Leveraging neural networks to estimate parameters with confidence intervals

Abstract This manuscript presents a proof of concept for the estimation of parameters in a bioprocess while providing reliable confidence intervals. Specifically, Bayesian inference is used to estimate the uncertainty in the prediction of a parameter due to the presence of measurement noise in the process. The resultant joint probability distribution is utilized to infer the confidence interval of the resultant estimates. This method is numerically applied using a technique known as nested sampling. This algorithm iteratively samples parameters from a pre‐determined range of values to compare model predictions and obtain a probability density function. One challenge typically associated with this algorithm is in the determination of the prediction error, especially when a high‐fidelity dynamic model is being utilized. For the motivating example in the present manuscript, where a high‐fidelity simulated bioprocess is being considered, the use of the high‐fidelity model provided by Sartorius AG as part of the estimation algorithm poses computational challenges. To overcome this challenge, a universal approximator such as a parameterized neural network is used. This neural network is designed to simulate the results of the first principles model (while also capturing the dependence of the model parameters on the output), and once trained can provide near instantaneous results making the use of nested sampling computationally tractable for the application. Simulation results demonstrate the feasibility and capability of the proposed approach.