用神经网络参数化薄壳形状，实现可微优化设计。
Neural parametric representations for thin-shell shape optimisation
- 用带周期激活函数的MLP映射中面顶点参数坐标到物理坐标。
- 在体积约束下通过梯度优化使结构柔度降低，验证了有效性。
- 适合复杂桁架-蒙皮结构，几何表达紧凑且表达力强。
薄壳结构的形状优化需要灵活且可微的几何表示以支持基于梯度的优化。本文提出一种基于周期激活函数神经网络的神经参数化表示（NRep），用于描述壳体中面。NRep采用多层感知机（MLP），将中面顶点的参数坐标映射为物理坐标。在体积约束条件下，以网络参数为设计变量，构建结构柔度最小化的形状优化问题，并使用梯度优化算法求解。基准算例与经典解对比表明该方法的有效性。由于NRep提供的紧凑而强大的几何表达能力，该方法在复杂桁架-蒙皮结构设计中具有潜力。
原文摘要 · Abstract (English)
Shape optimisation of thin-shell structures requires a flexible, differentiable geometric representation suitable for gradient-based optimisation. We propose a neural parametric representation (NRep) for the shell mid-surface based on a neural network with periodic activation functions. The NRep is defined using a multi-layer perceptron (MLP), which maps the parametric coordinates of mid-surface vertices to their physical coordinates. A structural compliance optimisation problem is posed to optimise the shape of a thin-shell parameterised by the NRep subject to a volume constraint, with the network parameters as design variables. The resulting shape optimisation problem is solved using a gradient-based optimisation algorithm. Benchmark examples with classical solutions demonstrate the effectiveness of the proposed NRep. The approach exhibits potential for complex lattice-skin structures, owing to the compact and expressive geometry representation afforded by the NRep.
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