Studying first passage problems using neural networks: A case study in the slit-well microfluidic device

Area of Science:

• Computational physics
• Nanotechnology
• Fluid dynamics

Background:

• First passage time problems are crucial in understanding particle dynamics.
• Traditional methods like particle simulations struggle with complex parameter spaces and geometry.
• Stochastic differential equation (SDE) models are commonly used but have limitations.

Purpose of the Study:

• To present deep neural network (DNN) solutions for a time-integrated Smoluchowski equation.
• To model the mean first passage time of nanoparticles in microfluidic devices.
• To establish continuous mappings between physical inputs and output metrics.

Main Methods:

• Solving the partial differential equation (PDE) model using a DNN-based approach.
• Utilizing a time-integrated Smoluchowski equation for nanoparticle transport.
• Comparing DNN method with traditional SDE simulations.

Main Results:

• DNNs effectively solve the Smoluchowski equation, providing continuous mappings from input parameters (voltage, diameter) to output metrics (first passage time, mobility).
• The DNN approach demonstrates synergy with the Smoluchowski model, offering advantages over SDE models.
• The method reliably handles geometry-modifying parameters, a challenge for other techniques.

Conclusions:

• DNNs offer a powerful and efficient alternative for solving complex first passage time problems.
• The combined DNN and Smoluchowski model approach provides unique capabilities for predicting nanoparticle transport.
• This method facilitates the analysis of microfluidic devices and similar systems with varying parameters and geometries.