Abstract Composition-dependent inter-diffusion coefficients are key parameters in many physical processes. Due to the under-determinedness of the governing diffusion equations, numerical methods either impose strict physical conditions on the samples or require a computationally onerous amount of data. To address such problems, we propose a novel inverse framework to recover the diffusion coefficients using a compressed sensing method, which in principle can be extended to alloy systems with arbitrary number of species. Comparing to conventional methods, the new approach does not impose any priori assumptions on the functional relationship between diffusion coefficients and concentrations, nor any preference on the locations of the samples, as long as it is in the diffused zone. It also requires much less data compared to least-squares approaches. Through a few numerical examples of ternary and quandary systems, we demonstrate the accuracy and robustness of the new method.

中文翻译：

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一种基于压缩感知方法计算依赖于成分的互扩散系数的有效方法

摘要 与成分相关的互扩散系数是许多物理过程中的关键参数。由于控制扩散方程的不确定性，数值方法要么对样品施加严格的物理条件，要么需要大量的计算数据。为了解决这些问题，我们提出了一种新的逆框架来使用压缩传感方法恢复扩散系数，原则上可以将其扩展到具有任意数量物种的合金系统。与传统方法相比，新方法不会对扩散系数和浓度之间的函数关系强加任何先验假设，也不会对样品的位置施加任何偏好，只要它位于扩散区即可。与最小二乘法相比，它还需要更少的数据。