An efficient Bayesian neural network surrogate algorithm for shape detection

We present an efficient Bayesian algorithm for identifying the shape of object from noisy far field data. The data is obtained by illuminating with one or more incident waves. Bayes' theorem provides a framework to find posterior distribution parameters that determine scatterer. compute using Markov Chain Monte Carlo (MCMC) method Gibbs sampler. principal novelty this work replace forward far-field-ansatz wave model (in unbounded region) in MCMC sampling neural-network-based surrogate hundreds times faster evaluate. demonstrate accuracy and efficiency our constructing distributions, medians confidence intervals non-convex shapes Gaussian random circle prior. References Y. Chen. Inverse scattering via Heisenberg’s uncertainty principle. Inv. Prob. 13 (1997), pp. 253–282. doi: 10.1088/0266-5611/13/2/005 D. Colton R. Kress. acoustic electromagnetic theory. 4th Edition. Vol. 93. Applied Mathematical Sciences. C112 Springer, 2019. 10.1007/978-3-030-30351-8 DeVore, B. Hanin, G. Petrova. Neural Network Approximation. Acta Num. 30 (2021), 327–444. 10.1017/S0962492921000052 M. Ganesh S. C. Hawkins. A reduced-order-model obstacle detection algorithm. 2018 MATRIX Annals. Ed. J. de Gier et al. 2020, 17–27. 10.1007/978-3-030-38230-8_2 Algorithm 975: TMATROM—A T-matrix reduced order software. ACM Trans. Math. Softw. 44.9 (2017), 1–18. 10.1145/3054945 Scattering stochastic boundaries: hybrid low- high-order quantification algorithms. ANZIAM 56 (2016), C312–C338. 10.21914/anziamj.v56i0.9313 Ganesh, Hawkins, Volkov. An class inverse Maxwell models R3. Comput. Phys. 398 (2019), p. 108881. 10.1016/j.jcp.2019.108881 L. Lamberg, K. Muinonen, Ylönen, Lumme. Spectral estimation circles spheres. Appl. 136 (2001), 109–121. 10.1016/S0377-0427(00)00578-1 T. Nousiainen McFarquhar. Light quasi-spherical ice crystals. Atmos. Sci. 61 (2004), 2229–2248. 10.1175/1520-0469(2004)061<2229:LSBQIC>2.0.CO;2 A. Palafox, Capistrán, Christen. Point cloud-based scatterer approximation affine invariant problem. Meth. 40 3393–3403. 10.1002/mma.4056 Raissi, P. Perdikaris, E. Karniadakis. Physics-informed neural networks: deep learning solving problems involving nonlinear partial differential equations. 378 686–707. 10.1016/j.jcp.2018.10.045 Stuart. problems: perspective. Numer. 19 (2010), 451–559. 10.1017/S0962492910000061 Veihelmann, Nousiainen, Kahnert, W. van der Zande. small feldspar particles simulated sphere geometry. Quant. Spectro. Rad. 100 (2006), 393–405. 10.1016/j.jqsrt.2005.11.053