Information-oriented experimental design combining data analysis and numerical computation for maximizing the informativeness of limited measurements

Abstract

The study addresses the problem of reducing the number of costly physical measurements in the calibration of mathematical models through the targeted selection of the most informative experimental conditions. The aim of the work is to develop a computational framework for information-oriented experimental design that combines numerical simulation, Bayesian calibration, and global optimization, providing adaptive selection of measurement points based on the data already accumulated. A two-dimensional stationary heat conduction problem in a heterogeneous plate is used as a test case, in which the temperature field is modeled using the finite element method with unknown thermal conductivity coefficients of two materials. Uncertainty in the parameters is described using a Bayesian approach, where prior distributions are successively updated according to virtual measurement data with the use of Markov chain Monte Carlo algorithms. The criterion for selecting the next measurement point is based on maximizing the expected information gain according to Kullback–Leibler divergence, which is equivalent to minimizing the expected variance of posterior parameter estimates, and is implemented using the differential evolution algorithm. The efficiency of the approach is compared with the classical uniform grid design in terms of the rate of reduction in posterior standard deviations, the dynamics of the mean-square prediction error of the temperature field, and the number of measurements required to achieve the desired calibration accuracy. It is shown that the information-oriented strategy ensures an exponentially faster reduction of uncertainty and allows at least a twofold decrease in the required number of measurements while maintaining or improving prediction accuracy across the entire field. Additionally, computational cost estimates demonstrate that the increase in time required to select the next measurement point is offset by significant savings in resources due to the reduction in the scope of physical experiments. Sensitivity analysis with respect to the quality of prior information confirms the robustness of the methodology and its capability to correct initially biased assumptions, making the proposed approach a promising tool for a wide range of applied problems where measurement cost is a critical constraint.