IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v161y2019icp2-12.html
   My bibliography  Save this article

Integral equations and machine learning

Author

Listed:
  • Keller, Alexander
  • Dahm, Ken

Abstract

As both light transport simulation and reinforcement learning are ruled by the same Fredholm integral equation of the second kind, reinforcement learning techniques may be used for photorealistic image synthesis: Efficiency may be dramatically improved by guiding light transport paths by an approximate solution of the integral equation that is learned during rendering. In the light of the recent advances in reinforcement learning for playing games, we investigate the representation of an approximate solution of an integral equation by artificial neural networks and derive a loss function for that purpose. The resulting Monte Carlo and quasi-Monte Carlo methods train neural networks with standard information instead of linear information and naturally are able to generate an arbitrary number of training samples. The methods are demonstrated for applications in light transport simulation.

Suggested Citation

  • Keller, Alexander & Dahm, Ken, 2019. "Integral equations and machine learning," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 2-12.
  • Handle: RePEc:eee:matcom:v:161:y:2019:i:c:p:2-12
    DOI: 10.1016/j.matcom.2019.01.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475419300308
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2019.01.010?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. Keller, Alexander, 2001. "Hierarchical Monte Carlo image synthesis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(1), pages 79-92.
    2. David Silver & Aja Huang & Chris J. Maddison & Arthur Guez & Laurent Sifre & George van den Driessche & Julian Schrittwieser & Ioannis Antonoglou & Veda Panneershelvam & Marc Lanctot & Sander Dieleman, 2016. "Mastering the game of Go with deep neural networks and tree search," Nature, Nature, vol. 529(7587), pages 484-489, January.
    3. David Silver & Julian Schrittwieser & Karen Simonyan & Ioannis Antonoglou & Aja Huang & Arthur Guez & Thomas Hubert & Lucas Baker & Matthew Lai & Adrian Bolton & Yutian Chen & Timothy Lillicrap & Fan , 2017. "Mastering the game of Go without human knowledge," Nature, Nature, vol. 550(7676), pages 354-359, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Parand, K. & Aghaei, A.A. & Jani, M. & Ghodsi, A., 2021. "A new approach to the numerical solution of Fredholm integral equations using least squares-support vector regression," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 114-128.

    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. Yuchen Zhang & Wei Yang, 2022. "Breakthrough invention and problem complexity: Evidence from a quasi‐experiment," Strategic Management Journal, Wiley Blackwell, vol. 43(12), pages 2510-2544, December.
    2. Omar Al-Ani & Sanjoy Das, 2022. "Reinforcement Learning: Theory and Applications in HEMS," Energies, MDPI, vol. 15(17), pages 1-37, September.
    3. Zhang, Yihao & Chai, Zhaojie & Lykotrafitis, George, 2021. "Deep reinforcement learning with a particle dynamics environment applied to emergency evacuation of a room with obstacles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 571(C).
    4. Jun Li & Wei Zhu & Jun Wang & Wenfei Li & Sheng Gong & Jian Zhang & Wei Wang, 2018. "RNA3DCNN: Local and global quality assessments of RNA 3D structures using 3D deep convolutional neural networks," PLOS Computational Biology, Public Library of Science, vol. 14(11), pages 1-18, November.
    5. Haoran Wang & Shi Yu, 2021. "Robo-Advising: Enhancing Investment with Inverse Optimization and Deep Reinforcement Learning," Papers 2105.09264, arXiv.org.
    6. Weifan Long & Taixian Hou & Xiaoyi Wei & Shichao Yan & Peng Zhai & Lihua Zhang, 2023. "A Survey on Population-Based Deep Reinforcement Learning," Mathematics, MDPI, vol. 11(10), pages 1-17, May.
    7. Yifeng Guo & Xingyu Fu & Yuyan Shi & Mingwen Liu, 2018. "Robust Log-Optimal Strategy with Reinforcement Learning," Papers 1805.00205, arXiv.org.
    8. Xueqing Yan & Yongming Li, 2023. "A Novel Discrete Differential Evolution with Varying Variables for the Deficiency Number of Mahjong Hand," Mathematics, MDPI, vol. 11(9), pages 1-21, May.
    9. Pujin Wang & Jianzhuang Xiao & Ken’ichi Kawaguchi & Lichen Wang, 2022. "Automatic Ceiling Damage Detection in Large-Span Structures Based on Computer Vision and Deep Learning," Sustainability, MDPI, vol. 14(6), pages 1-24, March.
    10. Jianjun Chen & Weihao Hu & Di Cao & Bin Zhang & Qi Huang & Zhe Chen & Frede Blaabjerg, 2019. "An Imbalance Fault Detection Algorithm for Variable-Speed Wind Turbines: A Deep Learning Approach," Energies, MDPI, vol. 12(14), pages 1-15, July.
    11. Lu Wang & Wenqing Ai & Tianhu Deng & Zuo‐Jun M. Shen & Changjing Hong, 2020. "Optimal production ramp‐up in the smartphone manufacturing industry," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(8), pages 685-704, December.
    12. Yuchao Dong, 2022. "Randomized Optimal Stopping Problem in Continuous time and Reinforcement Learning Algorithm," Papers 2208.02409, arXiv.org, revised Sep 2023.
    13. Shijun Wang & Baocheng Zhu & Chen Li & Mingzhe Wu & James Zhang & Wei Chu & Yuan Qi, 2020. "Riemannian Proximal Policy Optimization," Computer and Information Science, Canadian Center of Science and Education, vol. 13(3), pages 1-93, August.
    14. Morato, P.G. & Andriotis, C.P. & Papakonstantinou, K.G. & Rigo, P., 2023. "Inference and dynamic decision-making for deteriorating systems with probabilistic dependencies through Bayesian networks and deep reinforcement learning," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    15. Yi Cheng & Chuzhi Zhao & Pradeep Neupane & Bradley Benjamin & Jiawei Wang & Tongsheng Zhang, 2023. "Applicability and Trend of the Artificial Intelligence (AI) on Bioenergy Research between 1991–2021: A Bibliometric Analysis," Energies, MDPI, vol. 16(3), pages 1-15, January.
    16. Iwao Maeda & David deGraw & Michiharu Kitano & Hiroyasu Matsushima & Hiroki Sakaji & Kiyoshi Izumi & Atsuo Kato, 2020. "Deep Reinforcement Learning in Agent Based Financial Market Simulation," JRFM, MDPI, vol. 13(4), pages 1-17, April.
    17. Li, Wenqing & Ni, Shaoquan, 2022. "Train timetabling with the general learning environment and multi-agent deep reinforcement learning," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 230-251.
    18. Bo Hu & Jiaxi Li & Shuang Li & Jie Yang, 2019. "A Hybrid End-to-End Control Strategy Combining Dueling Deep Q-network and PID for Transient Boost Control of a Diesel Engine with Variable Geometry Turbocharger and Cooled EGR," Energies, MDPI, vol. 12(19), pages 1-15, September.
    19. Elsisi, Mahmoud & Amer, Mohammed & Dababat, Alya’ & Su, Chun-Lien, 2023. "A comprehensive review of machine learning and IoT solutions for demand side energy management, conservation, and resilient operation," Energy, Elsevier, vol. 281(C).
    20. Justin J. Boutilier & Timothy C. Y. Chan, 2023. "Introducing and Integrating Machine Learning in an Operations Research Curriculum: An Application-Driven Course," INFORMS Transactions on Education, INFORMS, vol. 23(2), pages 64-83, January.

    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:matcom:v:161:y:2019:i:c:p:2-12. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.