Abstract
Earlier, a method for constructing an initial approximation for solving the inverse problem of acoustics by a gradient method based on a convolutional neural network trained to predict the distribution of velocities in a medium from wave response was proposed [9]. It was shown that the neural network trained on responses from simple layered media can be successfully used for solving the inverse problem for a significantly more complex model. In this paper, we present algorithms for processing data about epidemics and an example of applying a neural network for modeling the propagation of COVID-19 in Novosibirsk region (Russia) based only on data. A neural network NN-COVID-19 that uses data about the epidemics is constructed. It is shown that this neural network predicts the propagation of COVID-19 for five days by an order of magnitude better than SEIR-HCD. When a new variant (Omicron) appeared, this neural network was able to predict (after retraining) the propagation of the epidemics more accurately. Note that the proposed neural network uses not only epidemiological data but also social ones (such as holidays, restrictive measures, etc.). The proposed approach makes it possible to refine mathematical models. A comparison of the curves constructed by SEIR-HCD model and by the neural network shows that the plots of solutions of the direct problem almost coincide with the plots constructed by the neural network. This helps refine coefficients of the differential model.
REFERENCES
N. Zyatkov and O. Krivorotko, “Forecasting recessions in the US economy using machine learning methods,” 17th Int. Asian school-seminar “Optimization problems of complex systems” (OPCS), 2021, pp 139–146. https://doi.org/10.1109/OPCS53376.2021.9588678
S. Chen S. and W. Guo, “Auto-encoders in deep learning – a review with new perspectives,” Mathematics 11, 1–54 (2023).
Gui Jie, Sun Zhenan, Wen Yonggang, Tao Dacheng, and Ye. Jieping, “A review on generative adversarial networks: Algorithms, theory, and applications,” IEEE Trans. Knowl. Data Eng. 35 (4), 3313–3332 (2023).
J. Ling, R. Jones, and J. Templeton, “Physics-informed machine learning: A new paradigm for computational mechanics,” Comput. Meth. Appl. Mech. Eng. 309, 209–233 (2016).
M. Leyva-Vallina and Z. Nagy, “Data-driven vs. physics-based modeling: A comparison from an industrial perspective,” Chemic. Eng. Sci. 182, 80–93 (2018).
Y. Huang, J. Zhang, X. Yang, C. F. Drury, W. D. Reynolds, and C. S. Tan, “Comparing the performance of machine learning algorithms for predicting soil organic carbon stocks in different land use systems,” Geoderma 375, 114448 (2020).
S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Discovering governing equations from data by sparse identification of nonlinear dynamical systems,” Proc. Nation. Acad. Sci. 113 (15), 3932–3937 (2016).
O. I. Krivorot’ko and S. I. Kabanikhin, Mathematical Models of COVID-19 Spread, Preprint of Sobolev Institute of Mathematics, Sib. Branch of Russ. Acad. of Sciences, Novosibirsk, 2022, no. 300, 63 pp.
I. B. Petrov, A. S. Stankevich, and A. V. Vasyukov, “On the search of an initial approximation in the wave inversion problem using convolutional neural networks,” Dokl. Ross. Akad. Nauk 2023.
B. Nikparvar, M. M. Rahman, F. Hatami, et al., “Spatio-temporal prediction of the COVID-19 pandemic in US counties: Modeling with a deep LSTM neural network,” Sci. Rep. 11, 21715 (2021).
M. Shawaqfah and F. Almomani, “Forecast of the outbreak of COVID-19 using artificial neural network: Case study Qatar, Spain, and Italy,” Result. Phys. 27, 104484 (2021).
M. A. Guzev and E. Yu. Nikitina, “Dynamics of “imperial tails” on the example of coronavirus infection,” Dal’nevost. Mat. Zh. 22 (1), 38–50 (2022).
O. I. Krivorot’ko, S. I. Kabanikhin, N. Yu. Zyat’kov, A. Yu. Prikhod’ko, N. M. Prokhoshin, and M. A. Shishlenin, “Mathematical modeling and forecasting of COVID-19 in Moscow and Novosibirsk region,” Numer. Anal. Appl. 13 (4), 395–414 (2020).
O. I. Krivorotko and N. Y. Zyatkov, “Data-driven regularization of inverse problem for SEIR-HCD model of COVID-19 propagation in Novosibirsk region,” Eurasian J. Math. Comput. Appl. 10, 51–68 (2022).
T. Chen and C. Guestrin, “XGBoost: A scalable tree boosting system,” Proc. of the ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining, ACM, 2016, pp. 785–794.
S. Hochreiter and J. Schmidhuber, “Long short-term memory,” Neural Comput. 9 (8), 1735–1780 (1997).
N. Srivastava G. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov,” “Dropout: A simple way to prevent neural networks from overfitting,” J. Mach. Learn. Res. 15 (1), 1929–1958 (2014).
S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” Int. Conference on Machine Learning, 2015, Vol. 37, pp. 448–456.
V. Nair and G. E. Hinton, “Rectified linear units improve restricted Boltzmann machines,” Proc. of the 27th Int. Conference on Machine Learning (ICML-10), 2010, pp. 807–814.
Funding
This work was supported by the Mathematical Center in Akademgorodok, agreement with the Ministry of Science and Education of Russian Federation, project no. 075-15-2022-281.
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Dedicated to Igor Borisovich Petrov on the occasion of his 70th birthday
Translated by A. Klimontovich
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Krivorotko, O.I., Zyatkov, N.Y. & Kabanikhin, S.I. Modeling Epidemics: Neural Network Based on Data and SIR-Model. Comput. Math. and Math. Phys. 63, 1929–1941 (2023). https://doi.org/10.1134/S096554252310007X
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DOI: https://doi.org/10.1134/S096554252310007X