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Deep Learning based Spatially Dependent Acoustical Properties Recovery (2310.10970v2)

Published 17 Oct 2023 in cs.LG and eess.SP

Abstract: The physics-informed neural network (PINN) is capable of recovering partial differential equation (PDE) coefficients that remain constant throughout the spatial domain directly from physical measurements. In this work, we propose a spatially dependent physics-informed neural network (SD-PINN), which enables the recovery of coefficients in spatially-dependent PDEs using a single neural network, eliminating the requirement for domain-specific physical expertise. We apply the SD-PINN to spatially-dependent wave equation coefficients recovery to reveal the spatial distribution of acoustical properties in the inhomogeneous medium. The proposed method exhibits robustness to noise owing to the incorporation of a loss function for the physical constraint that the assumed PDE must be satisfied. For the coefficients recovery of spatially two-dimensional PDEs, we store the PDE coefficients at all locations in the 2D region of interest into a matrix and incorporate the low-rank assumption for such a matrix to recover the coefficients at locations without available measurements.

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References (38)
  1. “Elastic waves in plates with periodically placed inclusions,” J. Appl. Phys., vol. 75, no. 6, pp. 2845–2850, 1994.
  2. “On a finite-element method for solving the three-dimensional maxwell equations,” J. Comput. Phys., vol. 109, no. 2, pp. 222–237, 1993.
  3. “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,” J. Comput. Phys., vol. 378, pp. 686–707, 2019.
  4. “Physics informed deep learning (part i): Data-driven solutions of nonlinear partial differential equations,” arXiv preprint arXiv:1711.10561, 2017.
  5. “Physics informed deep learning (part ii): data-driven discovery of nonlinear partial differential equations,” arXiv preprint arXiv:1711.10566, 2017.
  6. “Discovering governing equations from data by sparse identification of nonlinear dynamical systems,” Proc. Natl. Acad. Sci., vol. 113, no. 15, pp. 3932–3937, 2016.
  7. “Data-driven discovery of partial differential equations,” Sci. Adv., vol. 3, no. 4, pp. e1602614, 2017.
  8. “Extracting sparse high-dimensional dynamics from limited data,” SIAM J. Appl. Math., vol. 78, no. 6, pp. 3279–3295, 2018.
  9. “PDE-Net: Learning PDEs from data,” in Proceedings of the 35th International Conference on Machine Learning. 2018, vol. 80, pp. 3208–3216, PMLR.
  10. “PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network,” J. Comput. Phys., vol. 399, pp. 108925, 2019.
  11. Data-driven science and engineering: Machine learning, dynamical systems, and control, Cambridge University Press, 2019.
  12. “Physics-aware gaussian processes in remote sensing,” Appl. Soft Comput., vol. 68, pp. 69–82, 2018.
  13. “Wave equation extraction from a video using sparse modeling,” in Proc.53th Asilomar Conf. on Circuits, Systems and Computers. IEEE, 2019, pp. 2160–2165.
  14. S. Zhang and G. Lin, “Robust data-driven discovery of governing physical laws with error bars,” Proc. Math. Phys. Eng. Sci., vol. 474, no. 2217, pp. 20180305, 2018.
  15. “Automated partial differential equation identification,” J. Acoust. Soc. Am., vol. 150, no. 4, pp. 2364–2374, 2021.
  16. “DL-PDE: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy data,” Commun. Comput. Phys., vol. 29, pp. 698–728, 2021.
  17. P. Pilar and N. Wahlström, “Physics-informed neural networks with unknown measurement noise,” arXiv preprint arXiv:2211.15498, 2022.
  18. R. Eldan and O. Shamir, “The power of depth for feedforward neural networks,” in Conference on learning theory. PMLR, 2016, pp. 907–940.
  19. “Introduction to multi-layer feed-forward neural networks,” Chemometr. Intell. Lab. Syst., vol. 39, no. 1, pp. 43–62, 1997.
  20. “Physics-informed neural networks for nonhomogeneous material identification in elasticity imaging,” in AAAI Fall 2020 Symposium on Physics-Guided AI to Accelerate Scientific Discovery, Washington DC, United States, Nov.11-14 2020, AAAI.
  21. “Physics-informed deep neural network for inhomogeneous magnetized plasma parameter inversion,” IEEE Antennas Wirel. Propag. Lett., vol. 21, no. 4, pp. 828–832, 2022.
  22. “Elasticity imaging using physics-informed neural networks: Spatial discovery of elastic modulus and poisson’s ratio,” Acta Biomater., vol. 155, pp. 400–409, 2023.
  23. “Data-driven spatially dependent PDE identification,” in 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2022, pp. 3383–3387.
  24. R. Liu and P. Gerstoft, “SD-PINN: Physics informed neural networks for spatially dependent PDEs,” in 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2023, pp. 1–5.
  25. M. J. Buckingham, “On the transient solutions of three acoustic wave equations: van wijngaarden’s equation, stokes’ equation and the time-dependent diffusion equation,” J. Acoust. Soc. Am., vol. 124, no. 4, pp. 1909–1920, 2008.
  26. Y. Chen and Y. Chi, “Harnessing structures in big data via guaranteed low-rank matrix estimation: Recent theory and fast algorithms via convex and nonconvex optimization,” IEEE Signal Process. Mag., vol. 35, no. 4, pp. 14–31, 2018.
  27. D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980, 2014.
  28. “Automatic differentiation in machine learning: a survey,” J. Mach. Learn. Res., vol. 18, pp. 1–43, 2018.
  29. M. A. Davenport and J. Romberg, “An overview of low-rank matrix recovery from incomplete observations,” IEEE J. Sel. Top. Signal Process., vol. 10, no. 4, pp. 608–622, 2016.
  30. “The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices,” arXiv preprint arXiv:1009.5055, 2010.
  31. “Typical and generic ranks in matrix completion,” Linear Algebra Appl., vol. 585, pp. 71–104, 2020.
  32. O. Klopp, “Noisy low-rank matrix completion with general sampling distribution,” Bernoulli, vol. 20, pp. 282–303, Feb. 2014.
  33. “Delving deep into rectifiers: Surpassing human-level performance on imagenet classification,” in Proceedings of the IEEE international conference on computer vision, 2015, pp. 1026–1034.
  34. H. Akima, “A new method of interpolation and smooth curve fitting based on local procedures,” J. ACM., vol. 17, no. 4, pp. 589–602, 1970.
  35. “Recovery of spatially varying acoustical properties via automated partial differential equation identification,” J. Acoust. Soc. Am., vol. 153, no. 6, pp. 3169–3180, 2023.
  36. “A singular value thresholding algorithm for matrix completion,” SIAM J. Optim., vol. 20, no. 4, pp. 1956–1982, 2010.
  37. W. F. Ames, Numerical methods for partial differential equations, Academic press, 2014.
  38. “Singular value decomposition and principal component analysis,” in A practical approach to microarray data analysis, pp. 91–109. Springer, 2003.

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