A Physics-Informed neural network (PINN) for parameter identification in analytical ultracentrifugation (AUC) analysis

In this paper, we develop a Physics-Informed Neural Network (PINN) for parameter estimation in Analytical Ultracentrifugation (AUC) analysis. We use a feed-forward dense network composed of multi-layer perceptrons to approximate the solution of the Lamm equation, which models the physics of the ultracentrifugation process. The sedimentation and diffusion coefficients are trainable parameters in the network. The loss function for the network combines several metrics, including the initial and boundary conditions, the residuals of the differential equation, and the difference between the neural network solution and the experimental data. To test the performance of this method, we first use simulated data from finite element solutions of the Lamm equation with known parameter values to train the network. Our results demonstrate that, even with relatively small observation datasets, our PINN generates excellent agreement with solutions of the Lamm equation, producing accurate parameter estimates for the sedimentation and diffusion coefficients, as well as the loading concentration. We further applied our PINN to actual experimental data collected on an Optima AUC instrument. Our PINN was modified to identify and remove the time and radially invariant noise components contained in the experimental data. We also successfully tested this technique on systems with solutes exhibiting concentration-dependent non-ideality, as well as on cases with unknown non-uniform initial concentrations. The results in this paper provide proof of concept for the application of neural networks to AUC analysis.