2022年
Bayesian modeling of pattern formation from one snapshot of pattern
Physical Review E
- ,
- 巻
- 106
- 号
- 開始ページ
- 065301
- 終了ページ
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1103/PhysRevE.106.065301
Partial differential equations (PDEs) 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 method, referred to as Bayesian modeling of PDEs (BM-PDEs), to estimate the best dynamical PDE for one snapshot of a objective pattern under the stationary state without ground truth. We apply BM-PDEs to nontrivial patterns, such as quasicrystals (QCs), a double gyroid, and Frank-Kasper structures. We also generate three-dimensional dodecagonal QCs from a PDE model. This is done by using the estimated parameters for the Frank-Kasper A15 structure, which closely approximates the local structures of QCs. Our method works for noisy patterns and the pattern synthesized without the ground-truth parameters, which are required for the application toward experimental data.
- リンク情報
-
- DOI
- https://doi.org/10.1103/PhysRevE.106.065301 本文へのリンクあり
- 共同研究・競争的資金等の研究課題
- 条件付き独立な観測に基づく統計的推測の理論と実践
- ID情報
-
- DOI : 10.1103/PhysRevE.106.065301
- ORCIDのPut Code : 124304656