Metrics for Bayesian Optimal Experiment Design under Model Misspecification

The conventional approach to Bayesian decision-theoretic experiment design involves searching over possible experiments to select a design that maximizes the expected value of a specified utility function. The expectation is over the joint distribution of all unknown variables implied by the statistical model that will be used to analyze the collected data. The utility function defines the objective of the experiment where a common utility function is the information gain. This article introduces an expanded framework for this process, where we go beyond the traditional Expected Information Gain criteria and introduce the Expected General Information Gain which measures robustness to the model discrepancy and Expected Discriminatory Information as a criterion to quantify how well an experiment can detect model discrepancy. The functionality of the framework is showcased through its application to a scenario involving a linearized spring mass damper system and an F-16 model where the model discrepancy is taken into account while doing Bayesian optimal experiment design.

Design of experiments for the calibration of history-dependent models via deep reinforcement learning and an enhanced Kalman filter

Experimental data is costly to obtain, which makes it difficult to calibrate complex models. For many models an experimental design that produces the best calibration given a limited experimental budget is not obvious. This paper introduces a deep reinforcement learning (RL) algorithm for design of experiments that maximizes the information gain measured by Kullback-Leibler (KL) divergence obtained via the Kalman filter (KF). This combination enables experimental design for rapid online experiments where traditional methods are too costly. We formulate possible configurations of experiments as a decision tree and a Markov decision process (MDP), where a finite choice of actions is available at each incremental step. Once an action is taken, a variety of measurements are used to update the state of the experiment. This new data leads to a Bayesian update of the parameters by the KF, which is used to enhance the state representation. In contrast to the Nash-Sutcliffe efficiency (NSE) index, which requires additional sampling to test hypotheses for forward predictions, the KF can lower the cost of experiments by directly estimating the values of new data acquired through additional actions. In this work our applications focus on mechanical testing of materials. Numerical experiments with complex, history-dependent models are used to verify the implementation and benchmark the performance of the RL-designed experiments.