Blind Localization and Complex Modulus Identification of a Viscoelastic Patch from Partial Frequency-Response Data Using a Multifrequency VPINN

Participating speaker: Maxime Auger (FEMTO-ST Institute, France).

Abstract: This work investigates the blind localization and identification of a viscoelastic patch in a clamped–free Euler–Bernoulli beam using partial complex-valued frequency-response measurements. A variational physics-informed neural network (VPINN) is trained across multiple excitation frequencies, combining a frequency-conditioned displacement surrogate with a shared spatially varying complex Young's modulus. The governing equation is enforced through a Petrov–Galerkin weak formulation restricted to the observation window, while trainable smooth plateau functions represent the unknown modulus distribution and patch interfaces. Training and checkpoint selection are oracle-free, relying on displacement validation, independent weak-residual diagnostics, and parameter stability without using reference material properties or true interface locations. Numerical results across six frequencies (500-3000 Hz) demonstrate millimetre-scale accuracy in locating both patch interfaces and accurate identification of the patch loss modulus. In contrast, the background loss modulus is primarily recovered as an effective mean, with its spatial distribution remaining weakly constrained. Despite an overall improving but oscillatory training trajectory, the proposed selection strategy identifies an admissible late-training compromise without assuming convergence to a unique inverse solution.