Bayesian Modelling of Pattern Formation from One Snapshot of Pattern
arXiv:2006.06125 · doi:10.1103/PhysRevE.106.065301
Abstract
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.
arXiv comment24 pages, 6 figures, Supplementary Information is available on http://www.wpi-aimr.tohoku.ac.jp/~yoshinaga/publication/Supplement20210922.pdf
References in corpus (31)
- Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
- Exchange Monte Carlo Method and Application to Spin Glass Simulations
- Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems
- Modeling Elasticity in Crystal Growth
- Modeling Elastic and Plastic Deformations in Non-Equilibrium Processing Using Phase Field Crystals
- Theoretical Model for Faraday Waves with Multiple-Frequency Forcing
- Optimized Interactions for Targeted Self-Assembly: Application to Honeycomb Lattice
- Self Assembly of Soft Matter Quasicrystals and Their Approximants
- Designed Interaction Potentials via Inverse Methods for Self-Assembly
- Controlled self-assembly of periodic and aperiodic cluster crystals
- Inverse methods for design of soft materials
- Perspective: Inverse methods for material design
- Turning Statistical Physics Models Into Materials Design Engines
- Growth modes of quasicrystals
- Inverse Design for Self Assembly via On-the-Fly Optimization
- Three-dimensional Phase Field Quasicrystals
- Simultaneous Estimation of Noise Variance and Number of Peaks in Bayesian Spectral Deconvolution
- Assembly of nothing: Equilibrium fluids with designed structured porosity
- Structured Bayesian Gaussian process latent variable model: applications to data-driven dimensionality reduction and high-dimensional inversion
- Inverse Design of Multicomponent Assemblies
- DL-PDE: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy data
- Inverse Design of Simple Pair Potentials for the Self-Assembly of Complex Structures
- From Close-Packed to Topologically Close-Packed: Formation of Laves Phases in Moderately Polydisperse Hard-Sphere Mixtures
- Estimating model evidence using data assimilation
- Non-Close-Packed Three-Dimensional Quasicrystals
- Multiple-scale structures: from Faraday waves to soft-matter quasicrystals
- Inverse design of charged colloidal particle interactions for self assembly into specified crystal structures
- Image Inversion and Uncertainty Quantification for Constitutive Laws of Pattern Formation
- Inverse design of two-dimensional structure by self-assembly of patchy particles
- Design of two-dimensional particle assemblies using isotropic pair interactions with an attractive well
- Topological defects of dipole patchy particles on a spherical surface