Metamodeling elastic wave propagation using a mixed factorized Fourier encoder-decoder for online laser-ultrasound testing in additive manufacturing

Laser-ultrasound (LU) testing has emerged as a promising technique for characterizing the polycrystalline microstructure of metal components produced by wire-laser additive manufacturing (WLAM), with potential for real-time online application. Numerical models simulating elastic waves propagation provide valuable insights into the relationship between microstructural properties and laser-induced displacements, but their computational cost renders them impractical for automated high-throughput characterization. To overcome this limitation, we build a metamodel that maps a wide variety of two-dimensional anisotropic polycrystalline microstructures simplified but representative of features commonly observed in WLAM to simulated surface displacements. Addressing this challenging high-dimensional regression problem, several neural network surrogates are proposed. Their architectures include usual convolutional encoder-decoder elements and layers inspired from the Fourier neural operator (FNO) framework. Several variants of this novel combination are investigated. All metamodels can run both a forward and backward pass at least 100~times faster than a single forward call of the original model. Notably, the channel-wise factorized variant of the spectral layers, which is characterized by a relatively small number of parameters, achieved the lowest approximation error. The metamodel successfully captures the primary effects of anisotropy on wave propagation, even for low-anisotropy inputs not included in the training data. These findings represent a promising initial step towards addressing inversion problems and facilitating the development of online LU testing protocols in additive manufacturing.