A supervised learning model to predict length-scale dependent permeability of porous carbon composites

The computation of permeability for porous carbon composites used as heat shield materials is an intensive and a tedious process. Surrogate modeling of physical simulations offer a significantly cheaper alternative to computing permeability. The main objective of this work is to develop a supervised learning model which approximates the physical simulations involving a single gaseous species through a porous material and capture the length-scale dependency of the material’s permeability. This length-scale dependency can be integrated in material response solvers to better simulate the physics of gas transport inside the material instead of assuming a constant value for the property. This work focuses on the development of an analytical function which relates the permeability of the porous material with the thermodynamic conditions and length-scale of the microstructure. The analytical function is realized using support vector regression (SVR) which is found to be a robust technique in order to capture the complex relationship between temperature, average pressure, and length-scale of the microstructure. The predicted values are found to have a maximum relative error of about 20 percent with the majority of the relative errors being less than 7 percent. The analytical function is validated against a range of inputs beyond the scope of trained values to justify the use of the developed supervised learning model. The capability of the developed model to capture the length-scale dependency on permeability is emphasized by noting the difference in predicted permeability and it’s accuracy for data points at either edges of the training domain.