Physics-informed neural networks (PINNs) for fluid mechanics: a review

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Greedy function approximation: A gradient boosting machine.

Function estimation/approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest-descent minimization. A general gradient descent “boosting” paradigm is developed for additive expansions based on any fitting criterion.Specific algorithms are presented for least-squares, least absolute deviation, and Huber-M loss functions for regression, and multiclass logistic likelihood for classification. Special enhancements are derived for the particular case where the individual additive components are regression trees, and tools for interpreting such “TreeBoost” models are presented. Gradient boosting of regression trees produces competitive, highly robust, interpretable procedures for both regression and classification, especially appropriate for mining less than clean data. Connections between this approach and the boosting methods of Freund and Shapire and Friedman, Hastie and Tibshirani are discussed.

Two-equation eddy-viscosity turbulence models for engineering applications

Two new two-equation eddy-viscosity turbulence models will be presented.They combine different elements of existing models that are considered superior to their alternatives.The first model, referred to as the baseline (BSL) model, utilizes the original k-u model of Wilcox in the inner region of the boundary layer and switches to the standard A>e model in the outer region and in free shear flows.It has a performance similar to the Wilcox model, but avoids that model's strong freestream sensitivity.The second model results from a modification to the definition of the eddy-viscosity in the BSL model, which accounts for the effect of the transport of the principal turbulent shear stress.The new model is called the shear-stress transport-model and leads to major improvements in the prediction of adverse pressure gradient flows.