Interpretable machine learning for multi-dimensional-input physical system output prediction based on multi-couples of causality feature

Abstract Machine learning algorithms with predictive accuracy and interpretability simultaneously are anticipating in assisting data-driven prognosis for physical systems of engineering. However, the poor interpretability of popular algorithms is restricting this pursuit. This study presents a paradigm for the interpretability prediction of time series output of multi-dimensional input physical system of engineering using the Gaussian mixture model (GMM) as the kernel. The fuzzy causality features between the system output and multiple system inputs are parametrically represented and modeled in two-dimensional probabilistic plane using multiple bivariate GMMs respectively, then the system output at the next moment can be predicted using established bivariate GMMs and real-time inputs. Two key technologies involving the inference pool for enhancing predicting accuracy of each bivariate GMM, and the dynamic weight for dynamically combining prediction results from multiple bivariate GMMs are proposed. The results of two experiments of engineering physical system demonstrate that the proposed method for the output prediction of high-dimensional-input physical system can rival the predictive performance of popular deep neural networks while providing statistical parameters with physical meaning; and it performs relatively higher accuracy in the task of generative prediction, which indirectly exhibits its scalability for new dataset with real-time variation of causality features.