论文标题
使用神经网络研究第一次通道问题：在狭缝孔微流体设备中的案例研究
Studying First Passage Problems using Neural Networks: A Case Study in the Slit-Well Microfluidic Device
论文作者
论文摘要
这项研究为时间融合的Smoluchowski方程提供了深层神经网络解决方案，该方程模拟了纳米颗粒的平均第一个通道时间，遍历了狭窄的微流体设备。这种物理场景代表了更广泛的参数化第一段问题，其中关键输出指标由问题参数和系统几何形状的复杂相互作用决定。具体而言，尽管这些类型的问题通常是使用随机微分方程模型的粒子模拟来研究的，但这里使用基于深神经网络的方法来求解相应的部分微分方程模型。结果表明，神经网络方法与时间集成的Smoluchowski模型协同：共同使用，这些模型用于构建从关键物理输入（应用电压和颗粒直径）到关键输出指标（平均第一个传递时间和有效的迁移率）的连续映射。特别是，这种功能是时间集成的Smoluchowski模型的独特优势，而不是相应的随机微分方程模型。此外，证明了神经网络方法可以轻松，可靠地处理几何变化参数，这通常很难使用其他方法来完成。
This study presents deep neural network solutions to a time-integrated Smoluchowski equation modeling the mean first passage time of nanoparticles traversing the slit-well microfluidic device. This physical scenario is representative of a broader class of parameterized first passage problems in which key output metrics are dictated by a complicated interplay of problem parameters and system geometry. Specifically, whereas these types of problems are commonly studied using particle simulations of stochastic differential equation models, here the corresponding partial differential equation model is solved using a method based on deep neural networks. The results illustrate that the neural network method is synergistic with the time-integrated Smoluchowski model: together, these are used to construct continuous mappings from key physical inputs (applied voltage and particle diameter) to key output metrics (mean first passage time and effective mobility). In particular, this capability is a unique advantage of the time-integrated Smoluchowski model over the corresponding stochastic differential equation models. Furthermore, the neural network method is demonstrated to easily and reliably handle geometry-modifying parameters, which is generally difficult to accomplish using other methods.
