  Although decades of effort have been devoted to building Physical-Conceptual
(PC) models for predicting the time-series evolution of geoscientific systems,
recent work shows that Machine Learning (ML) based Gated Recurrent Neural
Network technology can be used to develop models that are much more accurate.
However, the difficulty of extracting physical understanding from ML-based
models complicates their utility for enhancing scientific knowledge regarding
system structure and function. Here, we propose a physically-interpretable Mass
Conserving Perceptron (MCP) as a way to bridge the gap between PC-based and
ML-based modeling approaches. The MCP exploits the inherent isomorphism between
the directed graph structures underlying both PC models and GRNNs to explicitly
represent the mass-conserving nature of physical processes while enabling the
functional nature of such processes to be directly learned (in an interpretable
manner) from available data using off-the-shelf ML technology. As a proof of
concept, we investigate the functional expressivity (capacity) of the MCP,
explore its ability to parsimoniously represent the rainfall-runoff (RR)
dynamics of the Leaf River Basin, and demonstrate its utility for scientific
hypothesis testing. To conclude, we discuss extensions of the concept to enable
ML-based physical-conceptual representation of the coupled nature of
mass-energy-information flows through geoscientific systems.
