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

Andrew M Nagel1, Martin Magill1, Hendrick W de Haan1

  • 1Faculty of Science, University of Ontario Institute of Technology, 2000 Simcoe St N, Oshawa, Ontario, Canada L1H7K4.

Physical Review. E
|September 16, 2022
PubMed
Summary

Deep neural networks solve Smoluchowski equations for nanoparticle transport in microfluidics. This approach efficiently maps physical parameters to transport metrics, outperforming traditional simulation methods.

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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.

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  • 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.