A Mass‐Conserving‐Perceptron for Machine‐Learning‐Based Modeling of Geoscientific Systems

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. Plain Language Summary We develop a physically interpretable computational unit, referred to as the Mass‐Conserving‐Perceptron (MCP). Networks of such units can be used to model the conservative nature of the input‐state‐output dynamics of mass flows in geoscientific systems, while Machine Learning (ML) technology can be used to learn the functional nature of the physical processes governing such system behaviors. Testing using data from the Leaf River Basin demonstrates the considerable functional expressivity (capacity) and interpretability of even a single‐MCP‐node‐based model, while providing excellent predictive performance and the ability to conduct scientific hypothesis testing. The concept can easily be extended to facilitate ML‐based physical‐conceptual representation of the coupled nature of mass‐energy‐information flows through geoscientific systems, thereby facilitating the development of synergistic physics‐AI modeling approaches. Key Points We develop a physically interpretable unit (Mass‐Conserving‐Perceptron) that can be