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We present a new convolutional neural network (CNN)-based element-wise classification method to detect a random number of voids in a 2D plain strain solid subjected to elastodynamics. We consider that an elastic wave source excites the solid including a random number of voids, and wave responses are measured by sensors placed around the solid. We present a CNN for resolving the inverse problem, which is formulated as an element-wise classification problem. The CNN is trained to classify each element into a regular or void element from measured wave signals. To this end, we generate training data consisting of input-layer features (i.e., measured wave signals at sensors) and output-layer features (i.e., element types of all elements). When the training data are generated, we utilize the level-set method to avoid an expensive re-meshing process, which is otherwise needed for each different configuration of voids. We also analyze how effectively the CNN performs on blind test data from a non-level-set wave solver that explicitly models the boundary of voids using an unstructured, fine mesh. Numerical results show that the suggested approach can detect the locations, shapes, and sizes of multiple elliptical and circular voids in the 2D solid domain in the test data set as well as a blind test data set. 

Abstract We introduce a novel data‐informed convolutional neural network (CNN) approach that utilizes sparse ground motion measurements to accurately identify effective seismic forces in a truncated two‐dimensional (2D) domain. Namely, this paper presents the first prototype of a CNN capable of inferring domain reduction method (DRM) forces, equivalent to incident waves, across all nodes in the DRM layer. It achieves this from sparse measurement data in a multidimensional setting, even in the presence of incoherent incident waves. The method is applied to shear (SH) waves propagating into a domain truncated by a wave‐absorbing boundary condition (WABC). By effectively training the CNN using input‐layer features (surface sensor measurements) and output‐layer features (effective forces at a DRM layer), we achieve significant reductions in processing time compared to PDE‐constrained optimization methods. The numerical experiments demonstrate the method's effectiveness and robustness in identifying effective forces, equivalent to incoherent incident waves, at a DRM layer.