  A novel multiphysics-decision tree learning algorithm is presented for (1)
estimating transport properties in the variably saturated subsurface governed
by explicitly coupled equations for water, heat, and solute transport; and (2)
providing reduced order simulation of time-dependent pressure head,
temperature, and concentration with subsurface properties and/or changing
surface boundary conditions. We demonstrate that the proposed algorithm results
in about one order of magnitude less error in estimated parameters than the
traditional multiphysics numerical inversion. We further show that the
multiphysics-decision tree learning algorithm reduces the computational burden
associated of traditional parameter estimation with reductions in the number
Jacobian sensitivity calculations by as much as 90% and the number of
iterations required for convergence by up to an order of magnitude. A natural
outcome following convergence of the proposed learning algorithm is the reduced
order set of supervised decision tree learning models for predicting the
pressure head (Random Forest), and the temperature and concentration (Ensemble
Gradient Boosting) given knowledge of time, depth, and remaining pair of state
variables. The supervised reduced-order modeling is extended to unsupervised
machine learning for the simultaneous prediction of state variables by training
a Self-Organized Map using the joint multiphysics-decision tree learning
property estimates, stochastic boundary conditions, and subsurface state field
measurements. The reduced-order machine learning models provide a
computationally efficient alternative for studying the effects of changing
subsurface water, heat, and solute transport properties and/or surface boundary
conditions on coupled subsurface pressure head, temperature, and concentration.
