# Image features of a splashing drop on a solid surface extracted using a feedforward neural network

arXiv: https://arxiv.org/abs/2201.09541 · HTML: https://mlsanity.com/paper/2201.09541/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 71 references that are in the map.
- First posted on arXiv 24 Jan 2022.

## Builds on (most cited first, 8 of 8)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Physics guided machine learning using simplified theories](https://mlsanity.com/paper/2012.13343/) (2020)
- [Deep-learning of Parametric Partial Differential Equations from Sparse and Noisy Data](https://mlsanity.com/paper/2005.07916/) (2020)
- [Semi Conditional Variational Auto-Encoder for Flow Reconstruction and Uncertainty Quantification from Limited Observations](https://mlsanity.com/paper/2007.09644/) (2020)
- [Transfer learning for nonlinear dynamics and its application to fluid turbulence](https://mlsanity.com/paper/2009.01407/) (2020)

## Built on by (most cited first, 3 of 3)

- [Correlation between morphological evolution of splashing drop and exerted impact force revealed by interpretation of explainable artificial intelligence](https://mlsanity.com/paper/2309.10266/) (2023)
- [Predicting Energy Budgets in Droplet Dynamics: A Recurrent Neural Network Approach](https://mlsanity.com/paper/2403.16144/) (2024)
- [Features of a Splashing Drop on a Solid Surface and the Temporal Evolution extracted through Image-Sequence Classification using an Interpretable Feedforward Neural Network](https://mlsanity.com/paper/2207.00971/) (2022)

## Abstract (arXiv)

This article reports nonintuitive characteristic of a splashing drop on a solid surface discovered through extracting image features using a feedforward neural network (FNN). Ethanol of area-equivalent radius about 1.29 mm was dropped from impact heights ranging from 4 cm to 60 cm (splashing threshold 20 cm) and impacted on a hydrophilic surface. The images captured when half of the drop impacted the surface were labeled according to their outcome, splashing or nonsplashing, and were used to train an FNN. A classification accuracy higher than 96% was achieved. To extract the image features identified by the FNN for classification, the weight matrix of the trained FNN for identifying splashing drops was visualized. Remarkably, the visualization showed that the trained FNN identified the contour height of the main body of the impacting drop as an important characteristic differentiating between splashing and nonsplashing drops, which has not been reported in previous studies. This feature was found throughout the impact, even when one and three-quarters of the drop impacted the surface. To confirm the importance of this image feature, the FNN was retrained to classify using only the main body without checking for the presence of ejected secondary droplets. The accuracy was still higher than 82%, confirming that the contour height is an important feature distinguishing splashing from nonsplashing drops. Several aspects of drop impact are analyzed and discussed with the aim of identifying the possible mechanism underlying the difference in contour height between splashing and nonsplashing drops.