REFERENCES
1. Bagraev, N. T.; Kukushkin, S. A.; Osipov, A. V.; Ugolkov, V. L. Phase transitions in silicon-carbide epitaxial layers grown on a silicon substrate by the method of the coordinated substitution of atoms. Semiconductors 2022, 56, 321-4.
2. Costantini, J.; Guillaumet, M.; Lelong, G. Temperature-dependent optical absorption spectroscopy of ion irradiated silicon carbide epilayers on silicon. Appl. Phys. A. 2024, 130, 8025.
3. Bragin, A. V.; Pyanzin, D. V.; Sidorov, R. I.; Skvortsov, D. A. Recognition of dislocation structure of silicon carbide epitaxial layers by а neural network. Comput. Opt. 2020, 44, 653-9.
4. Mpilitos, C.; Amanatiadis, S.; Apostolidis, G.; Zygiridis, T.; Kantartzis, N.; Karagiannis, G. Development of a transmission line model for the thickness prediction of thin films via the infrared interference method. Technologies 2018, 6, 122.
5. Raissi, M.; Perdikaris, P.; Karniadakis, G. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 2019, 378, 686-707.
6. Li, G.; Ouyang, W.; Ouyang, W.; Liu, S. Static analysis of two-side supported 2-ply laminated glass panes through physics-informed neural networks. Eng. Struct. 2024, 309, 118038.
7. Wang, L.; Liu, G.; Wang, G.; Zhang, K. M‐PINN: a mesh‐based physics‐informed neural network for linear elastic problems in solid mechanics. Int. J. Numer. Methods. Eng. 2024, 125, e7444.
8. Ouyang, W.; Li, G.; Chen, L.; Liu, S. Physics‐informed neural networks for large deflection analysis of slender piles incorporating non‐differentiable soil‐structure interaction. Int. J. Numer. Anal. Methods. Geomech. 2024, 48, 1278-308.
9. Ye, X.; Ni, Y.; Ao, W. K.; Yuan, L. Modeling of the hysteretic behavior of nonlinear particle damping by Fourier neural network with transfer learning. Mech. Syst. Signal. Process. 2024, 208, 111006.
10. Peng, J.; Hua, Y.; Aubry, N.; Chen, Z.; Mei, M.; Wu, W. Data and physics-driven modeling for fluid flow with a physics-informed graph convolutional neural network. Ocean. Eng. 2024, 301, 117551.
11. Zhao, Y.; Li, D.; Wang, C.; Xi, H. An innovative end-to-end PINN-based solution for rapidly simulating homogeneous heat flow problems: an adaptive universal physics-guided auto-solver. Case. Stud. Therm. Eng. 2024, 56, 104277.
12. Cheng, C.; Zhang, G. Deep learning method based on physics informed neural network with resnet block for solving fluid flow problems. Water 2021, 13, 423.
13. Rui, E.; Chen, Z.; Ni, Y.; Yuan, L.; Zeng, G. Reconstruction of 3D flow field around a building model in wind tunnel: a novel physics-informed neural network framework adopting dynamic prioritization self-adaptive loss balance strategy. Eng. Appl. Comput. Fluid. Mech. 2023, 17, 2238849.
14. Jalili, D.; Jang, S.; Jadidi, M.; Giustini, G.; Keshmiri, A.; Mahmoudi, Y. Physics-informed neural networks for heat transfer prediction in two-phase flows. Int. J. Heat. Mass. Transf. 2024, 221, 125089.
15. Yadav, V.; Casel, M.; Ghani, A. RF-PINNs: reactive flow physics-informed neural networks for field reconstruction of laminar and turbulent flames using sparse data. J. Comput. Phys. 2025, 524, 113698.
16. Batuwatta-Gamage, C. P.; Rathnayaka, C.; Karunasena, H. C. P.; Jeong, H.; Karim, A.; Gu, Y. T. A novel physics-informed neural networks approach (PINN-MT) to solve mass transfer in plant cells during drying. Biosyst. Eng. 2023, 230, 219-41.
17. Oldenburg, J.; Borowski, F.; Schmitz, K.; Stiehm, M. Computation of flow through TAVI device by means of physics informed neural networks. Curr. Dir. Biomed. Eng. 2022, 8, 741-4.
18. Ma, Y.; Xu, X.; Yan, S.; Ren, Z. A preliminary study on the resolution of electro-thermal multi-physics coupling problem using physics-informed neural network (PINN). Algorithms 2022, 15, 53.
19. Wang, Y.; Fan, Q.; Dai, F.; Wang, R.; Ding, B. A physics-data-driven method for predicting surface and building settlement induced by tunnel construction. Comput. Geotech. 2025, 179, 107020.
20. Chen, S.; Ji, X.; Shao, H.; Zhang, Y. A physics-informed traffic state estimation model for freeways under sparse observation data. Transportmetrica. B. 2025, 13, 2564701.
21. Ren, P.; Rao, C.; Liu, Y.; Wang, J.; Sun, H. PhyCRNet: physics-informed convolutional-recurrent network for solving spatiotemporal PDEs. Comput. Methods. Appl. Mech. Eng. 2022, 389, 114399.
22. Markidis, S. The old and the new: can physics-informed deep-learning replace traditional linear solvers? Front. Big. Data. 2021, 4, 669097.
23. Wu, G.; Fang, Y.; Wang, Y.; Wu, G.; Dai, C. Predicting the dynamic process and model parameters of the vector optical solitons in birefringent fibers via the modified PINN. Chaos. Solitons. Fractals. 2021, 152, 111393.
24. Bai, X.; Wang, Y.; Zhang, W. Applying physics informed neural network for flow data assimilation. J. Hydrodyn. 2020, 32, 1050-8.
25. Jagtap, A. D.; Karniadakis, G. E. Extended physics-informed neural networks (XPINNs): a generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations. Commun. Comput. Phys. 2025, 28, 2002-41.
26. Mehta, P. P.; Pang, G.; Song, F.; Karniadakis, G. E. Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network. Fract. Calc. Appl. Anal. 2019, 22, 1675-88.
27. Qian, Y.; Zhang, Y.; Huang, Y.; Dong, S. Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: Error analysis and algorithms. J. Comput. Phys. 2023, 495, 112527.
28. Qian, Y.; Zhang, Y.; Dong, S. Error analysis and numerical algorithm for PDE approximation with hidden-layer concatenated physics informed neural networks. J. Comput. Phys. 2025, 530, 113906.
29. Liu, D.; Liu, Y.; Dang, H.; et al. The neutron transport equation in exact differential form. Sci. China. Phys. Mech. Astron. 2025, 68, 2642.
30. Son, H.; Lee, M. A PINN approach for identifying governing parameters of noisy thermoacoustic systems. J. Fluid. Mech. 2024, 984, A21.
31. Yan, S.; Chen, Y.; Cao, W.; Li, H. Enhancing U-Net with low-rank attention skip block for 3D point cloud segmentation. Neurocomputing 2025, 626, 129593.
32. Cao, X.; Chen, Y.; Cao, W. Proximal PanNet: a model-based deep network for pansharpening. AAAI. Conf. Artif. Intell. 2022, 36, 176-84.






