
    Mehmood A et al (2018) Intelligent computing to analyze the dynamics of magnetohydrodynamic flow over stretchable rotating disk model. Appl Soft Comput 67:8–28Google Scholar
  41. 41.
    Akbar S et al (2017) Design of bio-inspired heuristic techniques hybridized with sequential quadratic programming for joint parameters estimation of electromagnetic plane waves. Wirel Pers Commun 96(1):1475–1494Google Scholar
  42. 42.
    Raja MAZ, Mehmood A, Niazi SA, Shah SM (2016) Computational intelligence methodology for the analysis of RC circuit modelled with nonlinear differential order system. Neural Comput Appl 30:1–20Google Scholar
  43. 43.
    Zameer A et al (2017) Intelligent and robust prediction of short term wind power using genetic programming based ensemble of neural networks. Energy Convers Manag 134:361–372Google Scholar
  44. 44.
    Raja MAZ, Shah AA, Mehmood A, Chaudhary NI, Aslam MS (2018) Bio-inspired computational heuristics for parameter estimation of nonlinear Hammerstein controlled autoregressive system. Neural Comput Appl 29(12):1455–1474Google Scholar
  45. 45.
    Ayestarán RG (2018) Fast near-field multifocusing of antenna arrays including element coupling using neural networks. IEEE Antennas Wirel Propag Lett 17(7):1233–1237Google Scholar
  46. 46.
    Mehmood A, Aslam MS, Chaudhary NI, Zameer A, Raja MAZ (2018) Parameter estimation for Hammerstein control autoregressive systems using differential evolution. Signal Image Video Process 12(8):1603–1610Google Scholar
  47. 47.
    Raja MAZ, Asma K, Aslam MS (2018) Bio-inspired computational heuristics to study models of HIV infection of CD4+ T-cell. Int J Biomath 11(02):1850019MathSciNetzbMATHGoogle Scholar
  48. 48.
    Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3(2):95–99Google Scholar
  49. 49.
    Nabaei A, Hamian M, Parsaei MR, Safdari R, Samad-Soltani T, Zarrabi H, Ghassemi A (2018) Topologies and performance of intelligent algorithms: a comprehensive review. Artif Intell Rev 49(1):79–103Google Scholar
  50. 50.
    Ghodousian A, Babalhavaeji A (2018) An efficient genetic algorithm for solving nonlinear optimization problems defined with fuzzy relational equations and max-Lukasiewicz composition. Appl Soft Comput 69:475–492Google Scholar
  51. 51.
    Mashwani WK, Salhi A, Yeniay O, Hussian H, Jan MA (2017) Hybrid non-dominated sorting genetic algorithm with adaptive operators selection. Appl Soft Comput 56:1–18Google Scholar
  52. 52.
    Armaghani DJ, Hasanipanah M, Mahdiyar A, Majid MZA, Amnieh HB, Tahir MM (2018) Airblast prediction through a hybrid genetic algorithm-ANN model. Neural Comput Appl 29(9):619–629Google Scholar
  53. 53.
    Kerh T, Su YH, Mosallam A (2017) Incorporating global search capability of a genetic algorithm into neural computing to model seismic records and soil test data. Neural Comput Appl 28(3):437–448Google Scholar
  54. 54.
    Riazi A, Türker U (2018) A genetic algorithm-based search space splitting pattern and its application in hydraulic and coastal engineering problems. Neural Comput Appl 30(12):3603–3612Google Scholar
  55. 55.
    Arqub OA, Abo-Hammour Z (2014) Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm. Inf Sci 279:396–415MathSciNetzbMATHGoogle Scholar
  56. 56.
    Kolda TG, Lewis RM, Torczon V (2003) Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev 45(3):385–482MathSciNetzbMATHGoogle Scholar
  57. 57.
    Torczon V (1997) On the convergence of pattern search algorithms. SIAM J Optim 7(1):1–25MathSciNetzbMATHGoogle Scholar
  58. 58.
    Audet C, Hare W (2017) Generalised pattern search. In: Derivative-free and blackbox optimization. Springer series in operations research and financial engineering. Springer, Cham, pp 115–134Google Scholar
  59. 59.
    Haghdar K, Shayanfar HA (2018) Selective harmonic elimination with optimal DC sources in multilevel inverters using generalized pattern search. IEEE Trans Ind Inf 14(7):3124–3131Google Scholar
  60. 60.
    Tobón A, Peláez-Restrepo J, Villegas-Ceballos J, Serna-Garcés SI, Herrera J, Ibeas A (2017) Maximum power point tracking of photovoltaic panels by using improved pattern search methods. Energies 10(9):1316Google Scholar
  61. 61.
    Chouhdry ZUR, Hasan KM, Raja MAZ (2018) Design of reduced search space strategy based on integration of Nelder-Mead method and pattern search algorithm with application to economic load dispatch problem. Neural Comput Appl 30(12):3693–3705Google Scholar
  62. 62.
    Kumar KS, Bach F (2017) Active-set methods for submodular minimization problems. J Mach Learn Res 18(1):4809–4839MathSciNetzbMATHGoogle Scholar
  63. 63.
    Hungerländer P, Rendl F (2015) A feasible active set method for strictly convex quadratic problems with simple bounds. SIAM J Optim 25(3):1633–1659MathSciNetzbMATHGoogle Scholar
  64. 64.
    Kato A, Yabe H, Yamashita H (2015) An interior point method with a primal–dual quadratic barrier penalty function for nonlinear semidefinite programming. J Comput Appl Math 275:148–161MathSciNetzbMATHGoogle Scholar
  65. 65.
    Mehrotra S (1992) On the implementation of a primal-dual interior point method. SIAM J Optim 2(4):575–601MathSciNetzbMATHGoogle Scholar
  66. 66.
    Wright SJ (1997) Primal-dual interior-point methods, vol 54. SIAM, PhiladelphiazbMATHGoogle Scholar
  67. 67.
    Andersen ED, Roos C, Terlaky T (2003) On implementing a primal-dual interior-point method for conic quadratic optimization. Math Program 95(2):249–277MathSciNetzbMATHGoogle Scholar
  68. 68.
    Hintermüller M, Ito K, Kunisch K (2002) The primal-dual active set strategy as a semismooth Newton method. SIAM J Optim 13(3):865–888MathSciNetzbMATHGoogle Scholar
  69. 69.
    Koehler S, Danielson C, Borrelli F (2017) A primal-dual active-set method for distributed model predictive control. Opt Control Appl Methods 38(3):399–419MathSciNetzbMATHGoogle Scholar
  70. 70.
    Porcelli M, Simoncini V, Tani M (2015) Preconditioning of active-set Newton methods for PDE-constrained optimal control problems. SIAM J Sci Comput 37(5):S472–S502MathSciNetzbMATHGoogle Scholar
  71. 71.
    Oliveira EJ, Oliveira LW, Pereira JLR, Honório LM, Junior ICS, Marcato ALM (2015) An optimal power flow based on safety barrier interior point method. Int J Electr Power Energy Syst 64:977–985Google Scholar
  72. 72.
    Huo D, Le Blond S, Gu C, Wei W, Yu D (2018) Optimal operation of interconnected energy hubs by using decomposed hybrid particle swarm and interior-point approach. Int J Electr Power Energy Syst 95:36–46Google Scholar
  73. 73.
    Zhou X, Yang J, Li Z, Tong D (2018) pth Moment synchronization of Markov switched neural networks driven by fractional Brownian noise. Neural Comput Appl 29(10):823–836Google Scholar
  74. 74.
    Lodhi S, Manzar MA, Raja MAZ (2019) Fractional neural network models for nonlinear Riccati systems. Neural Comput Appl 31(suppl 1):359–378Google Scholar
  75. 75.
    Peng X, Wu H (2018) Non-fragile robust finite-time stabilization and H performance analysis for fractionalorder delayed neural networks with discontinuous activations under the asynchronous switching. Neural Comput Appl.  https://doi.org/10.1007/s00521-018-3682-z Google Scholar
  76. 76.
    Akbar S, Zaman F, Asif M, Rehman AU, Raja MAZ (2018) Novel application of FO-DPSO for 2-D parameter estimation of electromagnetic plane waves. Neural Comput Appl.  https://doi.org/10.1007/s00521-017-3318-8 Google Scholar
  77. 77.
    Wang Y-Y, Zhang H, Qiu C-H, Xia S-R (2018) A novel feature selection method based on extreme learning machine and fractional-order Darwinian PSO. Comput Intell Neurosci 2018:5078268.  https://doi.org/10.1155/2018/5078268 Google Scholar
  78. 78.
    Pires ES, Machado JT, de Moura Oliveira PB, Cunha JB, Mendes L (2010) Particle swarm optimization with fractional-order velocity. Nonlinear Dyn 61(1–2):295–301zbMATHGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GujratGujratPakistan
  2. 2.School of Electrical and Electronic EngineeringUniversity of AdelaideAdelaideAustralia
  3. 3.Department of MathematicsCOMSATS University IslamabadAttockPakistan
  4. 4.Department of Electrical and Computer EngineeringCOMSATS University IslamabadAttockPakistan

Personalised recommendations