IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v464y2024ics0096300323005611.html
   My bibliography  Save this article

Model discovery of compartmental models with Graph-Supported Neural Networks

Author

Listed:
  • Aguilar-Canto, Fernando Javier
  • Brito-Loeza, Carlos
  • Calvo, Hiram

Abstract

In this proposal, our objective is to create a neural network for the discovery of models using compartmental models as systems of Ordinary Differential Equations (ODEs), employing Graph-Supported Neural Networks (GSNN). We design the GSNN as a graph of transition functions of the structure of the model to ensure that the three properties of the ODE solution are satisfied: additivity to one, positivity, and boundness. Rather than directly estimating the solution, these neural networks approximate the transition functions. We present theoretical evidence substantiating that our GSNN maintains these properties, along with approximation outcomes from both simulated and real-world data. These outcomes demonstrate that our GSNN outperforms the non-graph-supported approach for these issues, with instances where it even surpasses full model-based solutions and Recurrent Neural Networks. Furthermore, an evolutionary algorithm successfully generated a consistent model using the data, offering a comprehensive framework for neural network-based model discovery in these scenarios.

Suggested Citation

  • Aguilar-Canto, Fernando Javier & Brito-Loeza, Carlos & Calvo, Hiram, 2024. "Model discovery of compartmental models with Graph-Supported Neural Networks," Applied Mathematics and Computation, Elsevier, vol. 464(C).
    • Handle: RePEc:eee:apmaco:v:464:y:2024:i:c:s0096300323005611
    DOI: 10.1016/j.amc.2023.128392
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323005611
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.128392?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Volodymyr Mnih & Koray Kavukcuoglu & David Silver & Andrei A. Rusu & Joel Veness & Marc G. Bellemare & Alex Graves & Martin Riedmiller & Andreas K. Fidjeland & Georg Ostrovski & Stig Petersen & Charle, 2015. "Human-level control through deep reinforcement learning," Nature, Nature, vol. 518(7540), pages 529-533, February.
    2. Luís F. Seoane & Xaquín Loredo & Henrique Monteagudo & Jorge Mira, 2019. "Is the coexistence of Catalan and Spanish possible in Catalonia?," Palgrave Communications, Palgrave Macmillan, vol. 5(1), pages 1-9, December.
    3. Daniel M. Abrams & Steven H. Strogatz, 2003. "Modelling the dynamics of language death," Nature, Nature, vol. 424(6951), pages 900-900, August.
    4. Yinghao Chen & Hanyu Yu & Xiangyu Meng & Xiaoliang Xie & Muzhou Hou & Julien Chevallier, 2021. "Numerical solving of the generalized Black-Scholes differential equation using Laguerre neural network," Post-Print halshs-04250266, HAL.
    5. Bryan C Daniels & Ilya Nemenman, 2015. "Efficient Inference of Parsimonious Phenomenological Models of Cellular Dynamics Using S-Systems and Alternating Regression," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-14, March.
    6. Bryan C. Daniels & Ilya Nemenman, 2015. "Automated adaptive inference of phenomenological dynamical models," Nature Communications, Nature, vol. 6(1), pages 1-8, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Saavedra, Martín & Mira, Jorge & Muñuzuri, Alberto P. & Seoane, Luís F., 2023. "A spectrum of complexity uncovers Dunbar’s number and other leaps in social structure," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Michael Boissonneault & Paul Vogt, 2021. "A systematic and interdisciplinary review of mathematical models of language competition," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-12, December.
    3. Tulika Saha & Sriparna Saha & Pushpak Bhattacharyya, 2020. "Towards sentiment aided dialogue policy learning for multi-intent conversations using hierarchical reinforcement learning," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-28, July.
    4. Mahmoud Mahfouz & Angelos Filos & Cyrine Chtourou & Joshua Lockhart & Samuel Assefa & Manuela Veloso & Danilo Mandic & Tucker Balch, 2019. "On the Importance of Opponent Modeling in Auction Markets," Papers 1911.12816, arXiv.org.
    5. Imen Azzouz & Wiem Fekih Hassen, 2023. "Optimization of Electric Vehicles Charging Scheduling Based on Deep Reinforcement Learning: A Decentralized Approach," Energies, MDPI, vol. 16(24), pages 1-18, December.
    6. Jacob W. Crandall & Mayada Oudah & Tennom & Fatimah Ishowo-Oloko & Sherief Abdallah & Jean-François Bonnefon & Manuel Cebrian & Azim Shariff & Michael A. Goodrich & Iyad Rahwan, 2018. "Cooperating with machines," Nature Communications, Nature, vol. 9(1), pages 1-12, December.
      • Abdallah, Sherief & Bonnefon, Jean-François & Cebrian, Manuel & Crandall, Jacob W. & Ishowo-Oloko, Fatimah & Oudah, Mayada & Rahwan, Iyad & Shariff, Azim & Tennom,, 2017. "Cooperating with Machines," TSE Working Papers 17-806, Toulouse School of Economics (TSE).
      • Abdallah, Sherief & Bonnefon, Jean-François & Cebrian, Manuel & Crandall, Jacob W. & Ishowo-Oloko, Fatimah & Oudah, Mayada & Rahwan, Iyad & Shariff, Azim & Tennom,, 2017. "Cooperating with Machines," IAST Working Papers 17-68, Institute for Advanced Study in Toulouse (IAST).
      • Jacob Crandall & Mayada Oudah & Fatimah Ishowo-Oloko Tennom & Fatimah Ishowo-Oloko & Sherief Abdallah & Jean-François Bonnefon & Manuel Cebrian & Azim Shariff & Michael Goodrich & Iyad Rahwan, 2018. "Cooperating with machines," Post-Print hal-01897802, HAL.
    7. Sun, Alexander Y., 2020. "Optimal carbon storage reservoir management through deep reinforcement learning," Applied Energy, Elsevier, vol. 278(C).
    8. Yassine Chemingui & Adel Gastli & Omar Ellabban, 2020. "Reinforcement Learning-Based School Energy Management System," Energies, MDPI, vol. 13(23), pages 1-21, December.
    9. Woo Jae Byun & Bumkyu Choi & Seongmin Kim & Joohyun Jo, 2023. "Practical Application of Deep Reinforcement Learning to Optimal Trade Execution," FinTech, MDPI, vol. 2(3), pages 1-16, June.
    10. Lu, Yu & Xiang, Yue & Huang, Yuan & Yu, Bin & Weng, Liguo & Liu, Junyong, 2023. "Deep reinforcement learning based optimal scheduling of active distribution system considering distributed generation, energy storage and flexible load," Energy, Elsevier, vol. 271(C).
    11. Yuhong Wang & Lei Chen & Hong Zhou & Xu Zhou & Zongsheng Zheng & Qi Zeng & Li Jiang & Liang Lu, 2021. "Flexible Transmission Network Expansion Planning Based on DQN Algorithm," Energies, MDPI, vol. 14(7), pages 1-21, April.
    12. Bakalis, Evangelos & Galani, Alexandra, 2012. "Modeling language evolution: Aromanian, an endangered language in Greece," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4963-4969.
    13. Huang, Ruchen & He, Hongwen & Gao, Miaojue, 2023. "Training-efficient and cost-optimal energy management for fuel cell hybrid electric bus based on a novel distributed deep reinforcement learning framework," Applied Energy, Elsevier, vol. 346(C).
    14. Heather Williams & Andrew Scharf & Anna R. Ryba & D. Ryan Norris & Daniel J. Mennill & Amy E. M. Newman & Stéphanie M. Doucet & Julie C. Blackwood, 2022. "Cumulative cultural evolution and mechanisms for cultural selection in wild bird songs," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    15. Michelle M. LaMar, 2018. "Markov Decision Process Measurement Model," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 67-88, March.
    16. Zichen Lu & Ying Yan, 2024. "Temperature Control of Fuel Cell Based on PEI-DDPG," Energies, MDPI, vol. 17(7), pages 1-19, April.
    17. Yang, Ting & Zhao, Liyuan & Li, Wei & Zomaya, Albert Y., 2021. "Dynamic energy dispatch strategy for integrated energy system based on improved deep reinforcement learning," Energy, Elsevier, vol. 235(C).
    18. Wang, Xuan & Shu, Gequn & Tian, Hua & Wang, Rui & Cai, Jinwen, 2020. "Operation performance comparison of CCHP systems with cascade waste heat recovery systems by simulation and operation optimisation," Energy, Elsevier, vol. 206(C).
    19. Wang, Yi & Qiu, Dawei & Sun, Mingyang & Strbac, Goran & Gao, Zhiwei, 2023. "Secure energy management of multi-energy microgrid: A physical-informed safe reinforcement learning approach," Applied Energy, Elsevier, vol. 335(C).
    20. Parvez Farazi, Nahid & Zou, Bo & Tulabandhula, Theja, 2022. "Dynamic On-Demand Crowdshipping Using Constrained and Heuristics-Embedded Double Dueling Deep Q-Network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 166(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:464:y:2024:i:c:s0096300323005611. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.