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Physics informed surface autoencoders for thin shell analysis
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AI
DOI：10.1016/j.cma.2026.118764.png)
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Abstract
En 中文
We present a physics-informed surface autoencoder (PISA) framework for Kirchhoff-Love thin shell analysis. The method constructs global C1 surface parameterizations directly from unstructured point clouds for both single-patch surfaces homeomorphic to disks, and multi-patch parameterizations for closed genus-zero surfaces. In the multi-patch case, a classification network assigns probabilistic labels to points, and the autoencoder learns overlapping charts with smooth transitions, ensuring global C1 continuity. With the learned parameterizations, we introduce a decoder for the displacement field and compute differential geometric quantities such as the metric and second fundamental form in the reference and deformed surfaces. Then, we enforce equilibrium by minimizing the total potential energy. The approach is validated on classical shell benchmarks, including the Scordelis-Lo roof, pinched cylinder, and hemisphere under pressure. We showcase the flexibility of the framework with complex geometries such as the Stanford Bunny and dura mater. Compared with traditional spline-based parameterizations and existing machine learning approaches, PISA offers a pipeline for generating smooth surface maps for complex geometries and integrates the surface representation into the physics-informed solver. Importantly, the thin shell analysis pipeline proposed works directly with unstructured point cloud data. Thus, this PISA framework’s potential applications range from engineering structures to biological membranes such as heart valves, skin, and dura mater.
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