Skip to main content
SpringerLink
Log in

A granular recurrent neural network for multiple time series prediction

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

We present a computing scheme as a variant of a recently proposed granular recurrent neural network. Being deduced from a generic system of partial differential equations, this variant is able to capture the spatiotemporal variability of some datasets and problems. The convergence of the computing scheme has been formally discussed. Some preliminary numerical experiments were first performed by using synthetic datasets, inferring some particular partial differential equations. Then two application examples were considered (by using publicly available datasets), namely the prediction of dissolved oxygen in surface water simultaneously at different depths (unlike the current literature) and the prediction of the concentration of particulate matter less than 2.5 \(\upmu\)m in diameter at different sites. The numerical results show the potential of the approach for forecast against well-known techniques such as Long Short-Term Memory networks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Bessa RJ, Trindade A, Miranda V (2015) Spatial-temporal solar power forecasting for smart grids. IEEE Trans Ind Inf 11(1):232–241

    Google Scholar 

  2. Tascikaraoglu A (2018) Evaluation of spatio-temporal forecasting methods in various smart city applications. Renew Sustain Energy Rev 82:424–435

    Google Scholar 

  3. Wan H, Guo S, Yin K, Liang X, Lin Y (2019) CTS-LSTM: LSTM-based neural networks for correlated time series prediction, in press

  4. Asadi R, Regan AC (2020) A spatio-temporal decomposition based deep neural network for time series forecasting. Appl Soft Comput 87:105963

    Google Scholar 

  5. Xu W, Wang Q, Chen R (2018) Spatio-temporal prediction of crop disease severity for agricultural emergency management based on recurrent neural networks. Geoinformatica 22:363–381

    Google Scholar 

  6. Wetzel RG (2001) Limnology: lake and river ecosystems, 3rd edn. Academic Press, San Diego, CA

    Google Scholar 

  7. Song C et al (2017) Health burden attributable to ambient PM2.5 in China. Environ Pollut 223:575–586

    Google Scholar 

  8. Hull V, Parrella L, Falcucci M (2008) Modelling dissolved oxygen dynamics in coastal lagoons. Ecol Model 211:468–480

    Google Scholar 

  9. Long BT (2020) Inverse algorithm for Streeter-Phelps equation in water pollution control problem. Math Comput Simul 171:119–126

    MathSciNet  MATH  Google Scholar 

  10. Boano F, Revelli R, Ridolfi L (2006) Stochastic modelling of DO and BOD components in a stream with random inputs. Adv Water Resour 29:1341–1350

    Google Scholar 

  11. Olyaie E, Abyaneh HZ, Mehr AD (2017) A comparative analysis among computational intelligence techniques for dissolved oxygen prediction in Delaware River. Geosci Front 8(3):517–527

    Google Scholar 

  12. Liu Y, Zhang Q, Song L, Chen Y (2019) Attention-based recurrent neural networks for accurate short-term and long-term dissolved oxygen prediction. Comput Elect Agric 165:104964

    Google Scholar 

  13. Frieder CA, Nam SH, Martz TR, Levin LA (2012) High temporal and spatial variability of dissolved oxygen and pH in a nearshore California kelp forest. Biogeoscience 9:3917–3930

    Google Scholar 

  14. Noges T, Kangro K (2005) Primary production of phytoplankton in a strongly stratified temperate lake. Hydrobiologia 547:105–122

    Google Scholar 

  15. Keshtegar B, Heddam S (2018) Modeling daily dissolved oxygen concentration using modified response surface method and artificial neural network: a comparative study. Neural Comput Appl 30:2995–3006

    Google Scholar 

  16. Antanasijevic D, Pocajt V, Peric-Grujic A, Ristic M (2020) Multilevel split of high-dimensional water quality data using artificial neural networks for the prediction of dissolved oxygen in the Danube River. Neural Comput Appl 32:3957–3966

    Google Scholar 

  17. Li S, Xie G, Ren J, Yang Y, Xu X (2020) Urban PM2.5 concentration prediction via attention-based CNN-LSTM. Appl Sci 10(6):1953

    Google Scholar 

  18. Zhao Y (2020) Spatial-temporal correlation-based ISTM algorithm and its application in PM2.5 prediction. Revue Intel Artif 34(1):29–38

    Google Scholar 

  19. Aquino G, Zacarias A, Rubio JDJ, Pacheco J, Gutierrez GJ, Ochoa G, Balcazar R, Cruz DR, Garcia E, Novoa JF (2020) Novel nonlinear hypothesis for the delta parallel robot modeling. IEEE Access 8(1):46324–46334

    Google Scholar 

  20. Rubio JDJ (2009) SOFMLS: online self-organizing fuzzy modified least-squares network. IEEE Trans Fuz Syst 17(6):1296–1309

    Google Scholar 

  21. Chiang H-S, Chen M-Y, Huang Y-J (2019) Wavelet-based EEG processing for epilepsy detection using fuzzy entropy and associative Petri net. IEEE Access 7:103255–103262

    Google Scholar 

  22. Rubio JDJ (2020) Stability analysis of the modified Levenberg–Marquardt algorithm for the artificial neural network training. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3015200

    Article  Google Scholar 

  23. Meda-Campana JA (2018) On the estimation and control of nonlinear systems with parametric uncertainties and noisy outputs. IEEE Access 6:31968–31973

    Google Scholar 

  24. Hernandez G, Zamora E, Sossa H, Tellez G, Furlan F (2020) Hybrid neural networks for big data classification. Neurocomputing 390:327–340

    Google Scholar 

  25. Raissi M (2018) Deep hidden physics models: deep learning of nonlinear partial differential equations. J Mach Learn Res 19:1–24

    MathSciNet  MATH  Google Scholar 

  26. Lipton ZC (2018) The mythos of model interpretability. ACM Queue 16(3):1–27

    MathSciNet  Google Scholar 

  27. Itani S, Lecron F, Fortemps P (2019) Specifics of medical data mining for diagnosis aid: a survey. Exp Sys Appl 118:300–314

    Google Scholar 

  28. Colace F, Loia V, Tomasiello S (2019) Revising recurrent neural networks from a granular perspective. Appl Soft Comput 82:105535

    Google Scholar 

  29. Loia V, Parente D, Pedrycz W, Tomasiello S (2018) A granular functional network with delay: some dynamical properties and application to the sign prediction in social networks. Neurocomputing 321:61–1

    Google Scholar 

  30. Ying H (1998) General Takagi–Sugeno fuzzy systems with simplified linear rule consequent are universal controllers, models and filters. Inf Sci 108:91–107

    MathSciNet  MATH  Google Scholar 

  31. Bertone AM, Motta JR, Carvalho de Barros L, Gomide F (2017) Granular approximation of solutions of partial differential equations with fuzzy parameter. Gran Comput in press

  32. Silveira G, Barros L (2015) Analysis of the dengue risk by means of a Takagi–Sugeno-style model. Fuz Sets Syst 277(15):122–137

    MathSciNet  MATH  Google Scholar 

  33. Chen B-S, Chang Y-T (2009) Fuzzy state-space modeling and robust observer-based control design for nonlinear partial differential systems. IEEE Trans Fuz Syst 17(5):1025–1043

    Google Scholar 

  34. Matlab documentation www.mathworks.com/help/deeplearning/examples/ sequence-to-sequence-regression-using-deep-learning.html? searchHighlight=constant&s\_tid=doc\_srchtitle (accessed June 2020)

  35. Kiselak J, Lu Y, Svihra J, Szepe P, Stehlık M (2020) “SPOCU”: scaled polynomial constant unit activation function. Neural Comput Appl (in press)

  36. Zhu M, Min W, Wang Q, Zou S, Chen X PFLU and FPFLU: two novel non-monotonic activation functions in convolutional neural networks. Neurocomputing, 429, 110-117

  37. Regulation (EU) 2016/679 on the protection of natural persons with regard to the processing of personal data and on the free movement of such data, and repealing. Directive 95/46/EC (General Data Protection Regulation) [2016] OJ L119/1

  38. Bede B, Rudas IJ (2011) Approximation properties of fuzzy transforms. Fuz Sets Syst 180:20–40

    MathSciNet  MATH  Google Scholar 

  39. Lyche T, Schumaker LL (1975) Local spline approximation methods. J Approx Theory 15(4):294–325

    MathSciNet  MATH  Google Scholar 

  40. Pedrycz W, Vukovich W (2001) Granular neural networks. Neurocomputing 36:205–224. https://doi.org/10.1007/s40815-020-00903-z

    Article  MATH  Google Scholar 

  41. Bellman R, Casti J (1971) Differential differential quadrature and long-term integration. J Math Anal Appl 34:235–238

    MathSciNet  MATH  Google Scholar 

  42. Jaeger H (2001) The echo state approach to analysing and training recurrent neural networks. German National Research Center Information Technology,St. Augustin, Germany, Technical Report 148

  43. Ryan TP (1997) Modern regression methods. Wiley, New York

    MATH  Google Scholar 

  44. Rousseeuw PJ, Leroy A (1987) Robust regression and outlier detection. Wiley, New York

    MATH  Google Scholar 

  45. Suykens JAK, De Brabanter J, Lukas L, Vandewalle J (2002) Neurocomputing 48:85–105

    Google Scholar 

  46. Ding S, Ma G, Shi Z (2014) A rough RBF neural network based on weighted regularized extreme learning machine. Neural Process Lett 40:245–260

    Google Scholar 

  47. Merikoski JK, Urpala U, Virtanen A (1997) A best upper bound for the 2-norm condition number of a matrix. Lin Alg Appl 254:355–365

    MathSciNet  MATH  Google Scholar 

  48. Jin L, Nikifork N, Gupta MM (1994) Absolute stability conditions for discrete-time neural networks. IEEE Trans Neural Netw 5:954–964

    Google Scholar 

  49. Devaney RL (1989) An introduction to chaotic dynamical systems. Addison-Wesley, Reading

    MATH  Google Scholar 

  50. Horn RA, Johnson CA (1985) Matrix analysis. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  51. Kiselak J, Lu Y, Svihra J, Szepe P, Stehlık M (2020) Correction to: “SPOCU”: scaled polynomial constant unit activation function. Neural Comput Appl

  52. Buyukasık SA, Pashaev OK (2013) Exact solutions of forced Burgers equations with time variable coefficients. Commun Nonlin Sci Num Sim 18:1635–1651

    MathSciNet  MATH  Google Scholar 

  53. https://www.bco-dmo.org/dataset-deployment/455062 (accessed June 2020)

  54. Zhang S, Guo B, Dong A, He J, Xu Z, Chen SX (2017) Cautionary tales on air-quality improvement in Beijing. Proceed R Soc A 473(2205):20170457

    Google Scholar 

  55. https://archive.ics.uci.edu/ml/datasets/Beijing+Multi-Site+Air-Quality+Data Accessed June 2020

  56. http://climate.weatheroffice.gc.ca/prods_servs/normals_documentation_e.html Accessed June 2020

Download references

Acknowledgements

Dr. Stefania Tomasiello acknowledges support from the IT Academy programme.

Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Tartu, Tartu, Estonia

    Stefania Tomasiello

  2. Dipartimento di Scienze Aziendali - Management and Innovation Systems (DISA-MIS), Università degli Studi di Salerno, Fisciano, Italy

    Vincenzo Loia

  3. Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN, USA

    Abdul Khaliq

Authors
  1. Stefania Tomasiello
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vincenzo Loia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abdul Khaliq
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefania Tomasiello.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest to this work.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tomasiello, S., Loia, V. & Khaliq, A. A granular recurrent neural network for multiple time series prediction. Neural Comput & Applic 33, 10293–10310 (2021). https://doi.org/10.1007/s00521-021-05791-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-021-05791-4

Keywords

Search

Navigation