Detecting hidden structures from a static loading experiment: topology optimization meets physics-informed neural networks

Abstract: Most noninvasive imaging techniques utilize electromagnetic or acoustic waves originating from multiple locations and directions to identify hidden geometrical structures. Surprisingly, it is also possible to image hidden voids and inclusions buried within an object using a single static thermal or mechanical loading experiment by observing the response of the exposed surface of the body, but this problem is challenging to invert. Although physics-informed neural networks (PINNs) have shown promise as a simple-yet-powerful tool for problem inversion, they have not yet been applied to imaging problems with a priori unknown topology. Here, we introduce a topology optimization framework based on PINNs that identifies concealed geometries using exposed surface data from a single loading experiment, without prior knowledge of the number or types of shapes. We allow for arbitrary solution topology by representing the geometry using a material density field combined with a novel eikonal regularization technique. We validate our framework by detecting the number, locations, and shapes of hidden voids and inclusions in many example cases, in both 2D and 3D, and we demonstrate the method's robustness to noise and sparsity in the data. Our methodology opens a pathway for PINNs to solve geometry optimization problems in engineering.