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Scientific, Technological and Production Journal
ISSN 2079–3332 (print)
ISSN 3034-6835 (online)
founded in 2001

An algorithm for solving contact problems using deep machine learning technologies in mineral processing

Original articles: 2026 No 3

An algorithm for solving contact problems using deep machine learning technologies in mineral processing

DOI: 10.56195/20793332-2026-26-3-21-26

Read in pdf R. D. Pryazhevsky1, V. A. Atrushkevich2, E. Yu. Barmenkov1
  1. Federal State Budgetary Educational Institution of Higher Education, Russian State Geological Prospecting University named after Sergo Ordzhonikidze (MGRI), Moscow, Russian Federation
  2. Institute of Comprehensive Exploitation of Mineral Resources Russian Academy of Sciences, Moscow, Russian Federation
p. 21-26, No.3/2026
Abstract:
This paper develops and presents an algorithm for solving contact problems in solid mechanics using deep machine learning technologies. The method is based on the application of physically informed neural networks, which enables searching for solutions that directly satisfy systems of equilibrium differential equations and boundary conditions. A key feature of the proposed approach is the reduction of the original boundary value problem with one-sided contact constraints expressed as inequalities to an unconstrained optimization problem. For this purpose, a special loss function is constructed that incorporates the non-penetration and non-adhesion conditions into the neural network training procedure. The algorithm is demonstrated using representative examples of contact between a perfectly rigid stamp and elastic foundations modeled by Bernoulli-Euler and Timoshenko beams in a one-dimensional setting. It is shown that the method effectively determines both the sought-after displacement and pressure fields and the previously unknown contact region. The developed approach forms a computational basis for the creation of fast surrogate models relevant for modeling and optimizing mineral processing processes, such as crushing and grinding, in the context of energy conservation and crystal conservation.
Keywords:
contact problems, physically informed neural networks, beams, plates, machine learning, mathematical optimization, crystal conservation, crushing
For citation:
Pryazhevsky R.D., Atrushkevich V.A., Barmenkov E.Yu. An algorithm for solving contact problems using deep machine learning technologies in mineral processing. Mine Surveying and Subsurface Use. 2026; 26 (3): 21-26. (In Russ.). https://doi. org/10.56195/20793332-2026-26-3-21-26.
Information about the authors:
  1. Roman D. Pryazhevsky – Senior Lecturer, Department of Higher Mathematics and Physics, Federal State Budgetary Educational Institution of Higher Education “Sergo Ordzhonikidze Russian State University for Geological Prospecting”, Moscow, Russian Federation
  2. Victor A. Atrushkevich – Dr. Sci. (Eng.), Professor, Leading Research Scientist of the Department of Design Theory of Subsoil Development, Institute of Comprehensive Exploitation of Mineral Resources Russian Academy of Sciences, Moscow, Russian Federation
  3. Evgeny Yu. Barmenkov – Сand. Sci. (Eng.), Docent, Head of the Department of Mining and Technological Systems and Energy Complexes named after N.V. Tikhonov, Sergo Federal State Budgetary Educational Institution of Higher Education “Sergo Ordzhonikidze Russian State University for Geological Prospecting”, Moscow, Russian Federation
References:
  1. 1. Kingma D.P., Adam J.Ba. A Method for Stochastic Optimization. 2017. https://doi.org/10.48550/arXiv.1412.6980.
  2. 2. Mirjalili V. Python Machine Learning. Third Edition / Sebastian Raschka. Packt, 2019: 770 с.
  3. 3. Richthofer S., Wiskott L. Predictable feature analysis. 2015 IEEE 14th international conference on machine learning and applications (ICMLA). IEEE, 2015: 190-196.
  4. 4. Raparthy M., Dodda B. Predictive Maintenance in IoT Devices Using Time Series Analysis and Deep Learning. Journal of Ballistics. 2022; 35:01-10. https://doi.org/10.52783/dxjb.v35.113.
  5. 5. Лакшманан В., Робинсон С., Мунн М. Машинное обучение. Паттерны проектирования. Санкт-Петербург, 2022: 448. Laksmanan V., Robinson S., Munn M. Machine Learning. Design Patterns: Trans. from English. St. Petersburg, 2022: 448. (In Russ.).
  6. 6. Ensafi Y., Behmanesh A., Ghaemi R., et al. Time-series forecasting of seasonal items sales using machine learning - A comparative analysis. International Journal of Information Management Data Insights. 2022; 2 (1): 100058. https://doi.org/10.1016/j.jjimei.2022.100058.
  7. 7. Xue-heng Qiu, Le Zhang, Ye Ren et al. Ensemble deep learning for regression and time series forecasting. 2014 IEEE symposium on computational intelligence in ensemble learning (CIEL). IEEE; 2014: 1-6. https://doi.org/10.1109/CIEL.2014.7015739.
  8. 8. Goerg Georg. Forecastable component analysis. International conference on machine learning. PMLR. 2013: 64-72.
  9. 9. Вероятностное машинное обучение: введение. Москва, 2022: 940. Probabilistic machine learning: an introduction. Moscow, 2022: 940.
  10. 10. Benidis K., Bohlke-Schneider M., Flunkert V., et al. Probabilistic and Neural Time Series Modeling in Python. Journal of Machine Learning Research. 2020; 21 (116): 1-6.
  11. 11. Ciaburro G., Iannace G. Machine learning-based algorithms to knowledge extraction from time series data: A review. Data. 2021; 6 (6): 55. https:// doi.org/10.3390/data6060055.
  12. 12. Daw A., Bu J., Wang S., et al. Rethinking the importance of sampling in physics-informed neural networks. arXiv preprint, 2022. https://doi.org/ arXiv:2207.02338.
  13. 13. Frank M., Drikakis D., Charissis V. Machine-Learning Methods for Computational Science and Engineering. Computation. 2020; 8: 1-35. https:// doi.org/10.3390/computation8010015.
  14. 14. Maier H.R., Razavi S., Kapelan Z., et al. Introductory overview: Optimization using evolutionary algorithms and other metaheuristics. Environmental Modelling and Software. 2019; 114: 1-44. https://doi.org/10.1016/j.envsoft.2018.11.018.
  15. 15. Vadyala S.R., Betgeri S.N., Matthews J.C., et al. A review of physics-machine learning in civil engineering. Results in Engineering. 2022: 1-38. https://doi.org/10.48550/arXiv.2110.04600.

 

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