Learning the Physics of Pattern Formation from Images.,Physical Review Letters

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Learning the Physics of Pattern Formation from Images.
Physical Review Letters ( IF 8.1 ) Pub Date : 2020-02-14 , DOI: 10.1103/physrevlett.124.060201
Hongbo Zhao ₁ , Brian D Storey _{2,

3} , Richard D Braatz ₁ , Martin Z Bazant _{1,

4}

Affiliation

Using a framework of partial differential equation-constrained optimization, we demonstrate that multiple constitutive relations can be extracted simultaneously from a small set of images of pattern formation. Examples include state-dependent properties in phase-field models, such as the diffusivity, kinetic prefactor, free energy, and direct correlation function, given only the general form of the Cahn-Hilliard equation, Allen-Cahn equation, or dynamical density functional theory (phase-field crystal model). Constraints can be added based on physical arguments to accelerate convergence and avoid spurious results. Reconstruction of the free energy functional, which contains nonlinear dependence on the state variable and differential or convolutional operators, opens the possibility of learning nonequilibrium thermodynamics from only a few snapshots of the dynamics.

中文翻译：

从图像中学习图案形成的物理原理。

使用偏微分方程约束优化的框架，我们证明了可以从一小套图案形成图像中同时提取多个本构关系。例如，仅给出Cahn-Hilliard方程，Allen-Cahn方程或动力密度泛函理论的一般形式，就可以包括相场模型中与状态有关的特性，例如扩散率，动力学前因子，自由能和直接相关函数。（相场晶体模型）。可以基于物理参数添加约束，以加速收敛并避免虚假结果。重构自由能泛函，其中包含对状态变量和微分或卷积算符的非线性依赖性，

更新日期：2020-02-14

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