Physcis added and informed neural network for time-dependent prediction of droplet evaporation*

In this paper, a deep learning approach is proposed for predicting droplet evaporation over time, using image-based analysis. The method's key feature lies in the enhancement of prediction accuracy and reduced demand for extensive training data by incorporating physical laws into the learning process. Two methods introduce biases based on the underlying physics. Firstly, the contact angle and diameter are measured from training images, and this information is used to enhance the physical plausibility of predicted images. Secondly, the time-dependent changes in the contact angle and contact diameter of output images are monitored, ensuring their alignment with known physical phenomena such as receding angles—whether they are increasing, decreasing, or remaining constant—thus guiding the learning process of the neural network. Promising results showcase improved predictive capabilities for droplet evaporation. By combining image-based learning with physical constraints, an approach that presents a step towards accurate and efficient prediction of droplet evaporation phenomena is discussed. The potential applications of this approach encompass various fields, including materials science, engineering, and environmental studies. Overall, the successful integration of deep learning and physical principles to tackle complex and time-dependent processes is showcased, paving the way for advancements in droplet evaporation prediction and beyond.