Multioutput convolutional neural network for improved parameter extraction in time-resolved electrostatic force microscopy data

Time-resolved scanning probe microscopy methods, like time-resolved electrostatic force microscopy (trEFM), enable imaging of dynamic processes ranging from ion motion in batteries to electronic dynamics in microstructured thin film semiconductors for solar cells. Reconstructing the underlying physical dynamics from these techniques can be challenging due to the interplay of cantilever physics with the actual transient kinetics of interest in the resulting signal. Previously, quantitative trEFM used empirical calibration of the cantilever or feed-forward neural networks trained on simulated data to extract the physical dynamics of interest. Both these approaches are limited by interpreting the underlying signal as a single exponential function, which serves as an approximation but does not adequately reflect many realistic systems. Here, we present a multi-branched, multi-output convolutional neural network (CNN) that uses the trEFM signal in addition to the physical cantilever paramete..., The trained model parameters were obtained by training the convolutional neural network on a combination of simulated and voltage pulse data. All code can be found at: https://github.com/mdbresh/CNN_trEFM.
The voltage pulse dataset was obtained by applying voltage pulses following single- and bi-exponential functions with known parameters to a conductive substrate and collecting the response from an oscillating scanning probe cantilever. Additional details can be found in the preprint of the manuscript in the Methods section: https://doi.org/10.48550/arXiv.2502.03572.
The example time-resolved electrostatic force microscopy image was collected on a lead halide perovskite thin film sample with the following composition: Cs0.17FA0.83Pb(I0.85Br0.15)3. Details regarding sample preparation and data processing are described in the preprint of the manuscript in the Methods and Supporting Information sections: https://doi.org/10.48550/arXiv.2502.03572.
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[https://doi.org/10.5061/dryad.9zw3r22rv](https://doi.org/10.5061/dryad.9zw3r22rv)

Trained model parameters (best_model.pth), voltage pulse data, and example image topography and input data included in the [manuscript](https://doi.org/10.1021/acs.jcim.5c00267).

### Setup instructions:

1. Download the files in this Dryad repository (image_topography.npy, vpulse_labels.npy, vpulses.npy, best_model.pth, image_instfreq.npy, example_use.ipynb, and MultioutputCNN_for_trEFM.py).
2. Open the Jupyter notebook (example_use.ipynb) in your preferred IDE (e.g., Spyder or VS Code).
3. Follow instructions on how to load the datasets using Numpy and PyTorch libraries for Python. Visualizations in the notebook are created with the matplotlib library. A complete list of libraries needed is included in example_use.ipynb.
4. Further dataset descriptions, visualiza..., ,