Using physics to extend the range of machine learning models for an aerodynamic, hydraulic and combusting system: The toy model concept

Machine learning models used for energy conversion system optimization cannot extrapolate outside the bounds of training data and often produce physically unrealistic results when making predictions in regions of sparse training data. The toy model concept introduced in this work allows machine learning models to extrapolate to some extent and also reduces the possibility of physically unrealistic results. It uses physics to shrink the model input (feature space) of data-based models, so that extrapolations in the data-based feature space tend to become interpolations in the physics-based (toy variable) feature space. The physics-based model can be any model or experiment that can shrink the feature space without affecting interpolation and is termed a 'toy model' because it does not need to be accurate or make predictions of interest. The concept has been applied to model experimental data obtained from three complex systems: a. Aerodynamic forces on a spinning and vibrating baseball with inclined axis of rotation (toy model: CFD model), b. Hydraulic turbine efficiency (toy model: PIV images of flow through stationary blades), and c. Combustion generated engine emissions (toy model: system-level 1-D model). All extrapolations were converted into interpolations for the first two systems while a 75% conversion was achieved for the emission predictions. The engine toy model produced 736,281 possible feature spaces from which one unique feature space was chosen for every prediction based on agreement between different machine learning algorithms. It is shown that the ability of the toy variables to reorganize the data is important, while their accuracy is relatively unimportant. The toy model concept was demonstrated to work with neural networks and regression, and can be used to increase model robustness or reduce training data requirements.