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.

翻译：尽管数十年来人们一直致力于构建物理-概念模型以预测地球科学系统的时间序列演化，但近期研究表明，基于机器学习的门控循环神经网络技术可开发出精度显著更高的模型。然而，从基于机器学习的模型中提取物理理解的困难性，限制了其在增强系统结构与功能科学认知方面的实用性。本文提出一种可物理解释的"质量守恒感知器"，作为弥合基于物理-概念建模方法与基于机器学习建模方法之间鸿沟的方案。该感知器利用物理-概念模型和门控循环神经网络底层有向图结构的内在同构性，显式表征物理过程的质量守恒特性，同时允许通过现有机器的学习技术从可用数据中直接学习（以可解释方式）此类过程的功能特性。作为概念验证，我们研究了质量守恒感知器的功能表达能力，探索其以简约方式表征叶子河流域降雨-径流动态的能力，并展示其在科学假设检验中的实用性。最后，我们讨论了将该概念扩展至地球科学系统中质量-能量-信息流耦合特性的基于机器学习物理-概念表征的可能性。