Using Machine Learning to Discover Parsimonious and Physically-Interpretable Representations of Catchment-Scale Rainfall-Runoff Dynamics

Due largely to challenges associated with physical interpretability of machine learning (ML) methods, and because model interpretability is key to credibility in management applications, many scientists and practitioners are hesitant to discard traditional physical-conceptual (PC) modeling approaches despite their poorer predictive performance. Here, we examine how to develop parsimonious minimally-optimal representations that can facilitate better insight regarding system functioning. The term minimally-optimal indicates that the desired outcome can be achieved with the smallest possible effort and resources, while parsimony is widely held to support understanding. Accordingly, we suggest that ML-based modeling should use computational units that are inherently physically-interpretable, and explore how generic network architectures comprised of Mass-Conserving-Perceptron can be used to model dynamical systems in a physically-interpretable manner. In the context of spatially-lumped catchment-scale modeling, we find that both physical interpretability and good predictive performance can be achieved using a distributed-state network with context-dependent gating and information sharing across nodes. The distributed-state mechanism ensures a sufficient number of temporally-evolving properties of system storage while information-sharing ensures proper synchronization of such properties. The results indicate that MCP-based ML models with only a few layers (up to two) and relativity few physical flow pathways (up to three) can play a significant role in ML-based streamflow modelling.