论文标题
从一个图案快照的图案形成的贝叶斯建模
Bayesian Modelling of Pattern Formation from One Snapshot of Pattern
论文作者
论文摘要
部分微分方程（PDE）已被广泛用于复制自然界的模式，并深入了解基础模式形成的机制。尽管已经提出了许多PDE模型，但它们依赖于物理定律和对称性的重新征用知识，并且开发一个模型来复制给定的所需模式仍然很困难。我们提出了一种新型方法，称为PDE的贝叶斯建模（BM-PDE），以估算一个在没有地面真相的固定状态下目标模式的一个快照的最佳动力学PDE。我们将BM-PDE应用于非平凡的模式，例如准晶体（QC），双爵士和弗兰克·卡斯珀结构。通过对QC的大约使用估计的参数，我们首次成功地生成了PDE模型的三维十二架QC。我们的方法适用于嘈杂的模式和没有地面真实参数的模式，这是应用于实验数据所必需的。
Partial differential equations (PDE) have been widely used to reproduce patterns in nature and to give insight into the mechanism underlying pattern formation. Although many PDE models have been proposed, they rely on the pre-request knowledge of physical laws and symmetries, and developing a model to reproduce a given desired pattern remains difficult. We propose a novel method, referred to as Bayesian modelling of PDE (BM-PDE), to estimate the best dynamical PDE for one snapshot of a target pattern under the stationary state without ground truth. We apply BM-PDE to nontrivial patterns,such as quasi-crystals (QCs), a double gyroid and Frank Kasper structures. By using the estimated parameters for the approximant of QCs, we successfully generate, for the first time,three-dimensional dodecagonal QCs from a PDE model. Our method works for noisy patterns and the pattern synthesised without the ground truth parameters, which are required for the application toward experimental data.
