Various real-world scientific applications involve the mathematical modeling of complex uncertain systems with numerous unknown parameters. Accurate parameter estimation is often practically infeasible in such systems, as the available training data may be insufficient and the cost of acquiring additional data may be very high. In such cases, it may be desirable to represent the uncertainty present in the model in a Bayesian paradigm, based on which one may design robust operators that retain good overall performance across all possible models. Furthermore, one may design optimal experiments that can effectively reduce the uncertainty so as to significantly enhance the performance of the robust operators.
While objective-based uncertainty quantification (objective-UQ) based on MOCU (mean objective cost of uncertainty) provides an effective means for quantifying uncertainty in complex systems, the high computational cost of estimating MOCU has been a practical challenge in applying it to real-world scientific/engineering problems.
In our recent work, we proposed a novel deep learning (DL) scheme to reduce the computational cost for objective-UQ via MOCU that can significantly accelerate MOCU estimation and optimal experimental design (OED).
Qihua Chen, Xuejin Chen, Hyun-Myung Woo, Byung-Jun Yoon, “Neural Message Passing for Objective-Based Uncertainty Quantification and Optimal Experimental Design,” Engineering Applications of Artificial Intelligence, Volume 123, Part A, 106171, 2023, https://doi.org/10.1016/j.engappai.2023.106171
In the above study, we trained a message-passing neural network (MPNN) as a surrogate MOCU estimator, incorporating a novel axiomatic constraint loss that improves the estimation performance, and ultimately, the OED outcomes. Our results show that the proposed scheme can accelerate MOCU-based OED by four to five orders of magnitude, without any visible performance loss.
For further details, the paper can be accessed at: [download paper]
Objective-UQ 