Using a neural network – Physics-based hybrid model to predict soil reaction fronts

Analytical and numerical solutions have been proposed to model reaction fronts to study soil formation. With growing access to large geo-datasets and powerful computational capacity, data-driven models are becoming increasingly useful. We therefore explored the use of a neural network (NN) guided by a physics-based model (PBM) to simulate the depth profile of feldspar dissolution in soils. Specifically, we explored this hybrid neural network (HNN) to see if it could predict reaction fronts as a function of important variables known from domain knowledge: site climate characteristics (temperature T ; precipitation P ), geomorphic parameters (soil residence time t ; erosion rate E ), and parent material mineralogy (quartz content Q ; albitic feldspar content of the feldspar A ). We evaluated the mean square error (MSE) for 63 HNNs, each using a different combination of training data (i.e., soil profiles) and environmental variables. The HNNs trained to four or five soil profiles that used a subset of t, T , Q , E , and A as predictor variables yielded lower MSEs than the PBM, and showed global convergence. At least two variables are needed to achieve an MSE within 1% of the corresponding PBM. The HNNs generally predicted the slope better than the depth of the front because the PBM was not used to predict depth. HNN results identify t and P as the most and least useful variable in predicting the reaction front, respectively. This is the first time a NN was hybridized to a PBM to simulate reactions in soils. As part of this effort, we developed a tool to identify cases which have converged to a global solution, and cases which present local solutions. The approach shows promise for future efforts but should be applied to larger sets of soil profile data and PBMs that predict both the depth and slope of reaction fronts. • We developed a physics-informed neural network to predict slopes of reaction fronts. • We developed a tool to identify neural network models presenting local solutions. • Residence time is the most useful variable in predicting the slope of a soil reaction front.