Studying First Passage Problems using Neural Networks: A Case Study in the Slit-Well Microfluidic Device

Abstract

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.

20 pages, 8 figures, 2 tables

References in corpus (3)

• PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain
• Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows
• Neural Network Solutions to Differential Equations in Non-Convex Domains: Solving the Electric Field in the Slit-Well Microfluidic Device