Galerkin approximation of dynamical quantities using trajectory data.
Galerkin approximation of dynamical quantities using trajectory data.
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DOI：
10.1063/1.5063730
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发表时间：
2018-10
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影响因子：
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通讯作者：
Erik H. Thiede;D. Giannakis;A. Dinner;J. Weare
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文献类型：
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作者：
Erik H. Thiede;D. Giannakis;A. Dinner;J. Weare
理解化学机制需要估计动态统计，如预期的命中时间，反应速率和提交者。在这里，我们提出了一个一般的框架来计算这些动态量近似边界值问题，使用动态运营商与Galerkin展开。在扩展中的基组的具体选择对应于使用马尔可夫状态模型的动态量的估计。更一般地，边界条件对基组的选择施加限制。我们演示了如何使用扩散映射的思想来构建替代基础。在我们的数值实验中，这个基础给出了与马尔可夫状态模型相当或更好的精度的结果。此外，我们表明，延迟嵌入可以减少信息丢失时，投影系统的动态模型建设，这大大提高了动态统计的估计，超过了标准的做法，增加了滞后时间。
Understanding chemical mechanisms requires estimating dynamical statistics such as expected hitting times, reaction rates, and committors. Here, we present a general framework for calculating these dynamical quantities by approximating boundary value problems using dynamical operators with a Galerkin expansion. A specific choice of basis set in the expansion corresponds to the estimation of dynamical quantities using a Markov state model. More generally, the boundary conditions impose restrictions on the choice of basis sets. We demonstrate how an alternative basis can be constructed using ideas from diffusion maps. In our numerical experiments, this basis gives results of comparable or better accuracy to Markov state models. Additionally, we show that delay embedding can reduce the information lost when projecting the system's dynamics for model construction; this improves estimates of dynamical statistics considerably over the standard practice of increasing the lag time.