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It is expensive to compute residual diffusivity in chaotic incompressible flows by solving advection-diffusion equation due to the formation of sharp internal layers in the advection dominated regime. Proper orthogonal decomposition (POD) is a classical method to construct a small number of adaptive orthogonal basis vectors for low cost computation based on snapshots of fully resolved solutions at a particular molecular diffusivity D0* . The quality of POD basis deteriorates if it is applied to D0<< D0* . To improve POD, we adapt a super-resolution generative adversarial deep neural network (SRGAN) to train a nonlinear mapping based on snapshot data at two values of D0* . The mapping models the sharpening effect on internal layers as D0 becomes smaller. We show through numerical experiments that after applying such a mapping to snapshots, the prediction accuracy of residual diffusivity improves considerably that of the standard POD.
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Machine-learning-powered extraction of molecular diffusivity from single-molecule images for super-resolution mapping
Abstract While critical to biological processes, molecular diffusion is difficult to quantify, and spatial mapping of local diffusivity is even more challenging. Here we report a machine-learning-enabled approach, pixels-to-diffusivity (Pix2D), to directly extract the diffusion coefficientDfrom single-molecule images, and consequently enable super-resolvedDspatial mapping. Working with single-molecule images recorded at a fixed framerate under typical single-molecule localization microscopy (SMLM) conditions, Pix2D exploits the often undesired yet evident motion blur,i.e., the convolution of single-molecule motion trajectory during the frame recording time with the diffraction-limited point spread function (PSF) of the microscope. Whereas the stochastic nature of diffusion imprints diverse diffusion trajectories to different molecules diffusing at the same givenD, we construct a convolutional neural network (CNN) model that takes a stack of single-molecule images as the input and evaluates aD-value as the output. We thus validate robustDevaluation and spatial mapping with simulated data, and with experimental data successfully characterizeDdifferences for supported lipid bilayers of different compositions and resolve gel and fluidic phases at the nanoscale.
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- Award ID(s):
- 2203518
- PAR ID:
- 10403677
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Communications Biology
- Volume:
- 6
- Issue:
- 1
- ISSN:
- 2399-3642
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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