Od regresije do neuronskih operatora: pregled metoda mašinskog učenja u procesnoj industriji sa primenama u digitalnim blizancima
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Jul 17, 2026
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Andrija Petrović
http://orcid.org/0000-0003-4516-495X
http://orcid.org/0000-0003-4516-495X
Apstrakt
Simulacija složenih procesnih jedinica u realnom vremenu — peći, razmenjivača toplote i reaktora — dugo je bila rezervisana za skupe PDE solvere i CFD alate. S druge strane, čisto crno-kutijski modeli mašinskog učenja često su krhki i fizički nekonzistentni. Ovaj rad daje pristupačan pregled metoda mašinskog učenja (ML) koje su danas relevantne za procesnu industriju, pri čemu se kao zajednički primer u celom radu koristi prenos toplote. Pregled počinje od klasične statistike i regresije, koje već decenijama čine osnovu mekih senzorskih merenja. Zatim se obrađuju nadgledano i nenadgledano učenje za detekciju anomalija (na primer, prljanje razmenjivača toplote), kao i duboko učenje za prognozu složenih vremenskih serija u nelinearnim termičkim postrojenjima. Glavni doprinos rada je sistematizacija nove generacije fizički informisanih metoda — fizički informisanih neuronskih mreža (PINN) i neuronskih operatora (DeepONet, Fourier Neural Operator) — kroz pet malih i reproducibilnih eksperimenata, svih iz oblasti prenosa toplote. Posebna pažnja posvećena je ubrzanju koje neuronski operatori donose digitalnim blizancima: u našem eksperimentu, FNO je oko jedan red veličine brži od referentnog konačno-razlikatnog solvera, uz prihvatljivu tačnost. Rad se završava praktičnim vodičem za inženjere o tome kako izabrati ML metodu prema tipu problema, dostupnosti podataka i fizike, kao i zahtevima za rad u realnom vremenu.
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Kako citirati
PETROVIĆ, Andrija.
Od regresije do neuronskih operatora: pregled metoda mašinskog učenja u procesnoj industriji sa primenama u digitalnim blizancima.
Zbornik Međunarodnog kongresa o procesnoj industriji – Procesing, [S.l.], v. 39, n. 1, p. 121-136, july 2026.
Dostupno na: <http://izdanja.smeits.rs/index.php/ptk/article/view/8340>. Datum pristupa: 07 aug. 2026
Sekcija
Procesne tehnologije, operacije, aparati i mašine u procesnoj industriji
Reference
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[3] Qin, S. J., Survey on data-driven industrial process monitoring and diagnosis, Annual Reviews in Control, 36 (2012), 2, pp. 220–234.
[4] Ge, Z., Song, Z., Ding, S. X., Huang, B., Data mining and analytics in the process industry: The role of machine learning, IEEE Access, 5 (2017), pp. 20590–20616.
[5] LeCun, Y., Bengio, Y., Hinton, G., Deep learning, Nature, 521 (2015), 7553, pp. 436–444.
[6] Reis, M. S., Gins, G., Industrial process monitoring in the big data/Industry 4.0 era: From detec-tion, to diagnosis, to prognosis, Processes, 7 (2019), 7, p. 411.
[7] Raissi, M., Perdikaris, P., Karniadakis, G. E., Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differ-ential equations, Journal of Computational Physics, 378 (2019), pp. 686–707.
[8] Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., Yang, L., Physics-informed machine learning, Nature Reviews Physics, 3 (2021), 6, pp. 422–440.
[9] Cuomo, S., Di Cola, V. S., Giampaolo, F., Rozza, G., Raissi, M., Piccialli, F., Scientific ma-chine learning through physics-informed neural networks: Where we are and what's next, Jour-nal of Scientific Computing, 92 (2022), 3, p. 88.
[10] Lu, L., Jin, P., Pang, G., Zhang, Z., Karniadakis, G. E., Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators, Nature Machine Intelli-gence, 3 (2021), 3, pp. 218–229.
[11] Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., Anandkumar, A., Fourier neural operator for parametric partial differential equations, Proceed-ings, International Conference on Learning Representations, ICLR, 2021.
[12] Kovachki, N., Li, Z., Liu, B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A., Anandkumar, A., Neural operator: Learning maps between function spaces with applications to PDEs, Journal of Machine Learning Research, 24 (2023), 89, pp. 1–97.
[13] Rasheed, A., San, O., Kvamsdal, T., Digital twin: Values, challenges and enablers from a modeling perspective, IEEE Access, 8 (2020), pp. 21980–22012.
[14] Rasmussen, C. E., Williams, C. K. I., Gaussian Processes for Machine Learning, MIT Press, Cambridge, MA, USA, 2006.
[15] Kim, S., Lee, J., Kang, S., Predicting fouling resistance of plate heat exchangers using a recur-rent neural network, Applied Thermal Engineering, 153 (2019), pp. 823–831.
[16] Hughes, M. T., Kini, G., Garimella, S., Status, challenges, and potential for machine learning in understanding and applying heat transfer phenomena, Journal of Heat Transfer, 143 (2021), 12, p. 120802.
[17] Liu, F. T., Ting, K. M., Zhou, Z.-H., Isolation forest, Proceedings 2008 Eighth IEEE Interna-tional Conference on Data Mining, IEEE, Pisa, Italy, 2008, pp. 413–422.
[18] Goodfellow, I., Bengio, Y., Courville, A., Deep Learning, MIT Press, Cambridge, MA, USA, 2016.
[19] Hochreiter, S., Schmidhuber, J., Long short-term memory, Neural Computation, 9 (1997), 8, pp. 1735–1780.
[20] Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L., Polosukhin, I., Attention is all you need, Advances in Neural Information Processing Systems, NeurIPS, Long Beach, CA, USA, 2017, pp. 5998–6008.
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[22] Wang, S., Yu, X., Perdikaris, P., When and why PINNs fail to train: A neural tangent kernel perspective, Journal of Computational Physics, 449 (2022), p. 110768.
[23] Wen, G., Li, Z., Azizzadenesheli, K., Anandkumar, A., Benson, S. M., U-FNO: An en-hanced Fourier neural operator-based deep learning model for multiphase flow, Advances in Wa-ter Resources, 163 (2022), p. 104180.
[24] Pathak, J., Subramanian, S., Harrington, P., et al., FourCastNet: A global data-driven high-resolution weather model using adaptive Fourier neural operators, arXiv preprint arXiv:2202.11214, 2022.
[25] Lam, R., Sanchez-Gonzalez, A., Willson, M., et al., Learning skillful medium-range global weather forecasting, Science, 382 (2023), 6677, pp. 1416–1421.
[26] Yang, L., Meng, X., Karniadakis, G. E., B-PINNs: Bayesian physics-informed neural net-works for forward and inverse PDE problems with noisy data, Journal of Computational Phys-ics, 425 (2021), p. 109913.
[27] Willard, J., Jia, X., Xu, S., Steinbach, M., Kumar, V., Integrating scientific knowledge with machine learning for engineering and environmental systems, ACM Computing Surveys, 55 (2022), 4, pp. 1–37.
[28] Cai, S., Wang, Z., Wang, S., Perdikaris, P., Karniadakis, G. E., Physics-informed neural networks for heat transfer problems, Journal of Heat Transfer, 143 (2021), 6, p. 060801.