Rapid climate change has lead to widespread warming of land surface temperatures throughout the Arctic, thereby accelerating the thawing of perennially frozen, carbon-rich soil, most commonly referred to as permafrost. Subsurface modeling of heat and water transport plays a key role in understanding how past, present, and future changes in the climate affect the rate and extent of permafrost thaw. We propose a novel hybrid modeling approach for solving by reparameterizing it as a universal partial differential equation, where the inverse enthalpy operator is represented by a universal approximator. Such a method would alleviate one of the major numerical difficulties in the simulation of two-phase heat transport and would allow for efficient and flexible modeling of permafrost at large time scales.