Cubature-based uncertainty estimation for nonlinear regression models

Models are commonly utilized in chemical engineering to simulate real-world processes and phenomena. Given their role in guiding decision-making, accurately quantifying the uncertainty of these models is essential. Typically, these models are calibrated using experimental data that contain measurement errors, leading to uncertainty in the fitted model parameters. Current methods for estimating the prediction uncertainty of nonlinear regression models are often either computationally intensive or biased. In this study, we use sparse cubature formulas to estimate the prediction uncertainty of nonlinear regression models. Our findings indicate that this method provides a favorable balance between accuracy and computational efficiency, making it suitable for application in chemical engineering. We validate the performance of our proposed method through various regression case studies, including both theoretical toy models and practical models from chemical engineering.