Topologically consistent regression modeling exemplified for laminar burning velocity of ammonia-hydrogen flames

Data-driven regression models are generally calibrated by minimizing a representation error. However, optimizing the model accuracy may create nonphysical wiggles. In this study, we propose topological consistency as a new metric to mitigate these wiggles. The key enabler is Persistent Data Topology (PDT) which extracts a topological skeleton from discrete scalar field data. PDT identifies the extrema of the model based on a neighborhood analysis. The topological error is defined as the mismatch of extrema between the data and the model. The methodology is exemplified for the modeling of the Laminar Burning Velocity ($LBV$) of ammonia-hydrogen flames. Four regression models, Multi-layer Perceptron (MLP), eXtreme Gradient Boosting (XGBoost), Random Forest (RF), and Light Gradient Boosting Machine (Light GBM), are trained using the data generated by a modified GRI3.0 mechanism. In comparison, MLP builds a model that achieves the highest accuracy and preserves the topological structure of the data. We expect that the proposed topologically consistent regression modeling will enjoy many more applications in model calibration, model selection and optimization algorithms.