流体界面的形状相似潜空间：液滴形态的可逆降阶建模
A shape-similarity latent space for fluid interfaces: invertible reduced-order modelling of droplet morphology
- Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE)（国际数值工程方法中心）
- Universitat Politècnica de Catalunya – BarcelonaTech (UPC)（加泰罗尼亚理工大学）
- Escola Tècnica Superior d’Enginyers de Camins, Canals i Ports, Universitat Politècnica de Catalunya – BarcelonaTech (UPC)（加泰罗尼亚理工大学土木、航道与港口工程学院）
- Escola Politècnica Superior d’Enginyeria de Vilanova i la Geltrú (EPSEVG), Fluid Mechanics Department, Universitat Politècnica de Catalunya – BarcelonaTech (UPC)（加泰罗尼亚理工大学维尔诺瓦伊拉热特鲁高级工程学校）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
针对液滴破裂过程难以观测和模拟的问题，提出SHROM方法，结合平方根速度函数、邻接图和自编码器，构建可逆的低维形状潜空间，在30万轮廓上验证了潜空间语义性，但拓扑变化插值仍是局限。
中文摘要 AI 辅助
液滴在数十微秒内破裂，一次记录可能仅捕获约十二帧。若不重复实验，中间状态无法恢复，而模拟这些状态成本过高，难以覆盖整个操作范围。然而，这些状态整体上存在于语料库中：跨越设备驱动范围的实验活动产生的形态，类似于任何单次记录所遗漏的形态。利用这一点需要一种低维、可逆且忠实于形状而非采样的表示。本征正交分解提供了前两个特性，但在采样坐标中度量距离；流形学习提供了第三个特性，但没有映射回形状的途径；弹性形状分析提供了形状度量但没有降维坐标。SHROM综合了这三者。界面由其平方根速度函数表示，在该形状空间上构建邻接图，并训练自编码器在重建的同时惩罚图中邻居在潜空间中不相邻的情况。演示使用了301,539个喷墨液滴轮廓和四个拍摄的破裂序列。图项并未改善重建效果。它决定了潜空间中的位置是否具有意义：对原本相同的模型进行潜空间聚类，在没有该图项时以偶然水平恢复形状空间划分（ARI = 0.063 ± 0.059），而在启用该图项时为0.781 ± 0.049。波形参数以R² = 0.878 ± 0.026预测完整轮廓。负面结果以相同方式报告。图度量在五种选择中被证明无关紧要，插值误差饱和于重建极限，因此普通自编码器在该任务中领先。主要局限在于跨越拓扑变化的插值：正则化潜空间的任何分量都无法同时容纳单组分和破裂后的形状，而未正则化的自编码器则能自由混合它们。
英文摘要
A droplet breaks up in tens of microseconds, and a recording captures perhaps a dozen frames. The states in between cannot be recovered without repeating the experiment, and simulating them is too costly to sweep an operating envelope. Yet they are present in the corpus as a whole: a campaign spanning a device's actuation range produces morphologies resembling those any single recording missed. Exploiting that requires a representation that is low-dimensional, invertible, and faithful to shape rather than to sampling. Proper orthogonal decomposition supplies the first two but measures distance in sampled coordinates; manifold learning supplies the third but no map back to a shape; elastic shape analysis supplies a shape metric but no reduced coordinates. SHROM composes all three. Interfaces are represented by their square-root velocity functions, a neighbour graph is built over that shape space, and an autoencoder is trained to reconstruct while penalising latents in which graph neighbours are not latent neighbours. The demonstration uses 301,539 inkjet droplet contours and four filmed break-up sequences. The graph term does not improve reconstruction. It determines whether position in the latent carries meaning: clustering the latent of an otherwise identical model recovers the shape-space partition at chance level (ARI = 0.063 +/- 0.059), and at 0.781 +/- 0.049 with the term active. Waveform parameters predict the full contour at R^2 = 0.878 +/- 0.026. Negative results are reported in the same terms. The graph metric proved immaterial across five choices, and interpolation error saturates at the reconstruction limit, so a plain autoencoder leads that task. The main limitation is interpolation across a topology change: no component of the regularised latent holds both a single-component and a post-break-up shape, whereas an unregularised autoencoder mixes them freely.
