SedNet: A physics-informed operator-learning framework for rapid sedimentation velocity analytical ultracentrifugation analysis.

To date, analyzing data from sedimentation velocity analytical ultracentrifugation (SV-AUC) experiments has exclusively been performed using finite element method or other numerical solver-based techniques. These methods are slow, requiring repeated solving of the Lamm equation in order to obtain an accurate solution. In this paper, we demonstrate how the Lamm equation is alternatively solved accurately using machine learning's automatic differentiation by implementing it into the loss function of an inverse physics informed neural network (PINN). Subsequently, we confirm that by implementing the Lamm equation into a physics-informed deep operator network (PI-DeepONet), synthetic SV-AUC data can be easily generated and then inverted back into size distributions using a multi-layer perceptron (MLP). This combined PI-DeepONet and MLP creates an end-to-end framework, named SedNet, in which the Lamm equation is enforced via a physics-informed forward operator. We demonstrate how SedNet readily analyzes SV-AUC data and is generalized to real SV-AUC experimental data showing its potential applications as an analytical tool.