Abstract
Machine learning techniques are powerful predictive tools that continue to gain prominence with increasingly available computational power. Engineering design professionals often view machine learning tools through a skeptical lens due to their perceived detachment from the underlying physics. Machine learning tools, such as artificial neural networks and regression models, are fueled by training data, obtained either analytically or through physical collection, the use of such surrogate models introduces an additional source of uncertainty. Sources of uncertainty associated with machine learning models can originate from the collected data or from the training process itself. Validation and verification methods are especially important for machine learning applications due to their perceived disconnect from underlying physics, sensitivity to data accumulation uncertainties, and potential for under or over training the model itself. Despite all of these potential pitfalls, sufficient testing of machine learning models against segregated testing data and use of regularization tools to diagnose overfitting is not always employed by industry practioners. This paper will illustrate the use of topological data analysis (TDA), specifically persistent homology, a subset of algebraic topology, as an alternative means to achieve generalization of a predictive manifold produced through a machine learning model. Persistent homology will be used to seek out and identify the most meaningful and connected components within the data that forms the predicted manifold, with less connected components treated as noise to be disregarded. Therefore, the uncertainties associated with overfitting can be limited. The proposed method will be demonstrated through its application to a simple single-degree-of-freedom structural system to demonstrate its effectiveness in generalizing the resulting manifold and limiting the associated uncertainty.
