Mutual Information-Guided Multiobjective Learning Framework for Augmenting Incomplete Mechanism Models With Neural Networks

Mechanism models often have limited performance due to incompleteness, while neural networks are acknowledged to lack interpretability and extrapolation stability. Augmenting incomplete mechanism models with neural networks can achieve accurate prediction and naturally inherit mechanism models' interpretability and extrapolation stability. According to the original purpose of establishing mechanism models augmented with neural networks (MMANNs), their effectiveness depends on the accuracy of mechanism models. However, since the directly labeled data of the mechanism model or residuals are inaccessible, this effectiveness criterion is difficult to meet in practice. To overcome this challenge, we introduce two heuristic constraints for MMANNs, and propose a mutual information (MI) guided multiobjective learning framework. In this framework, except for minimizing the end-to-end error and the norm of residuals, the MI of the mechanism model and labeled data is maximized, while the MI of the residuals and labeled data is minimized. Compared with the other seven methods, the verification results of the three cases show that all four MMANNs trained under the proposed framework can learn more accurate mechanism parameters and have better extrapolation stability.