论文标题
标记粒子过程的自扩散矩阵的张量近似
Tensor approximation of the self-diffusion matrix of tagged particle processes
论文作者
论文摘要
本文的目的是研究一种新的数值方法，以近似在网格上定义的标记粒子过程的自扩散矩阵。虽然标准的数值方法利用了一些随机过程的经验偏差的经验平均值，因此会遇到统计噪声，但我们在这里提出了一种张量方法，以计算解决高维相互优化问题解决方案的近似值，这使得能够获得数值的自我差异配备。我们在这里使用的张量方法取决于迭代方案，该方案构建了利息量和经过精心调整的差异方法的低级别近似值，以评估在功能中产生的各种术语以最小化。特别是，我们在这里观察到，与经典方法相比，它的统计噪声要小得多。
The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of empirical means of deviations of some stochastic processes, and are thus subject to statistical noise, we propose here a tensor method in order to compute an approximation of the solution of a high-dimensional quadratic optimization problem, which enables to obtain a numerical approximation of the self-diffusion matrix. The tensor method we use here relies on an iterative scheme which builds low-rank approximations of the quantity of interest and on a carefully tuned variance reduction method so as to evaluate the various terms arising in the functional to minimize. In particular, we numerically observe here that it is much less subject to statistical noise than classical approaches.
