[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Novel physics informed-neural networks for estimation of hydraulic conductivity of green infrastructure as a performance metric by solving Richards–Richardson PDE

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

Abstract

Green infrastructure (GI) is an ecologically informed approach to stormwater management that is potentially sustainable and effective. Infiltration-based GI systems, including rain gardens, permeable pavements, green roofs infiltrate surface water and stormwater run-off to recharge ground water systems. However, these systems are susceptible to clogging and deterioration of their function, and we have limited understanding of the evolution of their function due to the lack of long-term monitoring. The ability of these systems to infiltrate water depends on the unsaturated hydraulic conductivity function K of the soil. We introduce a novel approach based on physics informed neural networks (PINNs) to estimate K of a homogeneous column of soil using data from volumetric water content sensors and by solving the Richards–Richardson partial differential equation (RRE). We introduce and compare two different deep neural network architectures to solve RRE and estimate K. To generate the ground truth, we simulate three types of soil water dynamics using HYDRUS-1D and compare the results of these two neural network architectures in terms of the estimation of K. We investigate the effect of inter-sensor placement on the estimation of K. Both architectures show satisfactory performance on homogeneous soil with three volumetric water content sensors with different advantages. PINN-based estimation of K can be used fundamental tool for assessment of the evolution of the performance of GI over time, while requiring as input only the data from simple soil moisture sensors that are easily installed at the time of GI construction or even retrofitted.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data availability

The dataset used in this study is available through Zenodo https://doi.org/https://doi.org/10.5281/zenodo.8173194.

References

  1. Badiu DL, Nita A, Iojă CI, Niţă MR (2019) Disentangling the connections: a network analysis of approaches to urban green infrastructure. Urban For Urban Green 41:211–220. https://doi.org/10.1016/j.ufug.2019.04.013

    Article  Google Scholar 

  2. Hanna E, Comín FA (2021) Urban green infrastructure and sustainable development: a review. Sustainability. https://doi.org/10.3390/su132011498

    Article  Google Scholar 

  3. Clary J, Leisenring M, Jones J, Hobson P, Strecker E (2020) International stormwater BMP database: 2020 summary statistics. Water Res Found 4968:1–118

    Google Scholar 

  4. William R, Gardoni P, Stillwell AS (2019) Reliability-based approach to investigating long-term clogging in green stormwater infrastructure. J Sustain Water Built Environ. https://doi.org/10.1061/jswbay.0000875

    Article  Google Scholar 

  5. Zhang K, Chui TFM (2019) A review on implementing infiltration-based green infrastructure in shallow groundwater environments: challenges, approaches, and progress. J Hydrol. https://doi.org/10.1016/j.jhydrol.2019.124089

    Article  Google Scholar 

  6. Lewellyn C, Lyons CE, Traver RG, Wadzuk BM (2016) Evaluation of seasonal and large storm runoff volume capture of an infiltration green infrastructure system. J Hydrol Eng. https://doi.org/10.1061/(asce)he.1943-5584.0001257

    Article  Google Scholar 

  7. Hopmans JW, Šimůnek J, Romano N, Durner W (2018) Inverse methods. Methods Soil Anal Part 4 Phys Methods. https://doi.org/10.2136/sssabookser5.4.c40

    Article  Google Scholar 

  8. Farthing MW, Ogden FL (2017) Numerical solution of richards’ equation: a review of advances and challenges. Soil Sci Soc Am J 81(6):1257–1269. https://doi.org/10.2136/sssaj2017.02.0058

    Article  CAS  Google Scholar 

  9. Tracy FT (2006) Clean two- and three-dimensional analytical solutions of Richards’ equation for testing numerical solvers. Water Resour Res. https://doi.org/10.1029/2005WR004638

    Article  Google Scholar 

  10. Cockett R, Heagy LJ, Haber E (2018) Efficient 3D inversions using the Richards equation. Comput Geosci 116:91–102. https://doi.org/10.1016/j.cageo.2018.04.006

    Article  ADS  Google Scholar 

  11. Bilionis I, Zabaras N (2014) Solution of inverse problems with limited forward solver evaluations: a Bayesian perspective. Inverse Probl. https://doi.org/10.1088/0266-5611/30/1/015004

    Article  MathSciNet  Google Scholar 

  12. Zha Y, Yang J, Zeng J, Tso CHM, Zeng W, Shi L (2019) Review of numerical solution of Richardson–Richards equation for variably saturated flow in soils. Wiley Interdiscip Rev Water. https://doi.org/10.1002/wat2.1364

    Article  Google Scholar 

  13. van Genuchten MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44:892–898

    Google Scholar 

  14. Brooks R, Corey A (1964) Hydraulic properties of porous media. Hydrol Pap Color State Univ 3(3):37

    Google Scholar 

  15. Barari A, Omidvar M, Ghotbi AR, Ganji DD, Barari A (2009) Numerical analysis of Richards’ problem for water penetration in unsaturated soils. Hydrol Earth Syst Sci Discuss 6(5):6359–6385

    ADS  Google Scholar 

  16. Tubini N (2021) Theoretical and numerical tools for studying the critical zone from plot to catchments. Doctoral dissertation, University of Trento [Online]. https://iris.unitn.it/retrieve/handle/11572/319821/498093/Tubini_2021_Theoretical_and_numerical_tools_for_studying_the_Critical_Zone_from_plot_to_catchments.pdf

  17. Rai PK, Tripathi S (2019) Gaussian process for estimating parameters of partial differential equations and its application to the Richards equation. Stoch Environ Res Risk Assess 33(8–9):1629–1649. https://doi.org/10.1007/s00477-019-01709-8

    Article  Google Scholar 

  18. Raissi M, Perdikaris P, Karniadakis GE (2018) Numerical Gaussian processes for time-dependent and nonlinear partial differential equations. SIAM J Sci Comput 40(1):A172–A198. https://doi.org/10.1137/17M1120762

    Article  MathSciNet  Google Scholar 

  19. Raissi M, Perdikaris P, Karniadakis GE (2017) Machine learning of linear differential equations using Gaussian processes. J Comput Phys 348:683–693. https://doi.org/10.1016/j.jcp.2017.07.050

    Article  MathSciNet  ADS  Google Scholar 

  20. Raissi M, Perdikaris P, Karniadakis GE (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. https://doi.org/10.1016/j.jcp.2018.10.045

    Article  MathSciNet  ADS  Google Scholar 

  21. Degen D et al (2023) Perspectives of physics-based machine learning for geoscientific applications governed by partial differential equations. Geosci Model Dev. https://doi.org/10.5194/gmd-16-7375-2023

  22. Cuomo S, Di Cola VS, Giampaolo F, Rozza G, Raissi M, Piccialli F (2022) Scientific machine learning through physics–informed neural networks: where we are and what’s next. J Sci Comput. https://doi.org/10.1007/s10915-022-01939-z

    Article  MathSciNet  Google Scholar 

  23. Cai S, Mao Z, Wang Z, Yin M, Karniadakis GE (2021) Physics-informed neural networks (PINNs) for fluid mechanics: a review. Acta Mech Sin Xuebao 37(12):1727–1738. https://doi.org/10.1007/s10409-021-01148-1

    Article  MathSciNet  ADS  Google Scholar 

  24. Mishra S, Molinaro R (2022) Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs. IMA J Numer Anal 42(2):981–1022. https://doi.org/10.1093/imanum/drab032

    Article  MathSciNet  Google Scholar 

  25. Yu J, Lu L, Meng X, Karniadakis GE (2022) Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. Comput Methods Appl Mech Eng. https://doi.org/10.1016/j.cma.2022.114823

    Article  MathSciNet  PubMed  PubMed Central  Google Scholar 

  26. Bandai T, Ghezzehei TA (2021) Physics-informed neural networks with monotonicity constraints for richardson-richards equation: estimation of constitutive relationships and soil water flux density from volumetric water content measurements. Water Resour Res. https://doi.org/10.1029/2020WR027642

    Article  Google Scholar 

  27. EPA (2016) Operation and maintenance of green infrastructure receiving runoff from roads and parking lots. https://www.epa.gov/sites/production/files/2016-11/documents/final_gi_maintenance_508.pdf

  28. Philip JR (1969) Theory of infiltration. Adv Hydrosci. https://doi.org/10.1016/b978-1-4831-9936-8.50010-6

    Article  Google Scholar 

  29. He K, Zhang X, Ren S, Sun J (2016) Deep residual learning for image recognition. Proc IEEE Comput Soc Conf Comput Vis Pattern Recognit 2016:770–778. https://doi.org/10.1109/CVPR.2016.90

    Article  Google Scholar 

  30. Loshchilov I, Hutter F (2019) Decoupled weight decay regularization. In: 7th International conference on learning representations ICLR 2019.

  31. Bandai T, Ghezzehei TA (2023) Applications of physics informed neural networks for modeling soil water dynamics. In: Abstract from 13th annual meeting interpore 2021. https://events.interpore.org/event/25/attachments/580/1179/2021_book-of-abstracts.pdf. Accessed 27 Nov 2023

  32. Güneş Baydin A, Pearlmutter BA, Andreyevich Radul A, Mark Siskind J (2018) Automatic differentiation in machine learning: a survey. J Mach Learn Res 18:1–43

    MathSciNet  Google Scholar 

  33. Glorot X, Bengio Y (2010) Understanding the difficulty of training deep feedforward neural networks. J Mach Learn Res 9:249–256

    Google Scholar 

  34. Simůnek J, Sejna M, Saito H, van Genuchten MT (2009) The HYDRUS-1D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably-saturated media. Environ Sci 3:1–240

  35. Holtzman R, Dentz M, Planet R, Ortin J (2023) Hysteresis of multiphase flow in porous and fractured media. In: Abstract from 11th annual meeting interpore 2019 Valencia, Valencia, Spain. https://orbit.dtu.dk/files/187391656/book_of_abstracts_interpore.pdf. Accessed 27 Nov 2023

Download references

Acknowledgements

The publicly available data used for this study (scenario 1 & 2) as well as the code for the second PINN architecture (based on Dr. Maziar Raissi PINN code) and the code used to transform “Nod_inf.out” files from Hydrus 1D to csv files created by Dr. Toshiyuki Bandai and Dr. Teamrat A. Ghezzehei were helpful for this study. This study was funded by the National Science Foundation, grant 1854827.

Funding

This study was funded by the National Science Foundation, Grant 1854827.

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Pittsburgh, Pittsburgh, PA, USA

    Mahmoud Elkhadrawi & Murat Akcakaya

  2. Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, PA, USA

    Carla Ng

  3. Department of Geology and Environmental Science, University of Pittsburgh, Pittsburgh, PA, USA

    Daniel J. Bain, Emelia E. Sargent & Emma V. Stearsman

  4. Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL, USA

    Kimberly A. Gray

Authors
  1. Mahmoud Elkhadrawi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carla Ng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniel J. Bain
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Emelia E. Sargent
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Emma V. Stearsman
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Kimberly A. Gray
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Murat Akcakaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mahmoud Elkhadrawi.

Ethics declarations

Conflict of interest

The authors have no competing interests to declare that are relevant to the content of this article.

Additional information

Publisher's Note

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

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (TIFF 1789 KB)

Supplementary file2 (TIFF 1861 KB)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Elkhadrawi, M., Ng, C., Bain, D.J. et al. Novel physics informed-neural networks for estimation of hydraulic conductivity of green infrastructure as a performance metric by solving Richards–Richardson PDE. Neural Comput & Applic 36, 5555–5569 (2024). https://doi.org/10.1007/s00521-023-09378-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-023-09378-z

Keywords

Search

Navigation