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

TL;DR

This paper introduces a physically-interpretable Mass Conserving Perceptron (MCP) that combines physical principles with machine learning to model geoscientific systems more accurately and transparently.

Contribution

It proposes a novel MCP model that explicitly encodes mass conservation, bridging physical models and ML, and demonstrates its effectiveness in modeling rainfall-runoff dynamics.

Findings

MCP can represent mass-conserving physical processes.

MCP effectively models rainfall-runoff dynamics.

The approach facilitates scientific hypothesis testing.

Abstract

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.