Machine learning approach to predicting the hysteresis of water retention curves of porous media

Abstract

In this study, we develop a machine learning modeling approach to the prediction of the hysteretic Boundary Drying (BD) curves of unsaturated porous media from the known Boundary Wetting (BW) curves, measured at a constant void ratio. The relationship between the families of BW and BD curves of the porous media is considered to consist of regular and random constituents, and it is represented by a limited set of N known pairs of these curves. Prediction of the desired BD curve from its associated known BW curve of some porous medium is obtained as a product of two mappings: (i) a nonlinear mapping of the known BW curve to its corresponding Hypothetical Drying (HD) curve, as defined in ”The modified dependent-domain theory of hysteresis” of Mualem (1984, 2009) and (ii) a linear mapping of this HD curve to the desired BD curve. The latter mapping is performed by an optimization algorithm based on a training set of k known BW-BD pairs (k≤N) of the k corresponding porous media. The predicted BD curves indicate a generally good agreement with the measured ones. An advantage of the proposed approach is the possibility of permanently updating the suggested model by incorporating new measured data.