Physics-informed neural networks for predicting Rhodamine diffusion coefficient

Accurate measurement of drug diffusion coefficients is essential to optimize drug delivery systems. We focus on Rhodamine as a model compound to simulate drug behaviour and use its widely doc- umented diffusive behaviour as a benchmark for in silico studies. In this study, we developed an experimental setup to track Rhodamine diffusion in water, generating spatio-temporal concentra- tion data. These images are input for a physics-informed neural network (PINN) [1] to inversely solve diffusion PDE determining the Rhodamine diffusion coefficient. Figure a and b show the digital image of the Rhodamine concentration front at initial condition and t = 2s, respectively. Figure c shows the corresponding PINN predictions of the Rhodamine concentration with the error map (Figure d). The predicted diffusion coefficient of D = 3.7 × 10−10 m2 s−1 for rhodamine in water, which is in good agreement with the range of values previously reported [2]. This exper- imental and computational framework provides a platform for diffusion coefficient determination without requiring extensive calibration experiments. Future work will extend this methodology to track Rhodamine binding with proteins, employing an enhanced PINN architecture coupled with reaction-diffusion equations solving for diffusion coefficients, reaction rate, and reaction order.