Seeing through sound: assessing physics-informed sound-speed inversion in an acoustic waveguide

This internship assesses whether Physics-Informed Neural Networks (PINNs) can perform quantitative sound-speed inversion in a two-dimensional acoustic waveguide. We formulate the Helmholtz problem in total-eld and scattered-eld forms and develop from scratch an all-at-once JAX implementation, with one complex waveeld network per acquisition and a sound-speed network shared across acquisitions. A systematic forward calibration shows that Fourier features and careful loss balancing are decisive for learning oscillatory wave- elds at the frequencies considered. In inversion, predicting the scattered eld eliminates the homogeneous warm-up and reduces end-to-end training time by about 10%, but yields no systematic accuracy gain. The best reconstruction instead combines a physics-based sign prior, c ≤ c0, with a two-stage frequency curriculum, reaching a contrast-normalised error of 0.34 ± 0.01. This result remains prior-dependent: under broad material bounds, most reconstructions perform worse than the homogeneous map according to the same metric, despite partially recovering the defect locally. Moreover, a normalised trace loss of order 10−7 can coexist with an interior pressure error of about 20%, showing that a small loss does not certify the reconstruction. No classical full-waveform-inversion baseline is included. The main contribution is therefore a reproducible benchmark, a from-scratch dierentiable implementation, and a multi-seed evaluation methodology for comparing modelling and optimisation choices, together with an explicit diagnosis of the remaining obstacles to reliable PINN-based inversion.