A Framework for Parameter Estimation and Uncertainty Quantification in Systems Biology Using Quantile Regression and Physics-Informed Neural Networks.

Abstract

A framework for parameter estimation and uncertainty quantification is crucial for understanding the mechanisms of biological interactions within complex systems and exploring their dynamic behaviors beyond what can be experimentally observed. Despite recent advances, challenges remain in achieving the high accuracy of parameter estimation and uncertainty quantification at moderate computational costs. To tackle these challenges, we developed a novel approach that integrates the quantile method with Physics-Informed Neural Networks (PINNs). This method utilizes a network architecture with multiple parallel outputs, each corresponding to a distinct quantile, facilitating a comprehensive characterization of parameter estimation and its associated uncertainty. The effectiveness of the proposed approach was validated across three study cases, where it was compared to the Monte Carlo dropout (MCD) and the Bayesian methods. Furthermore, a larger-scale model was employed to further demonstrate the excellent performance of the proposed approach. Our approach exhibited significantly superior efficacy in parameter estimation and uncertainty quantification. This highlights its great promise to broaden the scope of applications in system biology modeling.