Deep-learning-based surrogate model of laser-induced elastic wave propagation in metallic microstructures with elongated grains

The displacement field of laser-induced elastic waves propagating at the surface contains information about the physical properties of the medium at shallow depths (Rayleigh wavelength). This information can be used to characterize the polycrystalline microstructure of metal components produced by Wire-Laser Additive Manufacturing (WLAM). Such components typically exhibit elongated grains due to high temperature gradients. Theoretical models relating the scattering and attenuation of bulk waves to grain geometry have been proposed; including a 2D model to predict effects of 3D grain shape and rotation [1]. The models highlight the influence of grain elongation and the possibility of extracting microstructure properties from attenuation. Effective properties can also be estimated by using FE simulations of elastic wave propagation in randomly generated microstructures [2]. The use of laser-ultrasound (LU) techniques to probe the material health of beads deposited during a WLAM process is a promising approach. These techniques can also be used to characterize the microstructure in situ. Although numerical simulations can link a microstructure to a synthetic B-scan, they take too long to enable online inspection. This study explores the use of deep neural networks (DNN) as a surrogate model for mapping microstructure (input) and synthetic B-scans (output). DNNs have demonstrated satisfactory performance in surrogate modelling of 3D seismic wave propagation in heterogeneous isotropic media [3], as well as in generating realistic ultrasonic inspection data using a multi-fidelity framework that includes simulations and measurements [4]. As a preliminary step, we created a simulation database to train state-of-the-art DNN models. The architectures were inspired by convolutional neural networks and (Factorized-)Fourier Neural Operators (FNO, FFNO). The simulations were simplified 2D adaptations of configurations and FE simulations presented in [2] and adapted to a laser source. The heterogeneous media had random grain shapes and crystal orientations, with variable overall anisotropy, orientation, and elongation between each simulation. Initial findings indicate that all trained DNNs are able to provide fair mappings of microstructure to synthetic B-scan at a faster rate than the FE model. The areas that correspond to the arrival of coherent transient surface acoustic waves have the lowest relative approximation error, while structural noise is approximated fairly well but appears to be more challenging to learn. FFNO-based models produced the most accurate results, albeit with longer computational time. The simplified configurations have shown promising results and will be extended to cases that are more representative. Acknowledgments This work was part of COLUMBO project (ANR-21-CE08-0026) funded by the French National Agency for Research (ANR). Authors would like to thank A. Imperiale for optimising the FE code into CIVA and F. Lehmann for sharing her FFNO scripts. References [1] J. C. Victoria Giraldo et al., J. Phys. Conf. Series, (2024) [2] V. Dorval et al., Proc. Eu. Conf. NDT, (2023) [3] F. Lehmann et al.,Comp. Meth. Appli. Mech. Eng., 420, (2024). [4] Granados et al., NDT&E Int., 139, (2023) Nerlikar et al., ‘‘A physics-embedded deep-learning framework for efficient multi-fidelity modelling